YAMAGUCHI Kazuaki | |
Graduate School of Engineering / Department of Electrical and Electronic Engineering | |
Associate Professor | |
Electro-Communication Engineering |
[Refereed]
International conference proceedings
International conference proceedings
The graph coloring problem is an important problem. Heuristics like greedy algorithms are often used for graph coloring problem, because it is not practical to apply exact solutions to large graphs. In this paper, we propose two greedy algorithms for the graph coloring problem. The proposed methods weight the vertices or edges of the complement of the input graph, and then extract the weighted clique of the graph. The solution is obtained by repeating this process until no vertices are left. Experimental results show that our methods are more suitable for graphs with high edge density than the previous methods.
Corresponding, The Institute of Electronics, Information and Communication Engineers, 01 Dec. 2021, 電子電子情報通信学会論文誌A 基礎・境界, J104-A (12), 258 - 266, Japanese[Refereed]
In this paper, parallelization techniques are proposed for the branch-and-bound algorithm OTClique for the maximum weight clique problem. OTClique consists of the precomputation phase and the branch-and-bound phase. The proposed algorithm parallelizes both of them. In the precomputation phase, the construction of optimal tables is parallelized. In the branch-and-bound phase, the proposed algorithm generates small subproblems and assigns them to threads. A technique to share lower and upper bounds is also proposed. Experiments using some benchmarks show that the proposed parallelization techniques improve the performance of OTClique. With an 8-core CPU, the computation time of OTClique becomes 6.91 times shorter on random graphs and 5.38 times on DIMACS benchmarks on average. (C) 2021 Elsevier B.V. All rights reserved.
Corresponding, ELSEVIER, Aug. 2021, DISCRETE OPTIMIZATION, 41, 100646 - 100646, English[Refereed]
Scientific journal
Given a set S of points in a region D, we consider the problem of placing labels of all the points in S. The label of each point p ∈ S is either placed inside D so as to touch p or placed outside D using a leader line. This style of labeling is called a mixed labeling. In this paper, we use slider models for the label placement inside D, and present exact algorithms for the problem of finding a label placement such that (a) the number of labels inside D is maximized and (b) the total sum of the lengths of leader lines inside D is minimized as the secondary objective.
The Institute of Electronics, Information and Communication Engineers, 01 Nov. 2020, 電子電子情報通信学会論文誌A 基礎・境界, J103-A (11), 278 - 282, Japanese[Refereed]
The maximum edge-weight clique problem is to find a clique whose sum of edge-weight is the maximum for a given edge-weighted undirected graph. The problem is NP-hard and some branch-and-bound algorithms have been proposed. In this paper, we propose a new exact algorithm based on branch-and-bound. It assigns edge-weights to vertices and calculates upper bounds using vertex coloring. By some computational experiments, we confirmed our algorithm is faster than previous algorithms.
Corresponding, Elsevier BV, Aug. 2020, Discrete Optimization, 37, 100583 - 100583, English[Refereed]
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We consider the problem of placing arrows, which indicate the direction of each edge in directed graph drawings, without making them overlap other arrows, vertices and edges as much as possible. The following two methods have been proposed for this problem. One is an exact algorithm for the case in which the position of each arrow is restricted to some discrete points. The other is a heuristic algorithm for the case in which the arrow is allowed to move continuously on each edge. In this paper, we assume that the arrow positions are not restricted to discrete points and propose an exact algorithm for the problem of finding an arrow placement such that (a) the weighted sum of the numbers of overlaps with edges, vertices and other arrows is minimized and (b) the sum of the distances between the arrows and their edges' terminal vertices is minimized as a secondary objective. The proposed method solves this problem by reducing it to a mixed integer linear programming problem. Since this is an exponential time algorithm, we add a simple procedure as preprocessing to reduce the running time. Experimental results show that the proposed method can find a better arrow placement than the previous methods and the procedure for reducing the running time is effective.
電子情報通信学会, Nov. 2019, 電子情報通信学会論文誌, E102-A (11), 1481 - 1489, English[Refereed]
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辺に重みが付与された無向グラフが与えられたとき,重みの和が最大となるクリークを求める問題を最大辺重みクリーク問題という.本稿ではこの問題に対する局所探索法において近傍を管理するためのデータ構造を2つ提案する.計算機実験により2つの局所探索法でデータ構造を比較し,提案法は従来法より性能が良いことを確認した.また,グラフの性質や計算機のメモリに応じて提案するデータ構造を使い分けることで,効率良く探索を行えることを確認した. The maximum edge-weight clique problem is to find the clique of maximum weight for a given edge-weighted undirected graph. In this paper, we propose two data structures to manage neighborhood in local search algorithms. By some computational experiments, we compared our proposal data structures with two local search algorithms and confirmed ours work better than a previous one. By applying proposal data structures properly, we confirmed local search algorithms work efficiently.
Corresponding, 情報処理学会, 15 Jul. 2018, 情報処理学会論文誌, 59 (7), 1415 - 1424, Japanese[Refereed]
Scientific journal
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International conference proceedings
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A new branch-and-bound algorithm for the maximum weight clique problem is proposed. The proposed algorithm consists of two phases, a precomputation phase and a branch and-bound phase. In the precomputation phase, the weights of maximum weight cliques in many small subgraphs are calculated and stored in optimal tables. In the branch and-bound phase, each problem is divided into smaller subproblems, and unnecessary subproblems are pruned using the optimal tables. We performed experiments with the proposed algorithm and five existing algorithms for several types of graphs. The results indicate that only the proposed algorithm can obtain exact solutions for all graphs and that it performs much faster than other algorithms for nearly all graphs. (C) 2017 Elsevier B.V. All rights reserved.
Corresponding, ELSEVIER SCIENCE BV, May 2017, DISCRETE APPLIED MATHEMATICS, 223, 120 - 134, English[Refereed]
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Given a vertex-weighted undirected graph, to find the vertex cover of minimum weight is called minimum weight vertex cover problem (MWVCP). It is known as an NP-hard problem. In this paper, a fast heuristic for MWVCP is proposed. Our algorithm is based on a simple algorithm called "list-heuristic." Experimenal results show that our algorithm calculates better solutions in shorter time than approximation algorithms for MWVCP.
Corresponding, IEEE COMPUTER SOC, Jun. 2016, 2016 IEEE/ACIS 15TH INTERNATIONAL CONFERENCE ON COMPUTER AND INFORMATION SCIENCE (ICIS), 341 - 345, English[Refereed]
International conference proceedings
[Refereed]
Scientific journal
The B-BANDWIDTH problem is a decision problem whether the bandwidth of a given graph is smaller than B, and it is NP-complete even if the graph is a small graph class of trees. Cygan and Pilipczuk proposed exponential time and space algorithms for B-BANDWIDTH with n/3 ≤ B where n is the number of vertices. In this paper, we propose two algorithms for the B-BANDWIDTH problem with n/4 ≤ B < n/3. These algorithms are extension of Cygan and Pilipczuk algorithms with restricted B. One of the algorithms takes O∗(4.5n) time and O∗(1.5n) space when n/4 ≤ B < n / 2 log2 1.5, and the other takes O∗(4.77n) time and O∗(1.59n) space when n / 2 log2 1.5 ≤ B < n/3. Our algorithms are fastest O∗(2n) space algorithms for n/4 ≤B < n/3. The 17th Korea-Japan Joint Workshop on Algorithms and Computation, July 13-15, 2014, Okinawa, Japan
WAAC, Jul. 2014, In Proceedings of the KOREA-JAPAN Joint Workshop on Algorithms and Computation, (2014), 44 - 49, English[Refereed]
International conference proceedings
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Research institution
本論文では,階層グラフの直交描画を求めるアルゴリズムを示す.ここで直交描画とは,各辺を垂直・水平線分からなる経路として描いたグラフ描画である.本論文では,与えられた階層グラフの辺集合から高階辺の集合を作成する方法,及びそれらの高階辺を描画する方法を提案する.後者の方法は,各高階辺の描画に2本の水平線分を用い得るものとして,辺交差数と水平線分が占めるy座標の個数をともに少なく抑えながら,直交描画を求めるものである.提案手法の有効性は計算機実験により示す.
一般社団法人電子情報通信学会, Mar. 2014, 電子情報通信学会論文誌. A, 基礎・境界, 97 (3), 178 - 196, Japanese[Refereed]
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International conference proceedings
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International conference proceedings
平面上に与えられた多数の点に名称などを示す文字列(ラベル)を付けるものとする.本研究では,文字列の縦書きと2行への折返しを許すものとして,多くの点にラベルを配置するアルゴリズムを提案する.提案手法は,各点に対しラベル配置位置の候補(ラベル候補)を定め,それらの中から最終的なラベル位置を決定するものであり,各点のラベル候補の個数を少なく抑えるための工夫をしている.
一般社団法人電子情報通信学会, 01 Nov. 2012, 電子情報通信学会論文誌. A, 基礎・境界 = The transactions of the Institute of Electronics, Information and Communication Engineers. A, 95 (11), 790 - 793, Japanese[Refereed]
Gを任意の連結無向グラフとし,その各頂点があらかじめ指定されたサイズのラベルをもつものとする.本論文ではまず,Gのある描画が与えられたときに,その描画中にラベルを配置する新しいアルゴリズムを提案する.この方法は,ラベルが対応する頂点と重なることを許しており,多くのラベルを配置することができる.本論文では次に,グラフGに対して,全頂点のラベルを配置した描画を求めるアルゴリズムを提案する.この方法は,各頂点を比較的小さなサイズの軸平行長方形で表すようなグラフ描画アルゴリズムとして用いることができる.これらの提案手法の有効性は計算機実験により示す.
一般社団法人電子情報通信学会, 01 Aug. 2012, 電子情報通信学会論文誌. A, 基礎・境界 = The transactions of the Institute of Electronics, Information and Communication Engineers. A, 95 (8), 669 - 682, Japanese[Refereed]
Scientific journal
各階層上の頂点の配置順序が指定された階層グラフを描画する際に,頂点の座標を決定する新しいアルゴリズムを提案する.提案法は,描画中の重み付き辺長の2乗の総和を小さくすることを目的としており,グラフの各階層を順に見ていき,それぞれの頂点の配置を動的計画法を用いて求めるものである.従来法の一つである優先度法との比較実験を行ったところ,提案法は,三つの評価基準に関して,より優れた描画を求めることができた.
一般社団法人電子情報通信学会, 01 Dec. 2011, 電子情報通信学会論文誌. A, 基礎・境界 = The transactions of the Institute of Electronics, Information and Communication Engineers. A, vol.J94-A (12), 960 - 973, Japanese[Refereed]
Scientific journal
グラフの階層描画において,連続しない階層上の頂点を結ぶ辺の上にはダミー頂点が設けられる.本論文では,まず,ダミー頂点を複数の辺に共有させる単純なアルゴリズムを提案し,計算機実験により,それがグラフを簡潔なものにするために有効であることを示す.ダミー頂点の共有を許す場合,処理後のグラフの頂点数や辺の本数をできるだけ少なくすることが望まれる.本研究では,問題の入力を連結3階層グラフに限定した場合でも,頂点数を最小化する問題及び辺数を最小化する問題がNP困難であることを示す.
一般社団法人電子情報通信学会, 01 Dec. 2011, 電子情報通信学会論文誌. A, 基礎・境界 = The transactions of the Institute of Electronics, Information and Communication Engineers. A, 94 (12), 950 - 959, Japanese[Refereed]
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各頂点の次数が4以下の任意の単純な無向グラフをGとする.本論文では,グラフ描画アルゴリズムをデフォルメ路線図作成に応用することを念頭において,Gの直線描画Gが与えられたときに,Gの直交描画を求めるアルゴリズムを提案する.提案手法による描画は,Gにおける頂点の相対的位置関係(頂点の座標の大小関係)を基本的に保存しており,各辺の折れ曲がり回数がたかだか4となるものである.本論文では次に,Gの直交描画に対し,道の形状を単純化するためのいくつかの処理を示す.最後に,提案手法とこれらの処理を用いて作成したデフォルメ路線図の例を示す.
一般社団法人電子情報通信学会, 01 Mar. 2011, 電子情報通信学会論文誌. A, 基礎・境界 = The transactions of the Institute of Electronics, Information and Communication Engineers. A, 94 (3), 180 - 191, Japanese[Refereed]
Scientific journal
平面上に与えられた多数の点に対し,名称などを表す文字列(ラベル)をできるだけ多く配置する問題について考える.本研究では,スライダーモデルとルール処理を組み合わせたラベル配置アルゴリズムを提案する.提案手法は,スライダーモデルで用いるラベル配置可能領域をルール処理で縮小あるいは削除していき,ラベル位置を決定するものである.提案手法が従来手法より高いラベル配置率を実現できることを,計算機実験によって示す.
一般社団法人電子情報通信学会, 01 Oct. 2009, 電子情報通信学会論文誌. A, 基礎・境界 = The transactions of the Institute of Electronics, Information and Communication Engineers. A, 92 (10), 699 - 704, Japanese[Refereed]
Scientific journal
有向グラフに対する代表的な描画アルゴリズムとして,階層的描画を求めるSugiyamaらの方法が知られている.この方法の第1段階はグラフの非閉路化を行うが,その際,帰還辺の本数を少なくすることを目標としている.本研究では,従来の方法を改良し,帰還辺の本数だけでなく,描画の階層数の削減にも有効な発見的アルゴリズムを提案する.
一般社団法人電子情報通信学会, 01 Jun. 2009, 電子情報通信学会論文誌. A, 基礎・境界 = The transactions of the Institute of Electronics, Information and Communication Engineers. A, 92 (6), 434 - 439, Japanese[Refereed]
Scientific journal
階層的グラフの描画において,辺の交差が少なくなるように各階層上の頂点の順序を決定する問題について,多くの研究が行われており,有効な発見的手法として重心法が知られている.本論文では,重心法を用いて得られた頂点順序に対し,局所探索法によって辺交差数を更に削減する方法を提案する.また,頂点が階層以外にもグループ分けされており,各階層で同一グループの頂点を連続して並べるものとした場合について考え,そのような場合に適用できるよう,重心法と局所探索法による方法を拡張する.
Corresponding, 一般社団法人電子情報通信学会, 01 Jan. 2009, 電子情報通信学会論文誌. A, 基礎・境界 = The transactions of the Institute of Electronics, Information and Communication Engineers. A, 92 (1), 55 - 61, Japanese[Refereed]
Scientific journal
平面上の複数の点に対して,名称などを表す文字列(ラベル)を配置することを考える.本研究では,ラベルサイズ最大化問題の一つの一般化として,達成すべきラベル配置率Pが指定されたときに,配置率がP以上になるラベル配置で,ラベルサイズができるだけ大きいものを求めるという問題を扱う.本論文ではまず,ラベル数最大化問題に対するWagnerらの方法を繰り返し実行することにより,上記の問題の解を求める単純な発見的アルゴリズムを示す.そして,いくつかの工夫を加えることにより,その実行時間と解の精度を改善する方法を提案し,計算核実験によってその効果を確認する.
Corresponding, 一般社団法人電子情報通信学会, 01 Dec. 2008, 電子情報通信学会論文誌. A, 基礎・境界 = The transactions of the Institute of Electronics, Information and Communication Engineers. A, 91 (12), 1223 - 1228, Japanese[Refereed]
Scientific journal
無向グラフを対象とした描画法の一つとして,川西らの方法が知られている.この方法は,いくつかの評価基準に関して,他の代表的な力指向描画法より優れた描画を得るものであるが,(i)最終的な描画が頂点の処理順序に依存し,その順序によっては不適切な描画になることがある,(ii)対応できるグラフのサイズが狭い範囲に限られている,という問題をもつ.本論文では,川西らの方法の頂点移動方法を改良することによって新しい描画法を提案し,その有効性を計算機実験により示す.
一般社団法人電子情報通信学会, 01 Oct. 2008, 電子情報通信学会論文誌. A, 基礎・境界 = The transactions of the Institute of Electronics, Information and Communication Engineers. A, 91 (10), 974 - 982, Japanese[Refereed]
Scientific journal
Given an undirected graph with weight for each vertex, the maximum weight clique problem is to find the clique of the maximum weight. Ostergard proposed a fast exact algorithm for solving this problem. We show his algorithm is not efficient for very dense graphs. We propose an exact algorithm for the problem, which is faster than Ostergard's algorithm in case the graph is dense. We show the efficiency of our algorithm with some experimental results.
The Institute of Electronics, Information and Communication Engineers, Jul. 2008, Proceedings of the 23rd International Technical Conference on Circuits/Systems, Computers and Communications, pp.317-320, F3-1, English[Refereed]
International conference proceedings
The maximum independent set problem is one of the most famous and well-studied NP-complete problems, and has some important applications. Some exact algorithms based on the branch-and-bound technique have been proposed for the problem. This paper deals with one of its variants, the maximum weight K(3)-free subgraph problem. This paper shows an interesting property of a K(3)-free graph, an exact algorithm for the problem and its efficiency with some computer experiments.
Corresponding, INT ASSOC ENGINEERS-IAENG, 2008, WORLD CONGRESS ON ENGINEERING 2008, VOLS I-II, Vol II, pp.834-837, 834 - 837, English[Refereed]
International conference proceedings
空間データを効率的に管理するための索引構造は地理情報システムなどで利用される.本論文では範囲検索の性能を向上させることを目的として,領域データを管理する新たなデータ構造を提案する.このデータ構造は,領域データの隣接関係を表したグラフを用いる.地図における領域データを用いた計算機実験により,提案したデータ構造の範囲検索性能が優れていることを示す.
Corresponding, 一般社団法人電子情報通信学会, 01 Feb. 2007, 電子情報通信学会論文誌. D, 情報・システム = The IEICE transactions on information and systems (Japanese edition), 90 (2), 586 - 591, Japanese[Refereed]
Scientific journal
高速な最近傍検索手法の一つとしてTLAESAが知られている.本論文では更なる高速化を目的として,TLAESAのデータ構造と検索アルゴリズムの改良を行う.更に解の精度を保証できるような近似κ近傍検索手法への拡張を提案する.提案手法は非常に低いエラー率で近似解を求めることができることを計算核実験により示す.
Corresponding, 一般社団法人電子情報通信学会, Jul. 2006, 電子情報通信学会論文誌, vol.J89-D, no.7, pp.1610-1616 (7), 1610 - 1616, Japanese[Refereed]
Scientific journal
平面上の点の集合が与えられたとき,できるだけ多くの点にラベルを付けることを目的としたアルゴリズムが数多く提案されているが,ラベルのサイズが大きい場合などには,ラベルを表示できない点が多数残ることがある.本研究では,そのような場合に,ラベルを表示できなかった点に対し,引出し線を用いてラベルの配置を試みるアルゴリズムを二つ提案し,それらの有効性を計算機実験により示す.
一般社団法人電子情報通信学会, Mar. 2006, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol.J89-A, no.3, pp.268-275 (3), 268 - 275, Japanese[Refereed]
Scientific journal
The 2-terminal shortest path problem is to find a shortest path between two specified vertices in a given graph G. In this paper, we consider this problem in the following situation: G is given before the two vertices are specified so that some preprocessing is allowed to reduce the response time. We present a method for calculating lower bounds of the length of the shortest path for any pair of vertices. Experimental results,show that the A* algorithm with our method performs much better than previous methods.
IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG, Feb. 2006, IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, E89A (2), 544 - 550, English[Refereed]
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International conference proceedings
優れた地図ラベル配置アルゴリズムの一つとして, Wagner and Wolffによる方法が知られている.本研究では, この方法を拡張することによって, 地点の消去を許さない場合と許す場合の両方について, 地点の優先度を考慮したラベル配置アルゴリズムを提案し, それらの有用性を計算機実験により示す.
一般社団法人電子情報通信学会, May 2005, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol.88-A, no.5, pp.677-681 (5), 677 - 681, Japanese[Refereed]
Scientific journal
グラフ描画中に頂点及び辺のラベルを配置する五つのアルゴリズムについて, ラベル配置率及び実行時間に関する比較を行った.計算機実験の結果では, 地図へのラベル配置を目的としたKameda and Imaiの方法に変更を加えたもの, 及び筆者らによる頂点ラベルの配置法と辺ラベルの配置法を組み合わせ, それに改良を加えたものが優れていた.
一般社団法人電子情報通信学会, May 2005, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol.88-A, no.5, pp.671-676 (5), 671 - 676, Japanese[Refereed]
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International conference proceedings
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Gを連結な無向グラフとし,その各辺が,あらかじめ決められたサイズのラベルをもつものとする.辺がラベルをもつ無向グラフの描画法としてこれまで主に検討されてきたアプローチは,まずラベルの情報を特に考慮せずにグラフの頂点と辺を描き,次に適切な位置に辺のラベルを配置するというものであった.しかしこのようなアプローチでは,グラフが密である場合やラベルのサイズが大きい場合に,配置できないラベルが多く残ることがある.そこで本論文では,各辺のラベルの配置位置を考慮しながら頂点や辺の位置を決定するグラフ描画アルゴリズムを提案する.そして,この方法で得られる描画に対してラベル配置アルゴリズムを実行すれば,既存の(ラベルをもたないグラフを描画対象とした)グラフ描画アルゴリズムで得られる描画に対して同じことを行う場合に比べ,ラベル配置率を大幅に改善できることを計算機実験により示す.
一般社団法人電子情報通信学会, 2003, 電子情報通信学会論文誌, J86-A(8),pp.848-859 (8), 848 - 859, Japanese[Refereed]
Scientific journal
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[Refereed]
International conference proceedings
Let G be a graph and Γ be its drawing on a plane. Each edge in G has a label of specified size. We consider the problem of placing edge labels in Γ in such a way that no label overlaps vertices, edges or other labels. Recently, Kakoulis and Tollis proposed a heuristic algorithm for this problem. In this paper, we improve their algorithm by refining the part for deciding the candidates of label positions and that for choosing the final label positions. Experimental results show that our algorithm can place more labels than the original one.
一般社団法人電子情報通信学会, 01 Mar. 2002, IEICE transactions on fundamentals of electronics, communications and computer sciences, 85 (3), 729, English[Refereed]
Gをグラフとし,гをGの平面上への描画とする.Gの各辺に対し,あらかじめラベルのサイズが決められているものとする.このとき,どのラベルも頂点や辺及び他のラベルと重ならないようにして,できるだけ多くの辺のラベルをг中に配置するという問題について考察する.最近,Kakoulis and Tollisは,この問題に対し,まず各辺のラベルを配置する位置の候補を複数個定め,次にそれらの中から最終的なラベル位置を選択するというヒューリスティクスを提案した.本研究では,ラベルの配置位置の候補を定める部分やラベル位置を選択する部分にいくつかの工夫をすることにより,この方法の改良を行う.そして,これによってラベル配置率が改善できることを計算機実験により示す.
一般社団法人電子情報通信学会, Mar. 2002, 電子情報通信学会論文誌, J85-A (3), 306 - 314, Japanese[Refereed]
Scientific journal
[Refereed]
Scientific journal
平面上の線分の集合を管理し得るデータ構造の一つとしてGBD木が知られている.GBD木により, 線分の効率的な挿入・削除と範囲検索が可能であるが, 長い線分が存在する場合に検索効率が低下することがある.この問題点に対処するため, 長い線分を複数個に分割することが提案されているが, その方法は非常に単純なものであり, 改善の余地が残されている.本研究では, 線分の新しい分割方法を提案し, GBD木の検索効率が更に改善できることを計算機実験により示す.
一般社団法人電子情報通信学会, Dec. 2000, 電子情報通信学会論文誌, J83-D-1 (12), 1300 - 1304, Japanese[Refereed]
Scientific journal
代表的な無向グラフ描画法の一つであるEadesのアルゴリズムは, 単純でプログラム化が容易であるという長所をもつが, 描画中に極端に長い辺や, 頂点と辺の近接を生じることがある.これらの問題点を解決するため, 本研究では, Eadesのアルゴリズムに頂点間及び頂点と辺の間の理想距離を導入し, それらに基づく力を定義する.計算機実験を行ったところ, この改良により, 描画中の辺の交差数は若干増加したものの, 辺の長さの一様性, 及び頂点と辺の近接数に関して大きく改善することができた.
一般社団法人電子情報通信学会, Sep. 2000, 電子情報通信学会論文誌, J83-A (9), 1117 - 1121, Japanese[Refereed]
Scientific journal
様々な構造の視覚化を目的として, グラフの自動描画法に関する研究が広く行われている.従来の無向グラフ描画法の多くは, 頂点の位置を決定した後, 辺を直線のみで描く.しかし, これは, 辺と頂点の近接(辺と頂点が近づきすぎる現象)や, 辺の交差を増加させる一つの原因となっている.本論文では, Kamadaらによるアルゴリズムをもとにして, 必要に応じて辺を折れ線や曲線で描く描画法を提案する.更に, 本方法が, 辺と頂点の近接や辺の交差数を減少させ, より構造の理解しやすい描画を得ることを実験的に示す.
一般社団法人電子情報通信学会, Apr. 2000, 電子情報通信学会論文誌, J83-A (4), 402 - 411, Japanese[Refereed]
Scientific journal
地図のように, 平面上のある範囲が複数の領域に分かれているとき, 個々の領域の位置や形状を示す情報を管理するための方式の一つとして, "2段階の木構造による領域情報管理法式"が知られている.これは, 領域が存在する範囲を2等分割する操作を, 分割された各部分内の領域が1種類になるまで再帰的に行い, その分割過程を2段階の木構造により表すというものである.このデータ構造を用いると, 指定された点を含む領域を求める点検索, 及び指定された面(小さな方形範囲)と共通部分をもつ領域をすべて求める面検索を効率的に行うことができる.本論文では, 2段階の木構造の新しい構成法を三つ提案する.最初の二つの方法は, 領域の角(各領域の周を構成する垂直・水平線分の端点)が存在する座標でのみ分割を行うもので, 従来方法に比べて, 木の節点数を大幅に減少させる.また, 三つ目の方法は, 動的計画法を用いることにより, 点検索時に訪問する節点数の期待値が最小となるように木構造を構成する.
一般社団法人電子情報通信学会, Jan. 2000, 電子情報通信学会論文誌, J83-D-1 (1), 134 - 142, Japanese[Refereed]
Scientific journal
動的な多次元点データの効率的な管理と高速な範囲検索が可能なデータ構造として, 様々なものが知られている. その中で, MD木は高いメモリ効率と範囲検索効率を示すことが報告されている. しかし, ある座標軸に関してソートされた順序でデータが投入されるとき, MD木の範囲検索効率が低下する場合がある. また, 木の作成時には, メモリ効率の向上を目的として領域の動的調整が頻繁に行われ, 作成時間が長くかかる原因となっている. 本研究では, MD木の領域分割法を改良することにより, 高いメモリ効率を保持したまま, これらの問題点を解決する方法を提案する.
一般社団法人電子情報通信学会, Mar. 1999, 電子情報通信学会論文誌, J82-D-I (3), 508 - 513, Japanese[Refereed]
Scientific journal
出発地,目的地なる2頂点s,tが指定されたグラフG=(V,E),妨害数なる正整数k,各辺の(正の)重みl(・)が与えられている.このとき,2人の競技者P1とP2が以下のルールに従ってゲームを行う. P1はsを出発地点とし,1回に一つの辺をたどって目標地点tまで行こうとする.P2は自分の手番にいくつかの辺を切断する.P2の切断できる辺の数はゲームを通じてk本までとする. P1, P2ともグラフ全体が見えているものとする.P1は自分の通る辺の長さの和(道のり)ができるだけ小さくなるようにし,P2はできるだけ大きくなるようにする.本論文では,2人が最善を尽くしたときの道のりをO(n^
[Refereed]
When a planar graph is drawn, the drawing plane is divided into several regions, each of which is called a face. A subgraph composing the periphery of a face is called a window. For each window W that exists in the drawing of a planar graph G, the total sum of the weights of the vertices and the edges is called the weight of the window W. Among all windows that can appear in drawings, the window with the maximum weight is called the maximum-weight-window of G. This paper considers the problem of determining the drawing with the maximum-weight-window. The result for this problem is already obtained for the case where the graph is 2-connected, as well as for the case where the graph is not necessarily 2-connected but all weights are nonnegative. This paper considers also the arbitrary planar graph with real-valued weights, and shows that the drawing with the maximum-weight-window can be determined in O(n + e) time. This result can be applied to the layout design for LSI and printed board, as well as to the diagram representation of the network. It can also be applied to the solution of the maximal planarization problem for the graph.
Lead, John Wiley and Sons Inc., 1996, Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi), 79 (8), 86 - 92, English[Refereed]
Scientific journal
平面グラフの描写は描かれている平面をいくつかの領域に分割しているが,それらの領域のそれぞれを面と呼び,各面の周を構成しているような部分グラフを窓と呼ぶ.平面グラフGの描写中に存在し得る各窓Wについて,その頂点と辺の重みの総和を窓Wの重みと呼ぶ.描写に現れ得るすべての窓のうちで重みが最大のものを,Gの最大重み窓と呼ぶ.本論文では最大重み窓をもつ描写を求める問題について考える.グラフが2連結である場合およびすべての重みが非負であり2連結とは限らない場合についての結果は既に得られていた.本論文では実数の重みの与えられた任意の平面グラフに対して,O(n+e)時間で最大重み窓をもつ描写を求めることができることを示す.この結果はLSIや印刷基板のレイアウト設計,ネットワークの図示などに応用をもち,また,グラフの極大平面化問題を解くことにも用いることができる.
Lead, 一般社団法人電子情報通信学会, Oct. 1995, 電子情報通信学会論文誌, J78-A (10), 1335 - 1340, Japanese[Refereed]
Scientific journal
一つの木の上の道の集合が与えられたとき,道に対応して頂点をもち,二つの道が交わるとき対応する頂点が辺で結ばれているようなグラフをパスグラフと呼ぶ.直線上の有限個の区間の集合Aが与えられたとき,Aに属する区間を頂点とし二つの区間が交わるとき間に辺を持つようなグラフを区間グラフと呼ぶ.本研究では,パスグラフにK本以下の本数の辺を付加して区間グラフに変換することができるか否かを判定する問題がNP完全であることを証明する.
Lead, 一般社団法人電子情報通信学会, 25 Sep. 1994, 電子情報通信学会論文誌. A, 基礎・境界, 77 (9), 1269 - 1275, Japanese[Refereed]
最大重みクリーク問題において、負の重みを許した問題はあまり研究されてこなかった。本稿では、頂点と辺に重みのあるグラフにおいて負の重みを許した最大重みクリーク問題に対して、分枝限定法に基づく厳密解法を提案する。
[情報処理学会関西支部], 10 Sep. 2021, 2021年度 情報処理学会関西支部 支部大会 講演論文集, 2021 (2021), 4p, Japanese線形順序付け問題は,辺に重みのついた有向グラフが与えられたときに,できるだけ逆向きの辺が生じないように頂点に順序を付ける問題である.この問題は,局所探索法でよい解が得られることが知られている.本発表では,局所探索に関する効率化を提案する.
[情報処理学会関西支部], 10 Sep. 2021, 情報処理学会関西支部支部大会講演論文集, 2021 (2021), 4p, JapaneseThe branch-and-bound method is used in many exact algorithms for optimization problems. In most case, those algorithms are implemented with the depth rst search. Other search strategies are rarely used because they require large storage areas. In this paper, we propose a new search strategy, the widening search. The widening search greedily nds a solution at rst, and then gradually widens the search space. The storage size required by the widening search is almost same as the depth rst search. We implemented the branch-and-bound algorithm for the maximum weight clique problem with the depth rst search and the widening search and compared their performances. Experimental results show that the solutions by the widening search are much better than the solutions by the depth rst search.
The Japanese Society for Artificial Intelligence, 06 Oct. 2014, JSAI Technical Report, SIG-FPAI, 95, 01, JapaneseWe consider an enumeration of directed binary perfect phylogenies from incomplete data. Recently, Kiyomi et al. proposed an enumeration algorithm for directed binary perfect phylogenies using ZDDs. A ZDD is a compact data structure for a family of sets provided with a rich family of set operations. Kiyomi's algorithm constructs a ZDD which represents all directed binary perfect phylogenies using these operations. On the other hand, Knuth proposed an algorithm for enumerating paths in a graph by using a ZDD. This method is based on a dynamic programming, and construct the objective ZDD, directly. In this paper, we propose an efficient algorithm for enumerating directed binary perfect phylogenies using the dynamic programming. We show an effectivity of our algorithm by computational experiment.
Information Processing Society of Japan (IPSJ), 10 May 2013, IPSJ SIG Notes, 2013 (10), 1 - 8, JapaneseWe consider an enumeration of directed binary perfect phylogenies from incomplete data. Recently, Kiyomi et al. proposed an enumeration algorithm for directed binary perfect phylogenies using ZDDs. A ZDD is a compact data structure for a family of sets provided with a rich family of set operations. Kiyomi's algorithm constructs a ZDD which represents all directed binary perfect phylogenies using these operations. On the other hand, Knuth proposed an algorithm for enumerating paths in a graph by using a ZDD. This method is based on a dynamic programming, and construct the objective ZDD, directly. In this paper, we propose an efficient algorithm for enumerating directed binary perfect phylogenies using the dynamic programming. We show an effectivity of our algorithm by computational experiment.
The Institute of Electronics, Information and Communication Engineers, 10 May 2013, IEICE technical report. Theoretical foundations of Computing, 113 (50), 63 - 70, JapaneseIn this article, we show an algorithm for finding an orthogonal drawing of a hierarchical graph. In an orthogonal drawing, each edge is drawn as a path consisting of vertical and horizontal line segments. We present a method for determining the x-coordinates of the vertices so that the total sum of the lengths of horizontal line segments becomes small. We also propose a method for drawing hyperedges. It uses at most two horizontal line segments to draw each hyperedge and can make both the number of edge crossings in the graph drawing and that of y-coordinates of the horizontal line segments small.
The Institute of Electronics, Information and Communication Engineers, 24 Apr. 2013, IEICE technical report. Theoretical foundations of Computing, 113 (14), 35 - 42, JapaneseGiven a vertex-weighted undirected graph, the problem to find the clique of maximum weight is the maximum weight clique problem. We propose a new exact algorithm based on the branch-and-bound. An upper bound of solution is calculated for each subproblem in branch-and-bound algorithms. Our algorithm makes some small subproblems, calculates their upper bounds by dynamic programming, and store the upper bounds to a table. In branch-and-bound, our algorithm calculates an upper bound fast by referring to the table. We confirm our algorithm is faster than other algorithms.
The Institute of Electronics, Information and Communication Engineers, 18 Mar. 2013, IEICE technical report. Theoretical foundations of Computing, 112 (498), 47 - 53, JapaneseGiven sites on a map and their labels with specified size, the label placement problem is to find an appropriate placement for each label. We consider the label placement problem in which the candidates for the position of each label are given. In this case the problem can be represented as the maximum independent set problem. In this paper, we propose a fast algorithm for finding a maximum independent set in a graph which is produced from the label placement problem. We show by some computer experiments that our algorithm is more efficient than the well-known algorithm.
The Institute of Electronics, Information and Communication Engineers, 19 Apr. 2006, IEICE technical report, 106 (29), 63 - 67, JapaneseGiven an undirected graph with weight for each vertex, the maximum weight clique problem is to find the clique of the maximum weight. When the maximum weight clique problem is solved with the branch-and-bound algorithm, it is important to calculate the tighter upper bounds of the weight of the maximum weight cliques quickly. Some exact algorithms to solve the maximum weight clique problem use the upper bound calculation with using longest paths on the graphs generated by some vertex sequences. In this paper, we propose a method to produce better vertex sequences. We show the efficiency of our algorithm with some experimental results.
The Institute of Electronics, Information and Communication Engineers, 15 Sep. 2005, IEICE technical report. Theoretical foundations of Computing, 105 (273), 39 - 42, JapaneseWe deal with the optimization problem that requies the maximum weighted clique of undirected graphs. Some exact algorithms based on the branch-and-bound method have been proposed. The computation time strongly depends on the tightness of upper bounds and the computation time of calculating upper bounds. In this paper we show a fast and simple algorithm for calculating upper bounds. We also show the effictiveness by some computational experiments.
The Institute of Electronics, Information and Communication Engineers, 18 Apr. 2005, IEICE technical report. Theoretical foundations of Computing, 105 (7), 1 - 4, JapaneseIn this paper, we consider the problem of labeling points in the plane. For this problem, Wagner et al. proposed an efficient algorithm. It creates several label candidates (candidtaes of label positions) for each point and then determines label positions from the candidates. By extending this method, we present two algorithms for labeling points with leader lines. Our methods first apply the algorithm by Wagner et al. to the given set of points. Then the methods create label candidates with a leader line for each unlabeled point, and choose label positions from such cadidates.
The Institute of Electronics, Information and Communication Engineers, 11 Mar. 2005, IEICE technical report. Theoretical foundations of Computing, 104 (743), 87 - 93, JapaneseWe show a method for calculating the upper bound of the weight of the maximum weighted clique problem with using comparability supergraphs. With our method, many algorithms for the maximum cadinality clique problem with using the branch-and-bound technique based on coloring are naturally extended to algorithms for the maximum weighted clique problem. Our method uses the maximum weighted clique in a comparability supergraph of the given graph at the bounding stage. We investigate the efficiency and the problems of our method some with some computational experiments.
The Institute of Electronics, Information and Communication Engineers, 15 Apr. 2004, IEICE technical report. Theoretical foundations of Computing, 104 (16), 25 - 30, EnglishIt is known that Lagrangean relaxation is useful to obtain tight upper bounds for some combinatorial optimization problems. However, for the maximum clique problem, utilizing Lagrangean relaxation in a straight-forward manner does not give tight upper bounds. In this paper, we present two methods for obtaining good upper bounds for this problem. In order to construct relaxed problems, the first method makes several chordal supergraphs of the given graph, while the second one creates several vertex induced chordal subgraphs. Experimental results show that our methods can compute better upper bounds than the simple Lagrangean relaxation.
The Institute of Electronics, Information and Communication Engineers, 11 Mar. 2003, IEICE technical report. Theoretical foundations of Computing, 102 (733), 15 - 22, JapaneseLet G be a graph and Γ be its drawing on a plane. Each edge in G has a label of specified size. We consider the problem of placing many edge labels in Γ in such a way that no label overlaps vertices, edges or other labels. Recently, Kakoulis and Tollis proposed a heuristic algorithm for this problem. In this paper, we improve their algorithm by refining the part for deciding the candidates of label positions and that for choosing the final label positions.
The Institute of Electronics, Information and Communication Engineers, 09 Apr. 2001, IEICE technical report. Theoretical foundations of Computing, 101 (5), 9 - 16, JapaneseWe deal with the problem to find a shortest path between two specified vertices. This problem can be efficiently solved with A^* algorithm, used in AI field, if we roughly know the distance from each vertex to the goal vertex. On the other hand, LAESA, one of nearest neighbor search algorithms, uses "approximate distance" to solve NNS problem efficiently. In this paper, we show that approximate disntace can be applied to A^* algorithm, and that we can efficiently obtain shortest paths with this method.
The Institute of Electronics, Information and Communication Engineers, 09 Apr. 2001, IEICE technical report. Theoretical foundations of Computing, 101 (5), 17 - 22, JapaneseThe range search performance of a BD(M) tree, which is a multi-layer data structure based on a BD tree, highly depends on the value of parameter n. In this paper, we present a multi-layer data structure, called an S2M structure. It includes two BD(M) trees with distinct values of n, and selects an appropreate one depending on the search condition. Experimental results show that S2M strucutures are superior to other multi-layer data structures, such as ST structures, MT structures and BD(M) trees, with respect to range search performance.
The Institute of Electronics, Information and Communication Engineers, 09 Mar. 2001, IEICE technical report. Theoretical foundations of Computing, 100 (705), 97 - 104, JapaneseGiven a point set S, the nearest neighor search problem is to construct a data structure so that the nearest point to a query point can be found quickly. LAESA is considered to be one of the most efficient data structure with size O(|S|), but its running time is linear to |S|. In this paper, we propose a new data structure with size O(|S|), cvp-structure. It requires about same number of distance computations as LAESA, and the time complexity is linear to the number of distance computations. Thus, our data structure is more effcient than LAESA.
The Institute of Electronics, Information and Communication Engineers, 06 Oct. 2000, IEICE technical report. Data engineering, 100 (351), 65 - 70, JapaneseNearest neighbor search is to find the nearest site to query point from a set S of n sites, and it is one of the important parts of pattern recognition. We introduce an improvement of LAESA to find nearest neighbors in general metric spaces. Our algorithm is especially efficient when distance computations are very expensive, and when the size of data structure is limited. The results of experiments show that in this case our algorithm finds nearest neighbors faster than LAESA, which can be considered as one of the most efficent algorithms so far.
The Institute of Electronics, Information and Communication Engineers, 11 Sep. 2000, IEICE technical report. Theoretical foundations of Computing, 100 (289), 9 - 15, JapaneseIn this paper, we consider the problem of placing vertex labels in a drawing of an undirected graph. Kamada has presented a very simple method for this problem. However, if the labels are not small, it often yields the overlaps between labels and other objects. This paper shows a method for placing many labels with no such overlaps. This method first determines, for each vertex v, the set of candidates of its label positions. At this step, the existence of edges around v and the label size of v are considered. Then, the method places labels one by one. If the label of a vertex v overlaps other vertices or labels, the label positions are locally adjusted or another candidate of label position for v is selected.
The Institute of Electronics, Information and Communication Engineers, 11 Sep. 2000, IEICE technical report. Theoretical foundations of Computing, 100 (289), 41 - 46, JapaneseThe class assignment problem is to assign students to classes within the capacity of each class, in such a way that it satisfies them as much as possible. We can consider the problem as a kind of resource allocation problems. It is generally impossible to assign the students so that all of them are satisfied. We propose an assignment algorithm which reduces students assigned to the classes they do not want. The results of experiments show that our algorithm produces less number of those students than other known algorithms, and also show that knowing other students' choices is not profitable for any students.
The Institute of Electronics, Information and Communication Engineers, 11 Sep. 2000, IEICE technical report. Theoretical foundations of Computing, 100 (289), 17 - 23, JapaneseThe k-center problem is one of the important NP optimization problems. The capacitated k-center problem is its more practical variation. Although a 6-approximation algorithm has been proposed, it is considered to be ineffective. In this paper, we present three heuristic algorithms for the capacitated k-center problem. Experimental results show that we can get better solutions more efficiently, by executing two of our methods sequentially.
Information Processing Society of Japan (IPSJ), 17 Jan. 2000, IPSJ SIG Notes, 2000 (5), 49 - 56, JapaneseA GBD tree is a data structure that can maintain a set of line segments on a plane. By using it, we can efficiently perform three kinds of operations; insertion, deletion and range search. However, the search performance is not good enough if long line segments exist. In order to improve it, a method for splitting long line segments was proposed. In this article, we show that some modifications of the splitting method further improve the search performance.
Information Processing Society of Japan (IPSJ), 17 Jan. 2000, IPSJ SIG Notes, 2000 (5), 81 - 87, JapaneseMany algorithms for finding nearest neighbours have been introduced recently. We introduce a new data structure and algorithm to find nearest neighbours in general metric spaces, where distance computations are very expensive. The results of experiments show that in some cases our algorithms find nearest neighbours with less distance computations than LAESA, which can be considered as one of the most efficient algorithms so far.
The Institute of Electronics, Information and Communication Engineers, 23 Jan. 1999, IEICE technical report. Theoretical foundations of Computing, 98 (562), 73 - 80, JapaneseIf each drawing of G_1=(V, E_1), G_2=(V, E_2),…, G_k=(V, E_k) is planar in a drawing of a graph G=(V, E_1 ∪ E_2 ∪…∪ E_k), the drawing of G is called a simultaneous planar drawing of G_1, G_2,…, and G_k. K-graphs sinultaneous planar problem is to examine if there exists any simultaneous planar drawing of G_1,…G_k or not. This paper proves that 3-graphs simultaneous planar problem is NP-complete.
The Institute of Electronics, Information and Communication Engineers, 26 Sep. 1997, IEICE technical report. Theoretical foundations of Computing, 97 (290), 1 - 4, JapaneseLet G = (V,A) be a directed graph with (positive) length l(a) for each a ∈ A, and two vertices s and t are specified. Two players, P1 and P2, play reciprocally on G according to the following rules until Pl reaches t. P1 attempts to move from starting points to destination t, moving along one arc during each turn. P2 deletes arcs, whose start points weren't visited by P1, from A during his turn. The number of arcs which P2 can delete within a game is K. Pl tries to keep the sum of the length of arcs which he passed through to a minimum value, while P2 attempts to make it as large as possible. What value will it be? In this paper, we show that, the problem can be solved in O(m + nlogn) time (m=|A|,n=|V|) in the case K=1, and that it is NP-hard in the case K≥2, even if l(a) = 1 for all a ∈ A.
The Institute of Electronics, Information and Communication Engineers, 16 Nov. 1995, IEICE technical report. Circuits and systems, 95 (351), 71 - 76, Japaneseグラフが変化する事を考慮にいれた最短経路問題の一つとして本稿では次のような問題を考える.
The Institute of Electronics, Information and Communication Engineers, 27 Mar. 1995, Proceedings of the IEICE General Conference, 1995, 3 - 3, JapaneseGiven a 2-connected graph G(V, E) and its one edge st(s, t ε V), an st-numbering is the numbering such that s is given the number 1, t is given the number |V|, and for all other vertices there are lower numbered adjacent vertices and higher numbered adjacent vertices. A Planar graph is a graph which can be drawn on a plane in such a way that no two edges cross each other. In this paper, for two planar graphs that have a common vertex set, we consider the problem of giving a numbering for those vertices that is an st-numbering for each graph. We show it is NP-complete.
Information Processing Society of Japan (IPSJ), 17 Mar. 1995, IPSJ SIG Notes, 1995 (32), 53 - 60, JapaneseAn undirected graph is called a path graph,if its vertices correspond to paths on a fixed tree and two vertices are connected by an edge if and only if their corresponding paths have non empty intersection.Let A be a set of intervals on a linearly ordered set. An undirected graph is called an interval graph,if its vertices correspond to intervals of A and two vertices are connected by an edge if and only if their corresponding intervals have non empty intersection.This paper proves that the problem of deciding whether we can transform a path graph to an interval graph by adding less than K edges is NP complete.
The Institute of Electronics, Information and Communication Engineers, 27 May 1993, IEICE technical report. Theoretical foundations of Computing, 93 (81), 15 - 20, JapaneseOral presentation
[Invited]
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電子情報通信学会
Apr. 1995 - PresentThe Operations Research Society of Japan
- PresentSociety for Industrial and Applied Mathematics
- PresentIEEE
- Present日本応用数理学会
- Present情報処理学会
- PresentIn this research, we have presented algorithms for finding an orthogonal drawing of a hierarchical graph. In an orthogonal drawing, each edge is drawn as a path consisting of vertical and horizontal line segments. The proposed algorithms include the following methods: (i) an algorithm for sharing dummy vertices, (ii) a method for creating hyperedges from the set of edges of the resultant graph, (iii) a method for determining the x-coordinates of the vertices so that the total sum of the lengths of horizontal line segments becomes small, and (iv) an algorithm for drawing hyperedges. The last algorithm (iv) uses at most two horizontal line segments to draw each hyperedge and can make the number of edge crossings in the graph drawing small.
In order to make graph drawing algorithms more effective for information visualization, we have developed the following algorithms :(1) an algorithm for producing an orthogonal drawing of a graph that basically preserves the relative vertex positions in a given straight-line drawing,(2) an algorithm for improving the quality of a straight-line drawing of a graph,(3) algorithms for determining the vertex coordinates and for sharing dummy vertices in a hierarchical graph drawing,(4) a force-oriented algorithm for drawing a disconnected graph, and(5) an algorithm for finding a graph drawing with rectangular vertices.
代表的な有向グラフ描画法として, 階層的描画を求めるSugiyamaらの方法が知られている. 本研究では, この方法の各ステップについて考察し, 従来の方法の改良を行った. また, 辺交差数と描画幅削減のため, 垂直・水平線分のみを用いて辺を描く方法を開発した. さらに, 頂点がラベルをもつグラフに対して, グラフ描画を求めた後, できるだけ大きな文字サイズを使ってラベルを配置する方法を提案した.
Competitive research funding