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Ryuhei Uehara

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Seoul National University

Timothy A Mousseau

University of South Carolina

University of Cologne

Sorbonne Université, Université Pierre et Marie Curie & CNRS

Vincent D . Costa

Emory University

University of Sarajevo

Gabrielle Hecht

Stanford University

Donna M Goldstein

University of Colorado, Boulder

Friedrich-Alexander-Universität Erlangen-Nürnberg

Milan Vukicevic

University of Belgrade, Faculty of Organizational Sciences

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Papers by Ryuhei Uehara

Complexity of the Maximum <i>k</i>-Path Vertex Cover Problem

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Oct 1, 2020

This paper introduces the maximization version of the kpath vertex cover problem, called the Maxi... more This paper introduces the maximization version of the kpath vertex cover problem, called the Maximum k-Path Vertex Cover problem (MaxP k VC for short): A path consisting of k vertices, i.e., a path of length k -1 is called a k-path. If a k-path P k includes a vertex v in a vertex set S , then we say that v or S covers P k . Given a graph G = (V, E) and an integer s, the goal of MaxP k VC is to find a vertex subset S ⊆ V of at most s vertices such that the number of k-paths covered by S is maximized. The problem MaxP k VC is generally NP-hard. In this paper we consider the tractability/intractability of MaxP k VC on subclasses of graphs. We prove that MaxP 3 VC remains NP-hard even for split graphs. Furthermore, if the input graph is restricted to graphs with constant bounded treewidth, then MaxP 3 VC can be solved in polynomial time.

Maximum k-path Vertex Cover Problem on Graph Classes

IEICE Technical Report; IEICE Tech. Rep., Dec 14, 2017

Optimization of 3Dcell microstructure cell using origami technology and computational origami

The Japan Society of Applied Physics, Jul 10, 2019

Triangulation with Many/Few Triangles

IEICE Technical Report; IEICE Tech. Rep., Sep 11, 2018

Complexity of the Maximum k-Path Vertex Cover Problem

Springer eBooks, 2018

This paper introduces the maximum version of the k-path vertex cover problem, called the Maximum ... more This paper introduces the maximum version of the k-path vertex cover problem, called the Maximum k-Path Vertex Cover problem (MaxP k VC for short): A path consisting of k vertices, i.e., a path of length k -1 is called a k-path. If a k-path P k includes a vertex v in a vertex set S, then we say that S or v covers P k . Given a graph G = (V, E) and an integer s, the goal of MaxP k VC is to find a vertex subset S ⊆ V of at most s vertices such that the number of k-paths covered by S is maximized. MaxP k VC is generally NP-hard. In this paper we consider the tractability/intractability of MaxP k VC on subclasses of graphs: We prove that MaxP3VC and MaxP4VC remain NP-hard even for split graphs and for chordal graphs, respectively. Furthermore, if the input graph is restricted to graphs with constant bounded treewidth, then MaxP3VC can be solved in polynomial time.

Parameterized complexity of independent set reconfiguration problems

Discrete Applied Mathematics, 2020

Suppose that we are given two independent sets I 0 and I r of a graph such that |I 0 | = |I r |, ... more Suppose that we are given two independent sets I 0 and I r of a graph such that |I 0 | = |I r |, and imagine that a token is placed on each vertex in I 0 . Then, the token jumping problem is to determine whether there exists a sequence of independent sets which transforms I 0 into I r so that each independent set in the sequence results from the previous one by moving exactly one token to another vertex. Therefore, all independent sets in the sequence must be of the same cardinality. This problem is PSPACE-complete even for planar graphs with maximum degree three. In this paper, we first show that the problem is W[1]-hard when parameterized only by the number of tokens. We then give an FPT algorithm for general graphs when parameterized by both the number of tokens and the maximum degree. Our FPT algorithm can be modified so that it finds an actual sequence of independent sets between I 0 and I r with the minimum number of token movements. We finally show that one of the results for token jumping can be extended to a more generalized reconfiguration problem for independent sets, called token addition and removal.

Enumeration of nonisomorphic interval graphs and nonisomorphic permutation graphs

Theoretical Computer Science, Feb 1, 2020

In this paper, a general framework for enumerating every element in a graph class is given. The m... more In this paper, a general framework for enumerating every element in a graph class is given. The main feature of this framework is that it is designed to enumerate only non-isomorphic graphs in a graph class. Each element in the class is output in a polynomial time delay. Applying this framework to the classes of interval graphs and permutation graphs, we give efficient enumeration algorithms for these graph classes. The experimental results are also provided. The catalogs of graphs in these graph classes are also provided.

Reconstruction of interval graphs

Theoretical Computer Science, Oct 1, 2010

The graph reconstruction conjecture is a long-standing open problem in graph theory. There are ma... more The graph reconstruction conjecture is a long-standing open problem in graph theory. There are many algorithmic studies related to it, such as DECK CHECKING, LEGITIMATE DECK, PREIMAGE CONSTRUCTION, and PREIMAGE COUNTING. We study these algorithmic problems by limiting the graph class to interval graphs. Since we can solve GRAPH ISOMOR-PHISM for interval graphs in polynomial time, DECK CHECKING for interval graphs is easily done in polynomial time. Since the number of interval graphs that can be obtained from an interval graph by adding a vertex and edges incident to it can be exponentially large, developing polynomial time algorithms for LEGITIMATE DECK, PREIMAGE CONSTRUCTION, and PREIMAGE COUNTING on interval graphs is not trivial. We present that these three problems are solvable in polynomial time on interval graphs.

Reconstruction Algorithms for Permutation Graphs and Distance-Hereditary Graphs (アルゴリズム(AL) Vol.2009-AL-126)

研究報告アルゴリズム（AL）, Sep 8, 2009

PREIMAGE CONSTRUCTION problem by Kratsch and Hemaspaandra naturally arose from the famous graph r... more PREIMAGE CONSTRUCTION problem by Kratsch and Hemaspaandra naturally arose from the famous graph reconstruction conjecture. It deals with the algorithmic aspects of the conjecture. We present an O(n 8) time algorithm for PREIMAGE CONSTRUCTION on permutation graphs and an O(n 4 (n + m)) time algorithm for PREIMAGE CONSTRUCTION on distance-hereditary graphs, where n is the number of graphs in the input, and m is the number of edges in a preimage. Since each graph of the input has n − 1 vertices and O(n 2) edges, the input size is O(n 3) (, or O(nm)). There are polynomial time isomorphism algorithms for permutation graphs and distance-hereditary graphs. However the number of permutation (distance-hereditary) graphs obtained by adding a vertex to a permutation (distance-hereditary) graph is generally exponentially large. Thus exhaustive checking of these graphs does not achieve any polynomial time algorithm. Therefore reducing the number of preimage candidates is the key point.

Swapping colored tokens on graphs

Theoretical Computer Science, Jun 1, 2018

We investigate the computational complexity of the following problem. We are given a graph in whi... more We investigate the computational complexity of the following problem. We are given a graph in which each vertex has an initial and a target color. Each pair of adjacent vertices can swap their current colors. Our goal is to perform the minimum number of swaps so that the current and target colors agree at each vertex. When the colors are chosen from {1, 2,. .. , c}, we call this problem c-Colored Token Swapping since the current color of a vertex can be seen as a colored token placed on the vertex. We show that c-Colored Token Swapping is NP-complete for c = 3 even if input graphs are restricted to connected planar bipartite graphs of maximum degree 3. We then show that 2-Colored Token Swapping can be solved in polynomial time for general graphs and in linear time for trees. Besides, we show that, the problem for complete graphs is fixedparameter tractable when parameterized by the number of colors, while it is known to be NP-complete when the number of colors is unbounded.

Bipartite Permutation Graphs Are Reconstructible

Discrete Mathematics, Algorithms and Applications, Aug 6, 2012

The graph reconstruction conjecture is a long-standing open problem in graph theory. The conjectu... more The graph reconstruction conjecture is a long-standing open problem in graph theory. The conjecture has been verified for all graphs with at most 11 vertices. Further, the conjecture has been verified for regular graphs, trees, disconnected graphs, unit interval graphs, separable graphs with no pendant vertex, outer-planar graphs, and unicyclic graphs. We extend the list of graph classes for which the conjecture holds. We give a proof that bipartite permutation graphs are reconstructible.

Exact Algorithms for the Max-Min Dispersion Problem

Lecture Notes in Computer Science, 2018

Given a set P of n elements, and a function d that assigns a non-negative real number d(p, q) for... more Given a set P of n elements, and a function d that assigns a non-negative real number d(p, q) for each pair of elements p, q ∈ P , we want to find a subset S ⊆ P with |S| = k such that the cost cost(S) = min{d(p, q) | p, q ∈ S} is maximized. This is the max-min k-dispersion problem. In this paper, exact algorithms for the max-min k-dispersion problem are studied. We first show the max-min k-dispersion problem can be solved in O(n ωk/3 log n) time. Then, we show two special cases in which we can solve the problem quickly.

Max-Min 3-Dispersion Problems

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Sep 1, 2021

Given a set P of n points on which facilities can be placed and an integer k, we want to place k ... more Given a set P of n points on which facilities can be placed and an integer k, we want to place k facilities on some points so that the minimum distance between facilities is maximized. The problem is called the k-dispersion problem. In this paper we consider the 3-dispersion problem when P is a set of points on a plane. Note that the 2-dispersion problem corresponds to the diameter problem. We give an O(n) time algorithm to solve the 3-dispersion problem in the \(L_{\infty }\) metric, and an O(n) time algorithm to solve the 3-dispersion problem in the \(L_1\) metric. Also we give an \(O(n^2\log n)\) time algorithm to solve the 3-dispersion problem in the \(L_2\) metric.

グラフ上の着色トークンの交換【JST・京大機械翻訳】

Theoretical Computer Science, 2018

Reconstruction Algorithms for Permutation Graphs and Distance-Hereditary Graphs

IEICE Transactions on Information and Systems, 2013

PREIMAGE CONSTRUCTION problem by Kratsch and Hemaspaandra naturally arose from the famous graph r... more PREIMAGE CONSTRUCTION problem by Kratsch and Hemaspaandra naturally arose from the famous graph reconstruction conjecture. It deals with the algorithmic aspects of the conjecture. We present an O(n 8) time algorithm for PREIMAGE CONSTRUCTION on permutation graphs and an O(n 4 (n + m)) time algorithm for PREIMAGE CONSTRUCTION on distance-hereditary graphs, where n is the number of graphs in the input, and m is the number of edges in a preimage. Since each graph of the input has n − 1 vertices and O(n 2) edges, the input size is O(n 3) (, or O(nm)). There are polynomial time isomorphism algorithms for permutation graphs and distance-hereditary graphs. However the number of permutation (distance-hereditary) graphs obtained by adding a vertex to a permutation (distance-hereditary) graph is generally exponentially large. Thus exhaustive checking of these graphs does not achieve any polynomial time algorithm. Therefore reducing the number of preimage candidates is the key point.

Competitive Diffusion on Weighted Graphs

Lecture Notes in Computer Science, 2015

Consider an undirected and vertex-weighted graph modeling a social network, where the vertices re... more Consider an undirected and vertex-weighted graph modeling a social network, where the vertices represent individuals, the edges do connections among them, and weights do levels of importance of individuals. In the competitive diffusion game, each of a number of players chooses a vertex as a seed to propagate his/her idea which spreads along the edges in the graph. The objective of every player is to maximize the sum of weights of vertices infected by his/her idea. In this paper, we study a computational problem of asking whether a pure Nash equilibrium exists in a given graph, and present several negative and positive results with regard to graph classes. We first prove that the problem is W[1]-hard when parameterized by the number of players even for unweighted graphs. We also show that the problem is NP-hard even for series-parallel graphs with positive integer weights, and is NP-hard even for forests with arbitrary integer weights. Furthermore, we show that the problem for forests of paths with arbitrary weights is solvable in pseudopolynomial time; and it is solvable in quadratic time if a given graph is unweighted. We also prove that the problem is solvable in polynomial time for chain graphs, cochain graphs, and threshold graphs with arbitrary integer weights.

Random Generation and Enumeration of Proper Interval Graphs

Lecture Notes in Computer Science, 2009

We investigate connected proper interval graphs without vertex labels. We first give the number o... more We investigate connected proper interval graphs without vertex labels. We first give the number of connected proper interval graphs of n vertices. Using this result, a simple algorithm that generates a connected proper interval graph uniformly at random up to isomorphism is presented. Finally an enumeration algorithm of connected proper interval graphs is proposed. The algorithm is based on reverse search, and it outputs each connected proper interval graph in O(1) time.

Sequentially Swapping Colored Tokens on Graphs

Lecture Notes in Computer Science, 2017

We consider a puzzle consisting of colored tokens on an n-vertex graph, where each token has a di... more We consider a puzzle consisting of colored tokens on an n-vertex graph, where each token has a distinct starting vertex and a set of allowable target vertices for it to reach, and the only allowed transformation is to sequentially move the chosen token along a path of the graph by swapping it with other tokens on the path.

Computational Complexity of Sequential Token Swapping Problem

IEICE Technical Report; IEICE Tech. Rep., Jun 17, 2016

Linear structure of bipartite permutation graphs and the longest path problem

Information Processing Letters, Jul 1, 2007

The class of bipartite permutation graphs is the intersection of two well known graph classes: bi... more The class of bipartite permutation graphs is the intersection of two well known graph classes: bipartite graphs and permutation graphs. A complete bipartite decomposition of a bipartite permutation graph is proposed in this note. The decomposition gives a linear structure of bipartite permutation graphs, and it can be obtained in O(n) time, where n is the number of vertices. As an application of the decomposition, we show an O(n) time and space algorithm for finding a longest path in a bipartite permutation graph.

Complexity of the Maximum <i>k</i>-Path Vertex Cover Problem

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Oct 1, 2020

This paper introduces the maximization version of the kpath vertex cover problem, called the Maxi... more This paper introduces the maximization version of the kpath vertex cover problem, called the Maximum k-Path Vertex Cover problem (MaxP k VC for short): A path consisting of k vertices, i.e., a path of length k -1 is called a k-path. If a k-path P k includes a vertex v in a vertex set S , then we say that v or S covers P k . Given a graph G = (V, E) and an integer s, the goal of MaxP k VC is to find a vertex subset S ⊆ V of at most s vertices such that the number of k-paths covered by S is maximized. The problem MaxP k VC is generally NP-hard. In this paper we consider the tractability/intractability of MaxP k VC on subclasses of graphs. We prove that MaxP 3 VC remains NP-hard even for split graphs. Furthermore, if the input graph is restricted to graphs with constant bounded treewidth, then MaxP 3 VC can be solved in polynomial time.

Maximum k-path Vertex Cover Problem on Graph Classes

IEICE Technical Report; IEICE Tech. Rep., Dec 14, 2017

Optimization of 3Dcell microstructure cell using origami technology and computational origami

The Japan Society of Applied Physics, Jul 10, 2019

Triangulation with Many/Few Triangles

IEICE Technical Report; IEICE Tech. Rep., Sep 11, 2018

Complexity of the Maximum k-Path Vertex Cover Problem

Springer eBooks, 2018

This paper introduces the maximum version of the k-path vertex cover problem, called the Maximum ... more This paper introduces the maximum version of the k-path vertex cover problem, called the Maximum k-Path Vertex Cover problem (MaxP k VC for short): A path consisting of k vertices, i.e., a path of length k -1 is called a k-path. If a k-path P k includes a vertex v in a vertex set S, then we say that S or v covers P k . Given a graph G = (V, E) and an integer s, the goal of MaxP k VC is to find a vertex subset S ⊆ V of at most s vertices such that the number of k-paths covered by S is maximized. MaxP k VC is generally NP-hard. In this paper we consider the tractability/intractability of MaxP k VC on subclasses of graphs: We prove that MaxP3VC and MaxP4VC remain NP-hard even for split graphs and for chordal graphs, respectively. Furthermore, if the input graph is restricted to graphs with constant bounded treewidth, then MaxP3VC can be solved in polynomial time.

Parameterized complexity of independent set reconfiguration problems

Discrete Applied Mathematics, 2020

Suppose that we are given two independent sets I 0 and I r of a graph such that |I 0 | = |I r |, ... more Suppose that we are given two independent sets I 0 and I r of a graph such that |I 0 | = |I r |, and imagine that a token is placed on each vertex in I 0 . Then, the token jumping problem is to determine whether there exists a sequence of independent sets which transforms I 0 into I r so that each independent set in the sequence results from the previous one by moving exactly one token to another vertex. Therefore, all independent sets in the sequence must be of the same cardinality. This problem is PSPACE-complete even for planar graphs with maximum degree three. In this paper, we first show that the problem is W[1]-hard when parameterized only by the number of tokens. We then give an FPT algorithm for general graphs when parameterized by both the number of tokens and the maximum degree. Our FPT algorithm can be modified so that it finds an actual sequence of independent sets between I 0 and I r with the minimum number of token movements. We finally show that one of the results for token jumping can be extended to a more generalized reconfiguration problem for independent sets, called token addition and removal.

Enumeration of nonisomorphic interval graphs and nonisomorphic permutation graphs

Theoretical Computer Science, Feb 1, 2020

In this paper, a general framework for enumerating every element in a graph class is given. The m... more In this paper, a general framework for enumerating every element in a graph class is given. The main feature of this framework is that it is designed to enumerate only non-isomorphic graphs in a graph class. Each element in the class is output in a polynomial time delay. Applying this framework to the classes of interval graphs and permutation graphs, we give efficient enumeration algorithms for these graph classes. The experimental results are also provided. The catalogs of graphs in these graph classes are also provided.

Reconstruction of interval graphs

Theoretical Computer Science, Oct 1, 2010

The graph reconstruction conjecture is a long-standing open problem in graph theory. There are ma... more The graph reconstruction conjecture is a long-standing open problem in graph theory. There are many algorithmic studies related to it, such as DECK CHECKING, LEGITIMATE DECK, PREIMAGE CONSTRUCTION, and PREIMAGE COUNTING. We study these algorithmic problems by limiting the graph class to interval graphs. Since we can solve GRAPH ISOMOR-PHISM for interval graphs in polynomial time, DECK CHECKING for interval graphs is easily done in polynomial time. Since the number of interval graphs that can be obtained from an interval graph by adding a vertex and edges incident to it can be exponentially large, developing polynomial time algorithms for LEGITIMATE DECK, PREIMAGE CONSTRUCTION, and PREIMAGE COUNTING on interval graphs is not trivial. We present that these three problems are solvable in polynomial time on interval graphs.

Reconstruction Algorithms for Permutation Graphs and Distance-Hereditary Graphs (アルゴリズム(AL) Vol.2009-AL-126)

研究報告アルゴリズム（AL）, Sep 8, 2009

PREIMAGE CONSTRUCTION problem by Kratsch and Hemaspaandra naturally arose from the famous graph r... more PREIMAGE CONSTRUCTION problem by Kratsch and Hemaspaandra naturally arose from the famous graph reconstruction conjecture. It deals with the algorithmic aspects of the conjecture. We present an O(n 8) time algorithm for PREIMAGE CONSTRUCTION on permutation graphs and an O(n 4 (n + m)) time algorithm for PREIMAGE CONSTRUCTION on distance-hereditary graphs, where n is the number of graphs in the input, and m is the number of edges in a preimage. Since each graph of the input has n − 1 vertices and O(n 2) edges, the input size is O(n 3) (, or O(nm)). There are polynomial time isomorphism algorithms for permutation graphs and distance-hereditary graphs. However the number of permutation (distance-hereditary) graphs obtained by adding a vertex to a permutation (distance-hereditary) graph is generally exponentially large. Thus exhaustive checking of these graphs does not achieve any polynomial time algorithm. Therefore reducing the number of preimage candidates is the key point.

Swapping colored tokens on graphs

Theoretical Computer Science, Jun 1, 2018

We investigate the computational complexity of the following problem. We are given a graph in whi... more We investigate the computational complexity of the following problem. We are given a graph in which each vertex has an initial and a target color. Each pair of adjacent vertices can swap their current colors. Our goal is to perform the minimum number of swaps so that the current and target colors agree at each vertex. When the colors are chosen from {1, 2,. .. , c}, we call this problem c-Colored Token Swapping since the current color of a vertex can be seen as a colored token placed on the vertex. We show that c-Colored Token Swapping is NP-complete for c = 3 even if input graphs are restricted to connected planar bipartite graphs of maximum degree 3. We then show that 2-Colored Token Swapping can be solved in polynomial time for general graphs and in linear time for trees. Besides, we show that, the problem for complete graphs is fixedparameter tractable when parameterized by the number of colors, while it is known to be NP-complete when the number of colors is unbounded.

Bipartite Permutation Graphs Are Reconstructible

Discrete Mathematics, Algorithms and Applications, Aug 6, 2012

The graph reconstruction conjecture is a long-standing open problem in graph theory. The conjectu... more The graph reconstruction conjecture is a long-standing open problem in graph theory. The conjecture has been verified for all graphs with at most 11 vertices. Further, the conjecture has been verified for regular graphs, trees, disconnected graphs, unit interval graphs, separable graphs with no pendant vertex, outer-planar graphs, and unicyclic graphs. We extend the list of graph classes for which the conjecture holds. We give a proof that bipartite permutation graphs are reconstructible.

Exact Algorithms for the Max-Min Dispersion Problem

Lecture Notes in Computer Science, 2018

Given a set P of n elements, and a function d that assigns a non-negative real number d(p, q) for... more Given a set P of n elements, and a function d that assigns a non-negative real number d(p, q) for each pair of elements p, q ∈ P , we want to find a subset S ⊆ P with |S| = k such that the cost cost(S) = min{d(p, q) | p, q ∈ S} is maximized. This is the max-min k-dispersion problem. In this paper, exact algorithms for the max-min k-dispersion problem are studied. We first show the max-min k-dispersion problem can be solved in O(n ωk/3 log n) time. Then, we show two special cases in which we can solve the problem quickly.

Max-Min 3-Dispersion Problems

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Sep 1, 2021

Given a set P of n points on which facilities can be placed and an integer k, we want to place k ... more Given a set P of n points on which facilities can be placed and an integer k, we want to place k facilities on some points so that the minimum distance between facilities is maximized. The problem is called the k-dispersion problem. In this paper we consider the 3-dispersion problem when P is a set of points on a plane. Note that the 2-dispersion problem corresponds to the diameter problem. We give an O(n) time algorithm to solve the 3-dispersion problem in the \(L_{\infty }\) metric, and an O(n) time algorithm to solve the 3-dispersion problem in the \(L_1\) metric. Also we give an \(O(n^2\log n)\) time algorithm to solve the 3-dispersion problem in the \(L_2\) metric.

グラフ上の着色トークンの交換【JST・京大機械翻訳】

Theoretical Computer Science, 2018

Reconstruction Algorithms for Permutation Graphs and Distance-Hereditary Graphs

IEICE Transactions on Information and Systems, 2013

PREIMAGE CONSTRUCTION problem by Kratsch and Hemaspaandra naturally arose from the famous graph r... more PREIMAGE CONSTRUCTION problem by Kratsch and Hemaspaandra naturally arose from the famous graph reconstruction conjecture. It deals with the algorithmic aspects of the conjecture. We present an O(n 8) time algorithm for PREIMAGE CONSTRUCTION on permutation graphs and an O(n 4 (n + m)) time algorithm for PREIMAGE CONSTRUCTION on distance-hereditary graphs, where n is the number of graphs in the input, and m is the number of edges in a preimage. Since each graph of the input has n − 1 vertices and O(n 2) edges, the input size is O(n 3) (, or O(nm)). There are polynomial time isomorphism algorithms for permutation graphs and distance-hereditary graphs. However the number of permutation (distance-hereditary) graphs obtained by adding a vertex to a permutation (distance-hereditary) graph is generally exponentially large. Thus exhaustive checking of these graphs does not achieve any polynomial time algorithm. Therefore reducing the number of preimage candidates is the key point.

Competitive Diffusion on Weighted Graphs

Lecture Notes in Computer Science, 2015

Consider an undirected and vertex-weighted graph modeling a social network, where the vertices re... more Consider an undirected and vertex-weighted graph modeling a social network, where the vertices represent individuals, the edges do connections among them, and weights do levels of importance of individuals. In the competitive diffusion game, each of a number of players chooses a vertex as a seed to propagate his/her idea which spreads along the edges in the graph. The objective of every player is to maximize the sum of weights of vertices infected by his/her idea. In this paper, we study a computational problem of asking whether a pure Nash equilibrium exists in a given graph, and present several negative and positive results with regard to graph classes. We first prove that the problem is W[1]-hard when parameterized by the number of players even for unweighted graphs. We also show that the problem is NP-hard even for series-parallel graphs with positive integer weights, and is NP-hard even for forests with arbitrary integer weights. Furthermore, we show that the problem for forests of paths with arbitrary weights is solvable in pseudopolynomial time; and it is solvable in quadratic time if a given graph is unweighted. We also prove that the problem is solvable in polynomial time for chain graphs, cochain graphs, and threshold graphs with arbitrary integer weights.

Random Generation and Enumeration of Proper Interval Graphs

Lecture Notes in Computer Science, 2009

We investigate connected proper interval graphs without vertex labels. We first give the number o... more We investigate connected proper interval graphs without vertex labels. We first give the number of connected proper interval graphs of n vertices. Using this result, a simple algorithm that generates a connected proper interval graph uniformly at random up to isomorphism is presented. Finally an enumeration algorithm of connected proper interval graphs is proposed. The algorithm is based on reverse search, and it outputs each connected proper interval graph in O(1) time.

Sequentially Swapping Colored Tokens on Graphs

Lecture Notes in Computer Science, 2017

We consider a puzzle consisting of colored tokens on an n-vertex graph, where each token has a di... more We consider a puzzle consisting of colored tokens on an n-vertex graph, where each token has a distinct starting vertex and a set of allowable target vertices for it to reach, and the only allowed transformation is to sequentially move the chosen token along a path of the graph by swapping it with other tokens on the path.

Computational Complexity of Sequential Token Swapping Problem

IEICE Technical Report; IEICE Tech. Rep., Jun 17, 2016

Linear structure of bipartite permutation graphs and the longest path problem

Information Processing Letters, Jul 1, 2007

The class of bipartite permutation graphs is the intersection of two well known graph classes: bi... more The class of bipartite permutation graphs is the intersection of two well known graph classes: bipartite graphs and permutation graphs. A complete bipartite decomposition of a bipartite permutation graph is proposed in this note. The decomposition gives a linear structure of bipartite permutation graphs, and it can be obtained in O(n) time, where n is the number of vertices. As an application of the decomposition, we show an O(n) time and space algorithm for finding a longest path in a bipartite permutation graph.