arXiv subjects

Tesshu Hanaka

Publications and source records attributed to Tesshu Hanaka.

At least 19 recordsLinked to original sources

arXiv2026

On the Complexity of Secluded Path Problems

This paper investigates the complexity of finding secluded paths in graphs. We focus on the \textsc{Short Secluded Path} problem and a natural new variant we introduce, \textsc{Shortest Secluded Path}. Formally, given an undirected graph $G=(V, E)$, two vertices $s,t\in V$, and two integers $k,l$, the \textsc{Short Secluded Path} problem asks whether there exists an $s$-$t$ path of length at most $k$ with at most $l$ neighbors. This problem is known to be computationally hard: it is W[1]-hard when parameterized by the path length $k$ or by cliquewidth, and para-NP-complete when parameterized by the number $l$ of neighbors. The fixed-parameter tractability is known for $k+l$ or treewidth. In this paper, we expand the parameterized complexity landscape by designing (1) an XP algorithm parameterized by cliquewidth and (2) fixed-parameter algorithms parameterized by neighborhood diversity and twin cover number, respectively. As a byproduct, our results also yield parameterized algorithms for the classic \textsc{$s$-$t$ $k$-Path} problem under the considered parameters. Furthermore, we introduce the \textsc{Shortest Secluded Path} problem, which seeks a shortest $s$-$t$ path with the minimum number of neighbors. In contrast to the hardness of the original problem, we reveal that this variant is solvable in polynomial time on unweighted graphs. We complete this by showing that for edge-weighted graphs, the problem becomes W[1]-hard yet remains in XP when parameterized by the shortest path distance between $s$ and $t$.

cs.DS↗

arXiv2026

Game-Theoretic and Algorithmic Analyses of Multi-Agent Routing under Crossing Costs

Coordinating the movement of multiple autonomous agents over a shared network is a fundamental challenge in algorithmic robotics, intelligent transportation, and distributed systems. The dominant approach, Multi-Agent Path Finding, relies on centralized control and synchronous collision avoidance, which often requires strict synchronization and guarantees of globally conflict-free execution. This paper introduces the Multi-Agent Routing under Crossing Cost model on mixed graphs, a novel framework tailored to asynchronous settings. In our model, instead of treating conflicts as hard constraints, each agent is assigned a path, and the system is evaluated through a cost function that measures potential head-on encounters. This ``crossing cost'', which is defined as the product of the numbers of agents traversing an edge in opposite directions, quantifies the risk of congestion and delay in decentralized execution. Our contributions are both game-theoretic and algorithmic. We model the setting as a congestion game with a non-standard cost function, prove the existence of pure Nash equilibria, and analyze the dynamics leading to them. Equilibria can be found in polynomial time under mild conditions, while the general case is PLS-complete. From an optimization perspective, minimizing the total crossing cost is NP-hard, as the problem generalizes Steiner Orientation. To address this hardness barrier, we design a suite of parameterized algorithms for minimizing crossing cost, with parameters including the number of arcs, edges, agents, and structural graph measures. These yield XP or FPT results depending on the parameter, offering algorithmic strategies for structurally restricted instances. Our framework provides a new theoretical foundation for decentralized multi-agent routing, bridging equilibrium analysis and parameterized complexity to support scalable and risk-aware coordination.

cs.MA↗

arXiv2025

Finding a Maximum Common (Induced) Subgraph: Structural Parameters Revisited

We study the parameterized complexity of the problems of finding a maximum common (induced) subgraph of two given graphs. Since these problems generalize several NP-complete problems, they are intractable even when parameterized by strongly restricted structural parameters. Our contribution in this paper is to sharply complement the hardness of the problems by showing fixed-parameter tractable cases: both induced and non-induced problems parameterized by max-leaf number and by neighborhood diversity, and the induced problem parameterized by twin cover number. These results almost completely determine the complexity of the problems with respect to well-studied structural parameters. Also, the result on the twin cover number presents a rather rare example where the induced and non-induced cases have different complexity.

cs.DS↗

arXiv2025

Finding a HIST: Chordality, Structural Parameters, and Diameter

A homeomorphically irreducible spanning tree (HIST) is a spanning tree with no degree-2 vertices, serving as a structurally minimal backbone of a graph. While the existence of HISTs has been widely studied from a structural perspective, the algorithmic complexity of finding them remains less understood. In this paper, we provide a comprehensive investigation of the HIST problem from both structural and algorithmic viewpoints. We present a simple characterization that precisely describes which chordal graphs of diameter at most~3 admit a HIST, leading to a polynomial-time decision procedure for this class. In contrast, we show that the problem is NP-complete for strongly chordal graphs of diameter~4. From the perspective of parameterized complexity, we establish that the HIST problem is W[1]-hard when parameterized by clique-width, indicating that the problem is unlikely to be efficiently solvable in general dense graphs. On the other hand, we present fixed-parameter tractable (FPT) algorithms when parameterized by treewidth, modular-width, or cluster vertex deletion number. Specifically, we develop an $O^*(4^{k})$-time algorithm parameterized by modular-width~$k$, and an FPT algorithm parameterized by the cluster vertex deletion number based on kernelization techniques that bound clique sizes while preserving the existence of a HIST. These results together provide a clearer understanding of the structural and computational boundaries of the HIST problem.

cs.CC↗

arXiv2025

Further Results on Rendering Geometric Intersection Graphs Sparse by Dispersion

Removing overlaps is a central task in domains such as scheduling, visibility, and map labelling. This can be modelled using graphs, where overlap removals correspond to enforcing a certain sparsity constraint on the graph structure. We continue the study of the problem Geometric Graph Edit Distance (GGED), where the aim is to minimise the total cost of editing a geometric intersection graph to obtain a graph contained in a specific graph class. For us, the edit operation is the movement of objects, and the cost is the movement distance. We present an algorithm for rendering the intersection graph of a set of unit circular arcs edgeless and $k$-clique-free in $O(n\log n)$ time, where $n$ is the number of arcs. The algorithm can be also used to solve an open case of the points-spreading problem on cyclic domains [Li \& Wang, CGT 2025]. We also show that GGED remains strongly NP-hard on unweighted interval graphs, solving an open problem of Honorato-Droguett et al. [WADS 2025]. We complement this result by showing that GGED is strongly NP-hard on sets of $d$-balls and $d$-cubes, for any $d\ge 2$. Finally, we present an XP algorithm (parameterised by the number of maximal cliques) that removes all edges from the intersection graph of a set of weighted unit intervals.

cs.CG↗

arXiv2025

Structural Parameters for Steiner Orientation

We consider the \textsc{Steiner Orientation} problem, where we are given as input a mixed graph $G=(V,E,A)$ and a set of $k$ demand pairs $(s_i,t_i)$, $i\in[k]$. The goal is to orient the undirected edges of $G$ in a way that the resulting directed graph has a directed path from $s_i$ to $t_i$ for all $i\in[k]$. We adopt the point of view of structural parameterized complexity and investigate the complexity of \textsc{Steiner Orientation} for standard measures, such as treewidth. Our results indicate that \textsc{Steiner Orientation} is a surprisingly hard problem from this point of view. In particular, our main contributions are the following: (1) We show that \textsc{Steiner Orientation} is NP-complete on instances where the underlying graph has feedback vertex number 2, treewidth 2, pathwidth 3, and vertex integrity 6; (2) We present an XP algorithm parameterized by vertex cover number $\mathrm{vc}$ of complexity $n^{\mathcal{O}(\mathrm{vc}^2)}$. Furthermore, we show that this running time is essentially optimal by proving that a running time of $n^{o(\mathrm{vc}^2)}$ would refute the ETH; (3) We consider parameterizations by the number of undirected or directed edges ($|E|$ or $|A|$) and we observe that the trivial $2^{|E|}n^{\mathcal{O}(1)}$-time algorithm for the former parameter is optimal under the SETH. Complementing this, we show that the problem admits a $2^{\mathcal{O}(|A|)}n^{\mathcal{O}(1)}$-time algorithm. In addition to the above, we consider the complexity of \textsc{Steiner Orientation} parameterized by $\mathrm{tw}+k$ (FPT), distance to clique (FPT), and $\mathrm{vc}+k$ (FPT with a polynomial kernel).

cs.DS↗

arXiv2025

Broadcasting under Structural Restrictions

In the Telephone Broadcast problem we are given a graph $G=(V,E)$ with a designated source vertex $s\in V$. Our goal is to transmit a message, which is initially known only to $s$, to all vertices of the graph by using a process where in each round an informed vertex may transmit the message to one of its uninformed neighbors. The optimization objective is to minimize the number of rounds. Following up on several recent works, we investigate the structurally parameterized complexity of Telephone Broadcast. In particular, we first strengthen existing NP-hardness results by showing that the problem remains NP-complete on graphs of bounded tree-depth and also on cactus graphs which are one vertex deletion away from being path forests. Motivated by this (severe) hardness, we study several other parameterizations of the problem and obtain FPT algorithms parameterized by vertex integrity (generalizing a recent FPT algorithm parameterized by vertex cover by Fomin, Fraigniaud, and Golovach [TCS 2024]) and by distance to clique, as well as FPT approximation algorithms parameterized by clique-cover and cluster vertex deletion. Furthermore, we obtain structural results that relate the length of the optimal broadcast protocol of a graph $G$ with its pathwidth and tree-depth. By presenting a substantial improvement over the best previously known bound for pathwidth (Aminian, Kamali, Seyed-Javadi, and Sumedha [arXiv 2025]) we exponentially improve the approximation ratio achievable in polynomial time on graphs of bounded pathwidth from $\mathcal{O}(4^\mathrm{pw})$ to $\mathcal{O}(\mathrm{pw})$.

cs.DS↗

arXiv2025

On the Complexity of Minimising the Moving Distance for Dispersing Objects

We study Geometric Graph Edit Distance (GGED), a graph-editing model to compute the minimum edit distance of intersection graphs that uses moving objects as an edit operation. We first show an $O(n\log n)$-time algorithm that minimises the total moving distance to disperse unit intervals. This algorithm is applied to render a given unit interval graph (i) edgeless, (ii) acyclic and (iii) $k$-clique-free. We next show that GGED becomes strongly NP-hard when rendering a weighted interval graph (i) edgeless, (ii) acyclic and (iii) $k$-clique-free. Lastly, we prove that minimising the maximum moving distance for rendering a unit disk graph edgeless is strongly NP-hard over the $L_1$ and $L_2$ distances.

cs.DS↗

arXiv2024

On the complexity of finding a spanning even tree in a graph

A tree is said to be even if for every pair of distinct leaves, the length of the unique path between them is even. In this paper we discuss the problem of determining whether an input graph has a spanning even tree. Hofmann and Walsh [Australas. J Comb. 35, 2006] proved that this problem can be solved in polynomial time on bipartite graphs. In contrast to this, we show that this problem is NP-complete even on planar graphs. We also give polynomial-time algorithms for several restricted classes of graphs, such as split graphs, cographs, cobipartite graphs, unit interval graphs, and block graphs.

cs.DS↗

arXiv2024

Basis sequence reconfiguration in the union of matroids

Given a graph $G$ and two spanning trees $T$ and $T'$ in $G$, Spanning Tree Reconfiguration asks whether there is a step-by-step transformation from $T$ to $T'$ such that all intermediates are also spanning trees of $G$, by exchanging an edge in $T$ with an edge outside $T$ at a single step. This problem is naturally related to matroid theory, which shows that there always exists such a transformation for any pair of $T$ and $T'$. Motivated by this example, we study the problem of transforming a sequence of spanning trees into another sequence of spanning trees. We formulate this problem in the language of matroid theory: Given two sequences of bases of matroids, the goal is to decide whether there is a transformation between these sequences. We design a polynomial-time algorithm for this problem, even if the matroids are given as basis oracles. To complement this algorithmic result, we show that the problem of finding a shortest transformation is NP-hard to approximate within a factor of $c \log n$ for some constant $c > 0$, where $n$ is the total size of the ground sets of the input matroids.

math.CO↗

arXiv2024

Parameterized Vertex Integrity Revisited

Vertex integrity is a graph parameter that measures the connectivity of a graph. Informally, its meaning is that a graph has small vertex integrity if it has a small separator whose removal disconnects the graph into connected components which are themselves also small. Graphs with low vertex integrity are extremely structured; this renders many hard problems tractable and has recently attracted interest in this notion from the parameterized complexity community. In this paper we revisit the NP-complete problem of computing the vertex integrity of a given graph from the point of view of structural parameterizations. We present a number of new results, which also answer some recently posed open questions from the literature. Specifically: We show that unweighted vertex integrity is W[1]-hard parameterized by treedepth; we show that the problem remains W[1]-hard if we parameterize by feedback edge set size (via a reduction from a Bin Packing variant which may be of independent interest); and complementing this we show that the problem is FPT by max-leaf number. Furthermore, for weighted vertex integrity, we show that the problem admits a single-exponential FPT algorithm parameterized by vertex cover or by modular width, the latter result improving upon a previous algorithm which required weights to be polynomially bounded.

cs.DS↗

arXiv2024

An improved spectral lower bound of treewidth

We show that for every $n$-vertex graph with at least one edge, its treewidth is greater than or equal to $n λ_{2} / (Δ+ λ_{2}) - 1$, where $Δ$ and $λ_{2}$ are the maximum degree and the second smallest Laplacian eigenvalue of the graph, respectively. This lower bound improves the one by Chandran and Subramanian [Inf. Process. Lett., 2003] and the subsequent one by the authors of the present paper [IEICE Trans. Inf. Syst., 2024]. The new lower bound is almost tight in the sense that there is an infinite family of graphs such that the lower bound is only $1$ less than the treewidth for each graph in the family. Additionally, using similar techniques, we also present a lower bound of treewidth in terms of the largest and the second smallest Laplacian eigenvalues.

math.CO↗

arXiv2024

Core Stability in Additively Separable Hedonic Games of Low Treewidth

Additively Separable Hedonic Game (ASHG) are coalition-formation games where we are given a graph whose vertices represent $n$ selfish agents and the weight of each edge $uv$ denotes how much agent $u$ gains (or loses) when she is placed in the same coalition as agent $v$. We revisit the computational complexity of the well-known notion of core stability of ASHGs, where the goal is to construct a partition of the agents into coalitions such that no group of agents would prefer to diverge from the given partition and form a new (blocking) coalition. Since both finding a core stable partition and verifying that a given partition is core stable are intractable problems ($Σ_2^p$-complete and coNP-complete respectively) we study their complexity from the point of view of structural parameterized complexity, using standard graph-theoretic parameters, such as treewidth.

cs.DS↗

arXiv2023

Algorithms for Optimally Shifting Intervals under Intersection Graph Models

In well-studied graph modification problems, adding and deleting vertices and edges are used as graph editing operations. We propose a model for graph modification on geometric intersection graphs called Geometric Graph Edit Distance that moves objects as an edit operation. Our results are mainly focused on interval graphs. In particular, we give a linear-time algorithm to find the minimum total moving distance to render an interval graph complete. The approach of this algorithm can be applied for: (i) rendering a unit square graph complete over the $L_1$ distance and (ii) attaining the existence of a $k$-clique on unit interval graphs. In addition, we provide LP-formulations to achieve several properties in the associated graph of unit intervals.

cs.DS↗

arXiv2023

On the complexity of list $\mathcal H$-packing for sparse graph classes

The problem of packing as many subgraphs isomorphic to $H \in \mathcal H$ as possible in a graph for a class $\mathcal H$ of graphs is well studied in the literature. Both vertex-disjoint and edge-disjoint versions are known to be NP-complete for $H$ that contains at least three vertices and at least three edges, respectively. In this paper, we consider ``list variants'' of these problems: Given a graph $G$, an integer $k$, and a collection $\mathcal L_{\mathcal H}$ of subgraphs of $G$ isomorphic to some $H \in \mathcal H$, the goal is to compute $k$ subgraphs in $\mathcal L_{\mathcal H}$ that are pairwise vertex- or edge-disjoint. We show several positive and negative results, focusing on classes of sparse graphs, such as bounded-degree graphs, planar graphs, and bounded-treewidth graphs.

cs.DS↗

arXiv2023

Structural Parameterizations of Vertex Integrity

The graph parameter vertex integrity measures how vulnerable a graph is to a removal of a small number of vertices. More precisely, a graph with small vertex integrity admits a small number of vertex removals to make the remaining connected components small. In this paper, we initiate a systematic study of structural parameterizations of the problem of computing the unweighted/weighted vertex integrity. As structural graph parameters, we consider well-known parameters such as clique-width, treewidth, pathwidth, treedepth, modular-width, neighborhood diversity, twin cover number, and cluster vertex deletion number. We show several positive and negative results and present sharp complexity contrasts. We also show that the vertex integrity can be approximated within an $\mathcal{O}(\log \mathsf{opt})$ factor.

cs.DS↗

arXiv2023

Finding a Minimum Spanning Tree with a Small Non-Terminal Set

In this paper, we study the problem of finding a minimum weight spanning tree that contains each vertex in a given subset $V_{\rm NT}$ of vertices as an internal vertex. This problem, called Minimum Weight Non-Terminal Spanning Tree, includes $s$-$t$ Hamiltonian Path as a special case, and hence it is NP-hard. In this paper, we first observe that Non-Terminal Spanning Tree, the unweighted counterpart of Minimum Weight Non-Terminal Spanning Tree, is already NP-hard on some special graph classes. Moreover, it is W[1]-hard when parameterized by clique-width. In contrast, we give a $3k$-vertex kernel and $O^*(2^k)$-time algorithm, where $k$ is the size of non-terminal set $V_{\rm NT}$. The latter algorithm can be extended to Minimum Weight Non-Terminal Spanning Tree with the restriction that each edge has a polynomially bounded integral weight. We also show that Minimum Weight Non-Terminal Spanning Tree is fixed-parameter tractable parameterized by the number of edges in the subgraph induced by the non-terminal set $V_{\rm NT}$, extending the fixed-parameter tractability of Minimum Weight Non-Terminal Spanning Tree to the general case. Finally, we give several results for structural parameterization.

cs.DS↗

arXiv2023

Maximizing Utilitarian and Egalitarian Welfare of Fractional Hedonic Games on Tree-like Graphs

Fractional hedonic games are coalition formation games where a player's utility is determined by the average value they assign to the members of their coalition. These games are a variation of graph hedonic games, which are a class of coalition formation games that can be succinctly represented. Due to their applicability in network clustering and their relationship to graph hedonic games, fractional hedonic games have been extensively studied from various perspectives. However, finding welfare-maximizing partitions in fractional hedonic games is a challenging task due to the nonlinearity of utilities. In fact, it has been proven to be NP-hard and can be solved in polynomial time only for a limited number of graph classes, such as trees. This paper presents (pseudo)polynomial-time algorithms to compute welfare-maximizing partitions in fractional hedonic games on tree-like graphs. We consider two types of social welfare measures: utilitarian and egalitarian. Tree-like graphs refer to graphs with bounded treewidth and block graphs. A hardness result is provided, demonstrating that the pseudopolynomial-time solvability is the best possible under the assumption P$\neq$NP.

cs.GT↗