arXiv subjects

Akira Suzuki

Publications and source records attributed to Akira Suzuki.

At least 19 recordsLinked to original sources

arXiv2026

Finding Shortest Reconfiguration Sequences on Independent Set Polytopes

We initiate the study of the shortest reconfiguration problem for independent sets under the adjacency relation derived from the independent set polytope. Given a graph and two independent sets, the problem asks for a shortest sequence transforming one into the other such that the subgraph induced by the symmetric difference of any two consecutive sets is connected. This is equivalent to finding a shortest path on the $1$-skeleton of the independent set polytope. We prove that the problem is NP-hard even on planar graphs of bounded degree, as well as on split graphs. Notably, the hardness for planar graphs of bounded degree still holds even when deciding whether the target can be reached in at most two steps. For split graphs, we further show the W[2]-hardness when parameterized by the number of steps, as well as the inapproximability of the optimal length. As a consequence, we prove that the length of a shortest path between two vertices of a 0/1 polytope in $\mathbb{R}^n$ described by $O(n)$ linear inequalities is hard to approximate within a factor of $(1-\varepsilon)\ln n$ for any constant $ε>0$, unless $P=NP$. On the positive side, we provide polynomial-time algorithms for block graphs, cographs, and bipartite chain graphs. Moreover, for paths and cycles, we show that the optimal length of the shortest reconfiguration sequence exactly matches a trivial upper bound.

cs.DS↗

arXiv2026

Computational Complexity of Swish

Swish is a card game in which players are given cards having symbols (hoops and balls), and find a valid superposition of cards, called a "swish." Dailly, Lafourcade, and Marcadet (FUN 2024) studied a generalized version of Swish and showed that the problem is solvable in polynomial time with one symbol per card, while it is NP-complete with three or more symbols per card. In this paper, we resolve the previously open case of two symbols per card, which corresponds to the original game. We show that Swish is NP-complete for this case. Specifically, we prove the NP-hardness when the allowed transformations of cards are restricted to a single (horizontal or vertical) flip or 180-degree rotation, and extend the results to the original setting allowing all three transformations. In contrast, when neither transformation is allowed, we present a polynomial-time algorithm. Combining known and our results, we establish a complete characterization of the computational complexity of Swish with respect to both the number of symbols per card and the allowed transformations.

cs.DS↗

arXiv2025

Spanning Trees with a Small Vertex Cover: the Complexity on Specific Graph Classes

In the context of algorithm theory, various studies have been conducted on spanning trees with desirable properties. In this paper, we consider the \textsc{Minimum Cover Spanning Tree} problem (MCST for short). Given a graph $G$ and a positive integer $k$, the problem determines whether $G$ has a spanning tree with a vertex cover of size at most $k$. We reveal the equivalence between \mcst\ and the \textsc{Dominating Set} problem when $G$ is of diameter at most~$2$ or $P_5$-free. This provides the intractability for these graphs and the tractability for several subclasses of $P_5$-free graphs. We also show that \mcst\ is NP-complete for bipartite planar graphs of maximum degree~$4$ and unit disk graphs. These hardness results resolve open questions posed in prior research. Finally, we present an FPT algorithm for {\mcst} parameterized by clique-width and a linear-time algorithm for interval graphs.

cs.DS↗

arXiv2025

Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules

In reconfiguration problems, we are given two feasible solutions to a graph problem and asked whether one can be transformed into the other via a sequence of feasible intermediate solutions under a given reconfiguration rule. While earlier work focused on modifying a single element at a time, recent studies have started examining how different rules impact computational complexity. Motivated by recent progress, we study Independent Set Reconfiguration (ISR) and Vertex Cover Reconfiguration (VCR) under the $k$-Token Jumping ($k$-TJ) and $k$-Token Sliding ($k$-TS) models. In $k$-TJ, up to $k$ vertices may be replaced, while $k$-TS additionally requires a perfect matching between removed and added vertices. It is known that the complexity of ISR crucially depends on $k$, ranging from PSPACE-complete and NP-complete to polynomial-time solvable. In this paper, we further explore the gradient of computational complexity of the problems. We first show that ISR under $k$-TJ with $k = |I| - μ$ remains NP-hard when $μ$ is any fixed positive integer and the input graph is restricted to graphs of maximum degree 3 or planar graphs of maximum degree 4, where $|I|$ is the size of feasible solutions. In addition, we prove that the problem belongs to NP not only for $μ=O(1)$ but also for $μ= O(\log |I|)$. In contrast, we show that VCR under $k$-TJ is in XP when parameterized by $μ= |S| - k$, where $|S|$ is the size of feasible solutions. Furthermore, we establish the PSPACE-completeness of ISR and VCR under both $k$-TJ and $k$-TS on several graph classes, for fixed $k$ as well as superconstant $k$ relative to the size of feasible solutions.

cs.CC↗

arXiv2025

Homotopy types of Hom complexes of graph homomorphisms whose codomains are cycles

For simple graphs $G$ and $H$, the Hom complex $\mathrm{Hom}(G,H)$ is a polyhedral complex whose vertices are the graph homomorphisms $G\to H$ and whose edges connect the pairs of homomorphisms which differ in a single vertex of $G$. Hom complexes play an important role in an algebro-topological approach to the graph coloring problem. It is known that $\mathrm{Hom}(G,H)$ is homotopy equivalent to a disjoint union of points and circles when both $G$ and $H$ are cycles. We generalize this known result by showing that the same holds whenever $G$ is connected and $H$ is a cycle. To this end, we explicitly construct the universal cover of each connected component of $\mathrm{Hom}(G,H)$ and prove that it is contractible. Additionally, we provide a simple criterion to determine whether the connected component containing a given homomorphism is homotopy equivalent to a point or circle.

math.CO↗

arXiv2025

Changing Induced Subgraph Isomorphisms Under Extended Reconfiguration Rules

In a reconfiguration problem, we are given two feasible solutions of a combinatorial problem and our goal is to determine whether it is possible to reconfigure one into the other, with the steps dictated by specific reconfiguration rules. Traditionally, most studies on reconfiguration problems have focused on rules that allow changing a single element at a time. In contrast, this paper considers scenarios in which $k \ge 2$ elements can be changed simultaneously. We investigate the general reconfiguration problem of isomorphisms. For the Induced Subgraph Isomorphism Reconfiguration problem, we show that the problem remains $\textsf{PSPACE}$-complete even under stringent constraints on the pattern graph when $k$ is constant. We then give two meta-theorems applicable when $k$ is slightly less than the number of vertices in the pattern graph. In addition, we investigate the complexity of the Independent Set Reconfiguration problem, which is a special case of the Induced Subgraph Isomorphism Reconfiguration problem.

cs.DS↗

arXiv2024

Not Just Streaks: Towards Ground Truth for Single Image Deraining

We propose a large-scale dataset of real-world rainy and clean image pairs and a method to remove degradations, induced by rain streaks and rain accumulation, from the image. As there exists no real-world dataset for deraining, current state-of-the-art methods rely on synthetic data and thus are limited by the sim2real domain gap; moreover, rigorous evaluation remains a challenge due to the absence of a real paired dataset. We fill this gap by collecting a real paired deraining dataset through meticulous control of non-rain variations. Our dataset enables paired training and quantitative evaluation for diverse real-world rain phenomena (e.g. rain streaks and rain accumulation). To learn a representation robust to rain phenomena, we propose a deep neural network that reconstructs the underlying scene by minimizing a rain-robust loss between rainy and clean images. Extensive experiments demonstrate that our model outperforms the state-of-the-art deraining methods on real rainy images under various conditions. Project website: https://visual.ee.ucla.edu/gt_rain.htm/.

cs.CV↗

arXiv2024

Finding Induced Subgraphs from Graphs with Small Mim-Width

In the last decade, algorithmic frameworks based on a structural graph parameter called mim-width have been developed to solve generally NP-hard problems. However, it is known that the frameworks cannot be applied to the Clique problem, and the complexity status of many problems of finding dense induced subgraphs remains open when parameterized by mim-width. In this paper, we investigate the complexity of the problem of finding a maximum induced subgraph that satisfies prescribed properties from a given graph with small mim-width. We first give a meta-theorem implying that various induced subgraph problems are NP-hard for bounded mim-width graphs. Moreover, we show that some problems, including Clique and Induced Cluster Subgraph, remain NP-hard even for graphs with (linear) mim-width at most 2. In contrast to the intractability, we provide an algorithm that, given a graph and its branch decomposition with mim-width at most 1, solves Induced Cluster Subgraph in polynomial time. We emphasize that our algorithmic technique is applicable to other problems such as Induced Polar Subgraph and Induced Split Subgraph. Since a branch decomposition with mim-width at most 1 can be constructed in polynomial time for block graphs, interval graphs, permutation graphs, cographs, distance-hereditary graphs, convex graphs, and their complement graphs, our positive results reveal the polynomial-time solvability of various problems for these graph classes.

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

Reconfiguration of Time-Respecting Arborescences

An arborescence, which is a directed analogue of a spanning tree in an undirected graph, is one of the most fundamental combinatorial objects in a digraph. In this paper, we study arborescences in digraphs from the viewpoint of combinatorial reconfiguration, which is the field where we study reachability between two configurations of some combinatorial objects via some specified operations. Especially, we consider reconfiguration problems for time-respecting arborescences, which were introduced by Kempe, Kleinberg, and Kumar. We first prove that if the roots of the initial and target time-respecting arborescences are the same, then the target arborescence is always reachable from the initial one and we can find a shortest reconfiguration sequence in polynomial time. Furthermore, we show if the roots are not the same, then the target arborescence may not be reachable from the initial one. On the other hand, we show that we can determine whether the target arborescence is reachable form the initial one in polynomial time. Finally, we prove that it is NP-hard to find a shortest reconfiguration sequence in the case where the roots are not the same. Our results show an interesting contrast to the previous results for (ordinary) arborescences reconfiguration problems.

cs.DS↗

arXiv2022

ZDD-Based Algorithmic Framework for Solving Shortest Reconfiguration Problems

This paper proposes an algorithmic framework for various reconfiguration problems using zero-suppressed binary decision diagrams (ZDDs), a data structure for families of sets. In general, a reconfiguration problem checks if there is a step-by-step transformation between two given feasible solutions (e.g., independent sets of an input graph) of a fixed search problem such that all intermediate results are also feasible and each step obeys a fixed reconfiguration rule (e.g., adding/removing a single vertex to/from an independent set). The solution space formed by all feasible solutions can be exponential in the input size, and indeed many reconfiguration problems are known to be PSPACE-complete. This paper shows that an algorithm in the proposed framework efficiently conducts the breadth-first search by compressing the solution space using ZDDs, and finds a shortest transformation between two given feasible solutions if exists. Moreover, the proposed framework provides rich information on the solution space, such as the connectivity of the solution space and all feasible solutions reachable from a specified one. We demonstrate that the proposed framework can be applied to various reconfiguration problems, and experimentally evaluate their performances.

cs.DS↗

arXiv2022

Reconfiguring k-path vertex covers

A vertex subset $I$ of a graph $G$ is called a $k$-path vertex cover if every path on $k$ vertices in $G$ contains at least one vertex from $I$. The \textsc{$k$-Path Vertex Cover Reconfiguration ($k$-PVCR)} problem asks if one can transform one $k$-path vertex cover into another via a sequence of $k$-path vertex covers where each intermediate member is obtained from its predecessor by applying a given reconfiguration rule exactly once. We investigate the computational complexity of \textsc{$k$-PVCR} from the viewpoint of graph classes under the well-known reconfiguration rules: $\mathsf{TS}$, $\mathsf{TJ}$, and $\mathsf{TAR}$. The problem for $k=2$, known as the \textsc{Vertex Cover Reconfiguration (VCR)} problem, has been well-studied in the literature. We show that certain known hardness results for \textsc{VCR} on different graph classes including planar graphs, bounded bandwidth graphs, chordal graphs, and bipartite graphs, can be extended for \textsc{$k$-PVCR}. In particular, we prove a complexity dichotomy for \textsc{$k$-PVCR} on general graphs: on those whose maximum degree is $3$ (and even planar), the problem is $\mathtt{PSPACE}$-complete, while on those whose maximum degree is $2$ (i.e., paths and cycles), the problem can be solved in polynomial time. Additionally, we also design polynomial-time algorithms for \textsc{$k$-PVCR} on trees under each of $\mathsf{TJ}$ and $\mathsf{TAR}$. Moreover, on paths, cycles, and trees, we describe how one can construct a reconfiguration sequence between two given $k$-path vertex covers in a yes-instance. In particular, on paths, our constructed reconfiguration sequence is shortest.

cs.DS↗

arXiv2022

Sorting Balls and Water: Equivalence and Computational Complexity

Various forms of sorting problems have been studied over the years. Recently, two kinds of sorting puzzle apps are popularized. In these puzzles, we are given a set of bins filled with colored units, balls or water, and some empty bins. These puzzles allow us to move colored units from a bin to another when the colors involved match in some way or the target bin is empty. The goal of these puzzles is to sort all the color units in order. We investigate computational complexities of these puzzles. We first show that these two puzzles are essentially the same from the viewpoint of solvability. That is, an instance is sortable by ball-moves if and only if it is sortable by water-moves. We also show that every yes-instance has a solution of polynomial length, which implies that these puzzles belong to in NP. We then show that these puzzles are NP-complete. For some special cases, we give polynomial-time algorithms. We finally consider the number of empty bins sufficient for making all instances solvable and give non-trivial upper and lower bounds in terms of the number of filled bins and the capacity of bins.

cs.CC↗

arXiv2022

Reconfiguration of Spanning Trees with Degree Constraint or Diameter Constraint

We investigate the complexity of finding a transformation from a given spanning tree in a graph to another given spanning tree in the same graph via a sequence of edge flips. The exchange property of the matroid bases immediately yields that such a transformation always exists if we have no constraints on spanning trees. In this paper, we wish to find a transformation which passes through only spanning trees satisfying some constraint. Our focus is bounding either the maximum degree or the diameter of spanning trees, and we give the following results. The problem with a lower bound on maximum degree is solvable in polynomial time, while the problem with an upper bound on maximum degree is PSPACE-complete. The problem with a lower bound on diameter is NP-hard, while the problem with an upper bound on diameter is solvable in polynomial time.

cs.DS↗

arXiv2021

SuperMat: Construction of a linked annotated dataset from superconductors-related publications

A growing number of papers are published in the area of superconducting materials science. However, novel text and data mining (TDM) processes are still needed to efficiently access and exploit this accumulated knowledge, paving the way towards data-driven materials design. Herein, we present SuperMat (Superconductor Materials), an annotated corpus of linked data derived from scientific publications on superconductors, which comprises 142 articles, 16052 entities, and 1398 links that are characterised into six categories: the names, classes, and properties of materials; links to their respective superconducting critical temperature (Tc); and parametric conditions such as applied pressure or measurement methods. The construction of SuperMat resulted from a fruitful collaboration between computer scientists and material scientists, and its high quality is ensured through validation by domain experts. The quality of the annotation guidelines was ensured by satisfactory Inter Annotator Agreement (IAA) between the annotators and the domain experts. SuperMat includes the dataset, annotation guidelines, and annotation support tools that use automatic suggestions to help minimise human errors.

cond-mat.supr-con↗

arXiv2020

Fixed-Parameter Algorithms for Graph Constraint Logic

Non-deterministic constraint logic (NCL) is a simple model of computation based on orientations of a constraint graph with edge weights and vertex demands. NCL captures \PSPACE\xspace and has been a useful tool for proving algorithmic hardness of many puzzles, games, and reconfiguration problems. In particular, its usefulness stems from the fact that it remains \PSPACE-complete even under severe restrictions of the weights (e.g., only edge-weights one and two are needed) and the structure of the constraint graph (e.g., planar \textsc{and/or}\xspace graphs of bounded bandwidth). While such restrictions on the structure of constraint graphs do not seem to limit the expressiveness of NCL, the building blocks of the constraint graphs cannot be limited without losing expressiveness: We consider as parameters the number of weight-one edges and the number of weight-two edges of a constraint graph, as well as the number of \textsc{and}\xspace or \textsc{or}\xspace vertices of an \textsc{and/or}\xspace constraint graph. We show that NCL is fixed-parameter tractable (FPT) for any of these parameters. In particular, for NCL parameterized by the number of weight-one edges or the number of \textsc{and}\xspace vertices, we obtain a linear kernel. It follows that, in a sense, NCL as introduced by Hearn and Demaine is defined in the most economical way for the purpose of capturing \PSPACE.

cs.DS↗

arXiv2020

Reconfiguration of Spanning Trees with Many or Few Leaves

Let $G$ be a graph and $T_1,T_2$ be two spanning trees of $G$. We say that $T_1$ can be transformed into $T_2$ via an edge flip if there exist two edges $e \in T_1$ and $f$ in $T_2$ such that $T_2= (T_1 \setminus e) \cup f$. Since spanning trees form a matroid, one can indeed transform a spanning tree into any other via a sequence of edge flips, as observed by Ito et al. We investigate the problem of determining, given two spanning trees $T_1,T_2$ with an additional property $Π$, if there exists an edge flip transformation from $T_1$ to $T_2$ keeping property $Π$ all along. First we show that determining if there exists a transformation from $T_1$ to $T_2$ such that all the trees of the sequence have at most $k$ (for any fixed $k \ge 3$) leaves is PSPACE-complete. We then prove that determining if there exists a transformation from $T_1$ to $T_2$ such that all the trees of the sequence have at least $k$ leaves (where $k$ is part of the input) is PSPACE-complete even restricted to split, bipartite or planar graphs. We complete this result by showing that the problem becomes polynomial for cographs, interval graphs and when $k=n-2$.

cs.DS↗

arXiv2020

Decremental Optimization of Dominating Sets Under the Reconfiguration Framework

Given a dominating set, how much smaller a dominating set can we find through elementary operations? Here, we proceed by iterative vertex addition and removal while maintaining the property that the set forms a dominating set of bounded size. This can be seen as the optimization variant of the dominating set reconfiguration problem, where two dominating sets are given and the question is merely whether they can be reached one from another through elementary operations. We show that this problem is PSPACE-complete, even if the input graph is a bipartite graph, a split graph, or has bounded pathwidth. On the positive side, we give linear-time algorithms for cographs, trees and interval graphs. We also study the parameterized complexity of this problem. More precisely, we show that the problem is W[2]-hard when parameterized by the upper bound on the size of an intermediary dominating set. On the other hand, we give fixed-parameter algorithms with respect to the minimum size of a vertex cover, or $d+s$ where $d$ is the degeneracy and $s$ is the upper bound of output solution.

cs.DM↗