Pub Date : 2026-05-01Epub Date: 2025-12-02DOI: 10.1016/j.jcss.2025.103738
Nicolas Bousquet , Clément Dallard , Maël Dumas , Claire Hilaire , Martin Milanič , Anthony Perez , Nicolas Trotignon
A graph H is an induced minor of G if there exists an induced minor model of H in G, that is, a collection of pairwise disjoint subsets of vertices of G labeled by the vertices of H, each inducing a connected subgraph in G, such that two vertices of H are adjacent if and only if there is an edge in G between the corresponding subsets. In this paper, we investigate structural properties of induced minor models, including bounds on treewidth and chromatic number of the subgraphs induced by minimal induced minor models. As algorithmic applications of our structural results, we make use of recent developments regarding tree-independence number to show that if H is the 4-wheel, the 5-vertex complete graph minus an edge, or a complete bipartite graph , then there is a polynomial-time algorithm to find in a given graph G an induced minor model of H in G, if there is one. We also develop an alternative polynomial-time algorithm for recognizing graphs that do not contain as an induced minor, which revolves around the idea of detecting the induced subgraphs whose presence is forced when the input graph contains as an induced minor. It turns out that all these induced subgraphs are Truemper configurations.
{"title":"Induced minor models. I. Structural properties and algorithmic consequences","authors":"Nicolas Bousquet , Clément Dallard , Maël Dumas , Claire Hilaire , Martin Milanič , Anthony Perez , Nicolas Trotignon","doi":"10.1016/j.jcss.2025.103738","DOIUrl":"10.1016/j.jcss.2025.103738","url":null,"abstract":"<div><div>A graph <em>H</em> is an induced minor of <em>G</em> if there exists an <em>induced minor model</em> of <em>H</em> in <em>G</em>, that is, a collection of pairwise disjoint subsets of vertices of <em>G</em> labeled by the vertices of <em>H</em>, each inducing a connected subgraph in <em>G</em>, such that two vertices of <em>H</em> are adjacent if and only if there is an edge in <em>G</em> between the corresponding subsets. In this paper, we investigate structural properties of induced minor models, including bounds on treewidth and chromatic number of the subgraphs induced by minimal induced minor models. As algorithmic applications of our structural results, we make use of recent developments regarding tree-independence number to show that if <em>H</em> is the 4-wheel, the 5-vertex complete graph minus an edge, or a complete bipartite graph <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn><mo>,</mo><mi>q</mi></mrow></msub></math></span>, then there is a polynomial-time algorithm to find in a given graph <em>G</em> an induced minor model of <em>H</em> in <em>G</em>, if there is one. We also develop an alternative polynomial-time algorithm for recognizing graphs that do not contain <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></math></span> as an induced minor, which revolves around the idea of detecting the induced subgraphs whose presence is forced when the input graph contains <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></math></span> as an induced minor. It turns out that all these induced subgraphs are Truemper configurations.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103738"},"PeriodicalIF":0.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145736653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2026-01-02DOI: 10.1016/j.jcss.2025.103753
Argyrios Deligkas , Eduard Eiben , Robert Ganian , Iyad Kanj , Dominik Leko , M.S. Ramanujan
In Graph Coordinated Motion Planning, we are given a graph G some of whose vertices are occupied by robots, and we are asked to route k marked robots to their destinations while avoiding collisions and without exceeding a given budget ℓ on the number of robot moves. We continue the recent investigation of the problem [ICALP 2024], focusing on the parameter k that captures the task of routing a small number of robots in a possibly crowded graph. We prove that the problem is W[1]-hard parameterized by ℓ even for , but fixed-parameter tractable parameterized by k plus the treedepth of G. We complement the latter algorithm with an NP-hardness reduction which shows that both parameters are necessary to achieve tractability.
{"title":"Routing few robots in a crowded network","authors":"Argyrios Deligkas , Eduard Eiben , Robert Ganian , Iyad Kanj , Dominik Leko , M.S. Ramanujan","doi":"10.1016/j.jcss.2025.103753","DOIUrl":"10.1016/j.jcss.2025.103753","url":null,"abstract":"<div><div>In <span>Graph Coordinated Motion Planning</span>, we are given a graph <em>G</em> some of whose vertices are occupied by robots, and we are asked to route <em>k</em> marked robots to their destinations while avoiding collisions and without exceeding a given budget <em>ℓ</em> on the number of robot moves. We continue the recent investigation of the problem [ICALP 2024], focusing on the parameter <em>k</em> that captures the task of routing a small number of robots in a possibly crowded graph. We prove that the problem is <span>W</span>[1]-hard parameterized by <em>ℓ</em> even for <span><math><mi>k</mi><mo>=</mo><mn>1</mn></math></span>, but fixed-parameter tractable parameterized by <em>k</em> plus the treedepth of <em>G</em>. We complement the latter algorithm with an <span>NP</span>-hardness reduction which shows that both parameters are necessary to achieve tractability.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103753"},"PeriodicalIF":0.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145924261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2026-01-08DOI: 10.1016/j.jcss.2026.103756
Qisheng Wang , Zhean Xu , Zhicheng Zhang
Given an array , the Range Minimum Query (RMQ) problem is to maintain a data structure that supports RMQ queries: given a range , find the index of the minimum element among , i.e., . In this paper, we propose a quantum data structure that supports RMQ queries and range updates, with an optimal time complexity for performing operations without preprocessing, compared to the classical .1 As an application, we obtain a time-efficient quantum algorithm for k-minimum finding without the use of quantum random access memory.
{"title":"Quantum data structure for range minimum query","authors":"Qisheng Wang , Zhean Xu , Zhicheng Zhang","doi":"10.1016/j.jcss.2026.103756","DOIUrl":"10.1016/j.jcss.2026.103756","url":null,"abstract":"<div><div>Given an array <span><math><mi>a</mi><mrow><mo>[</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>n</mi><mo>]</mo></mrow></math></span>, the Range Minimum Query (RMQ) problem is to maintain a data structure that supports RMQ queries: given a range <span><math><mo>[</mo><mi>l</mi><mo>,</mo><mi>r</mi><mo>]</mo></math></span>, find the index of the minimum element among <span><math><mi>a</mi><mrow><mo>[</mo><mi>l</mi><mo>.</mo><mo>.</mo><mi>r</mi><mo>]</mo></mrow></math></span>, i.e., <span><math><msub><mrow><mi>arg min</mi></mrow><mrow><mi>i</mi><mo>∈</mo><mo>[</mo><mi>l</mi><mo>,</mo><mi>r</mi><mo>]</mo></mrow></msub><mspace></mspace><mi>a</mi><mo>[</mo><mi>i</mi><mo>]</mo></math></span>. In this paper, we propose a quantum data structure that supports RMQ queries and range updates, with an <em>optimal</em> time complexity <span><math><mover><mrow><mi>Θ</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><msqrt><mrow><mi>n</mi><mi>q</mi></mrow></msqrt><mo>)</mo></math></span> for performing <span><math><mi>q</mi><mo>=</mo><mi>O</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> operations <em>without</em> preprocessing, compared to the classical <span><math><mover><mrow><mi>Θ</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><mi>n</mi><mo>+</mo><mi>q</mi><mo>)</mo></math></span>.<span><span><sup>1</sup></span></span> As an application, we obtain a time-efficient quantum algorithm for <em>k</em>-minimum finding <em>without</em> the use of <em>quantum random access memory</em>.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103756"},"PeriodicalIF":0.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146037161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2025-12-17DOI: 10.1016/j.jcss.2025.103751
João Marcos Brito , Thiago Marcilon , Nicolas A. Martins , Rudini Sampaio
In 2010, Brešar, Klavžar and Rall introduced the optimization variant of the graph domination game and the game domination number. This variant has been extensively investigated in the literature, with several papers published on this topic. Interestingly, the most common variant of combinatorial games, the normal variant, in which the last to play wins, had never been investigated for the graph domination game. In this paper, we start the study of the normal play of the domination game, which we call Normal Domination Game. We first prove that this game is PSPACE-complete even in graphs with diameter two. We also use the Sprague-Grundy theory to prove that Alice (the first player) wins in the path if and only if n is not a multiple of 4, and wins in the cycle if and only if for some integer k. Moreover, we obtain a polynomial time algorithm to decide the winner for any disjoint union of paths and cycles in the Normal Domination Game and its natural partizan variant. Finally, we also prove that the Misère Domination Game (the last to play loses) is PSPACE-complete, as are the natural partizan variants of the normal game and the misère game.
{"title":"The Normal Domination Game in graphs","authors":"João Marcos Brito , Thiago Marcilon , Nicolas A. Martins , Rudini Sampaio","doi":"10.1016/j.jcss.2025.103751","DOIUrl":"10.1016/j.jcss.2025.103751","url":null,"abstract":"<div><div>In 2010, Brešar, Klavžar and Rall introduced the optimization variant of the graph domination game and the game domination number. This variant has been extensively investigated in the literature, with several papers published on this topic. Interestingly, the most common variant of combinatorial games, the normal variant, in which the last to play wins, had never been investigated for the graph domination game. In this paper, we start the study of the normal play of the domination game, which we call <span>Normal Domination Game</span>. We first prove that this game is PSPACE-complete even in graphs with diameter two. We also use the Sprague-Grundy theory to prove that Alice (the first player) wins in the path <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> if and only if <em>n</em> is not a multiple of 4, and wins in the cycle <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> if and only if <span><math><mi>n</mi><mo>=</mo><mn>4</mn><mi>k</mi><mo>+</mo><mn>3</mn></math></span> for some integer <em>k</em>. Moreover, we obtain a polynomial time algorithm to decide the winner for any disjoint union of paths and cycles in the <span>Normal Domination Game</span> and its natural partizan variant. Finally, we also prove that the <span>Misère Domination Game</span> (the last to play loses) is PSPACE-complete, as are the natural partizan variants of the normal game and the misère game.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103751"},"PeriodicalIF":0.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145839598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2025-12-09DOI: 10.1016/j.jcss.2025.103748
Tesshu Hanaka , Noleen Köhler , Michael Lampis
Additively Separable Hedonic Games (ASHGs) are coalition-formation games where we are given a directed graph whose vertices represent n selfish agents and the weight of each arc uv denotes the preferences of u for v. We revisit the computational complexity of the well-known notion of core stability of symmetric 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 coalition. For Core Stability Verification (CSV), we first show the following hardness results: CSV remains coNP-complete on graphs of vertex cover 2; CSV is coW[1]-hard parameterized by vertex integrity when edge weights are encoded in unary; and CSV is coW[1]-hard parameterized by tree-depth even if all weights are from . We complement these results with essentially matching algorithms and an FPT algorithm parameterized by the treewidth tw plus the maximum degree Δ (improving a previous algorithm's dependence from to ). We then move on to study Core Stability (CS), which one would naturally expect to be even harder than CSV. We confirm this intuition by showing that CS is -complete even on graphs of bounded vertex cover number. On the positive side, we present a -time algorithm parameterized by , which is essentially optimal assuming the Exponential Time Hypothesis (ETH). Finally, we consider the notion of k-core stability: k denotes the maximum size of the allowed blocking (diverging) coalitions. We show that k-CSV is coW[1]-hard parameterized by k (even on unweighted graphs), while k-CS is NP-complete for all (even on graphs of bounded degree with bounded edge weights).
加法分离变量享乐游戏(ASHGs)结盟是游戏,我们给出了一个有向图的顶点代表n自私的代理和每个电弧紫外的重量表示偏好的u v .我们重温著名的计算复杂度的概念核心稳定对称ASHGs,目标是构造一个分区的代理商等联盟,没有群宁愿偏离给定的分区和组建一个新的联合政府。对于核心稳定性验证（CSV），我们首先证明了以下硬度结果：CSV在顶点覆盖2的图上保持conp完全；当边权为一元编码时，CSV是顶点完整性的coW[1]-hard参数化；即使所有权值都来自{−1,1}，CSV仍然是由树深度参数化的coW[1]-hard。我们用基本匹配的算法和由树宽tw加上最大程度Δ参数化的FPT算法来补充这些结果（将先前算法的依赖性从2O（twΔ2）提高到2O（twΔ））。然后我们继续学习核心稳定性（CS），人们自然会认为它比CSV更难。我们通过证明CS即使在有界顶点覆盖数的图上也是Σ2p-complete来证实这个直觉。在积极的方面，我们提出了一个由tw+Δ参数化的22O（Δtw）nO(1)时间算法，该算法本质上是最优的，假设指数时间假设（ETH）。最后，我们考虑了k核稳定性的概念：k表示允许的阻塞（发散）联盟的最大大小。我们证明k- csv是由k（即使在无权图上）硬参数化的，而k- cs对于所有k≥3（即使在边权有界的有界度图上）是np完全的。
{"title":"Core stability in additively separable hedonic games of low treewidth","authors":"Tesshu Hanaka , Noleen Köhler , Michael Lampis","doi":"10.1016/j.jcss.2025.103748","DOIUrl":"10.1016/j.jcss.2025.103748","url":null,"abstract":"<div><div>Additively Separable Hedonic Games (ASHGs) are coalition-formation games where we are given a directed graph whose vertices represent <em>n</em> selfish agents and the weight of each arc <em>uv</em> denotes the preferences of <em>u</em> for <em>v</em>. We revisit the computational complexity of the well-known notion of core stability of symmetric 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 coalition. For <span>Core Stability Verification</span> (CSV), we first show the following hardness results: <span>CSV</span> remains coNP-complete on graphs of vertex cover 2; <span>CSV</span> is coW[1]-hard parameterized by vertex integrity when edge weights are encoded in unary; and <span>CSV</span> is coW[1]-hard parameterized by tree-depth even if all weights are from <span><math><mo>{</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></span>. We complement these results with essentially matching algorithms and an FPT algorithm parameterized by the treewidth <span>tw</span> plus the maximum degree Δ (improving a previous algorithm's dependence from <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>O</mi><mo>(</mo><mrow><mi>tw</mi></mrow><msup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></msup></math></span> to <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>O</mi><mo>(</mo><mrow><mi>tw</mi></mrow><mi>Δ</mi><mo>)</mo></mrow></msup></math></span>). We then move on to study <span>Core Stability</span> (CS), which one would naturally expect to be even harder than <span>CSV</span>. We confirm this intuition by showing that <span>CS</span> is <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>p</mi></mrow></msubsup></math></span>-complete even on graphs of bounded vertex cover number. On the positive side, we present a <span><math><msup><mrow><mn>2</mn></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>O</mi><mo>(</mo><mi>Δ</mi><mrow><mi>tw</mi></mrow><mo>)</mo></mrow></msup></mrow></msup><msup><mrow><mi>n</mi></mrow><mrow><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span>-time algorithm parameterized by <span><math><mrow><mi>tw</mi></mrow><mo>+</mo><mi>Δ</mi></math></span>, which is essentially optimal assuming the Exponential Time Hypothesis (ETH). Finally, we consider the notion of <em>k</em>-core stability: <em>k</em> denotes the maximum size of the allowed blocking (diverging) coalitions. We show that <em>k</em><span>-CSV</span> is coW[1]-hard parameterized by <em>k</em> (even on unweighted graphs), while <em>k</em><span>-CS</span> is NP-complete for all <span><math><mi>k</mi><mo>≥</mo><mn>3</mn></math></span> (even on graphs of bounded degree with bounded edge weights).</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103748"},"PeriodicalIF":0.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145789682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2025-12-16DOI: 10.1016/j.jcss.2025.103752
Davi de Andrade , Júlio Araújo , Laure Morelle , Ignasi Sau , Ana Silva
A good edge-labeling (gel for short) of a graph G is a function such that, for any ordered pair of vertices of G, there do not exist two distinct increasing paths from x to y, where “increasing” means that the sequence of labels is non-decreasing. This notion was introduced by Bermond et al. (2013) [3] motivated by practical applications arising from routing and wavelength assignment problems in optical networks. Prompted by the lack of algorithmic results about the problem of deciding whether an input graph admits a gel, called GEL, we initiate its study from the viewpoint of parameterized complexity. We first introduce the natural version of GEL where one wants to use at most c distinct labels, which we call c-GEL, and we prove that it is NP-complete for every on very restricted instances. We then provide several positive results, starting with simple polynomial kernels for GEL and c-GEL parameterized by neighborhood diversity or vertex cover. As one of our main technical contributions, we present an FPT algorithm for GEL parameterized by the size of a modulator to a forest of stars, based on a novel approach via a 2-SAT formulation which we believe to be of independent interest. We also present FPT algorithms based on dynamic programming for c-GEL parameterized by treewidth and c, and for GEL parameterized by treewidth and the maximum degree. Finally, we answer positively a question of Bermond et al. (2013) [3] by proving the NP-completeness of a problem strongly related to GEL, namely that of deciding whether an input graph admits a so-called UPP-orientation.
{"title":"On the parameterized complexity of computing good edge-labelings","authors":"Davi de Andrade , Júlio Araújo , Laure Morelle , Ignasi Sau , Ana Silva","doi":"10.1016/j.jcss.2025.103752","DOIUrl":"10.1016/j.jcss.2025.103752","url":null,"abstract":"<div><div>A <em>good edge-labeling</em> (<span>gel</span> for short) of a graph <em>G</em> is a function <span><math><mi>λ</mi><mo>:</mo><mi>E</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>→</mo><mi>R</mi></math></span> such that, for any ordered pair of vertices <span><math><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> of <em>G</em>, there do not exist two distinct increasing paths from <em>x</em> to <em>y</em>, where “increasing” means that the sequence of labels is non-decreasing. This notion was introduced by Bermond et al. (2013) <span><span>[3]</span></span> motivated by practical applications arising from routing and wavelength assignment problems in optical networks. Prompted by the lack of algorithmic results about the problem of deciding whether an input graph admits a <span>gel</span>, called <span>GEL</span>, we initiate its study from the viewpoint of parameterized complexity. We first introduce the natural version of <span>GEL</span> where one wants to use at most <em>c</em> distinct labels, which we call <em>c</em>-GEL, and we prove that it is <span>NP</span>-complete for every <span><math><mi>c</mi><mo>≥</mo><mn>2</mn></math></span> on very restricted instances. We then provide several positive results, starting with simple polynomial kernels for <span>GEL</span> and <em>c</em>-<span>GEL</span> parameterized by neighborhood diversity or vertex cover. As one of our main technical contributions, we present an <span>FPT</span> algorithm for <span>GEL</span> parameterized by the size of a modulator to a forest of stars, based on a novel approach via a 2-<span>SAT</span> formulation which we believe to be of independent interest. We also present <span>FPT</span> algorithms based on dynamic programming for <em>c</em>-<span>GEL</span> parameterized by treewidth and <em>c</em>, and for <span>GEL</span> parameterized by treewidth and the maximum degree. Finally, we answer positively a question of Bermond et al. (2013) <span><span>[3]</span></span> by proving the <span>NP</span>-completeness of a problem strongly related to <span>GEL</span>, namely that of deciding whether an input graph admits a so-called UPP-orientation.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103752"},"PeriodicalIF":0.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145789683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2025-11-14DOI: 10.1016/j.jcss.2025.103733
Naoto Ohsaka
Combinatorial reconfiguration is a brand-new field studying algorithmic problems relating to the structure of the solution space. In this paper, we study the hardness of approximate versions of reconfiguration problems. For example, in the Maxmin SAT Reconfiguration problem, we are given a satisfiable Boolean formula and a pair of its satisfying assignments. The objective is to transform one satisfying assignment into the other by repeatedly flipping the value of a single variable, while maximizing the minimum fraction of satisfied clauses throughout the transformation. We prove a series of gap-preserving reductions to give evidence that several reconfiguration problems are -hard to approximate. Our starting point is a new working hypothesis called the Reconfiguration Inapproximability Hypothesis (RIH), which asserts that a gap version of Maxmin CSP Reconfiguration is -hard. Our main result is -hardness of approximating Maxmin 3-SAT Reconfiguration of bounded occurrence under RIH. The crux of its proof is a gap-preserving reduction from Maxmin 2-CSP Reconfiguration to itself of bounded degree. As an application of the main result, we demonstrate that under RIH, approximate versions of reconfiguration problems are -hard to approximate, including Nondeterministic Constraint Logic, Independent Set Reconfiguration, Clique Reconfiguration, Vertex Cover Reconfiguration, and 2-SAT Reconfiguration. We highlight that RIH has recently been proven by Hirahara and Ohsaka (STOC 2024) and Karthik C.S. and Manurangsi (2023).
{"title":"Gap preserving reductions between reconfiguration problems","authors":"Naoto Ohsaka","doi":"10.1016/j.jcss.2025.103733","DOIUrl":"10.1016/j.jcss.2025.103733","url":null,"abstract":"<div><div>Combinatorial reconfiguration is a brand-new field studying algorithmic problems relating to the structure of the solution space. In this paper, we study the hardness of <em>approximate versions</em> of reconfiguration problems. For example, in the <span>Maxmin SAT Reconfiguration</span> problem, we are given a satisfiable Boolean formula and a pair of its satisfying assignments. The objective is to transform one satisfying assignment into the other by repeatedly flipping the value of a single variable, while maximizing the minimum fraction of satisfied clauses throughout the transformation. We prove a series of gap-preserving reductions to give evidence that several reconfiguration problems are <span><math><mtext>PSPACE</mtext></math></span>-hard to approximate. Our starting point is a new working hypothesis called the <em>Reconfiguration Inapproximability Hypothesis</em> (RIH), which asserts that a gap version of <span>Maxmin CSP Reconfiguration</span> is <span><math><mtext>PSPACE</mtext></math></span>-hard. Our main result is <span><math><mtext>PSPACE</mtext></math></span>-hardness of approximating <span>Maxmin 3-SAT Reconfiguration</span> of bounded occurrence under RIH. The crux of its proof is a gap-preserving reduction from <span>Maxmin 2-CSP Reconfiguration</span> to itself of bounded degree. As an application of the main result, we demonstrate that under RIH, approximate versions of reconfiguration problems are <span><math><mtext>PSPACE</mtext></math></span>-hard to approximate, including <span>Nondeterministic Constraint Logic</span>, <span>Independent Set Reconfiguration</span>, <span>Clique Reconfiguration</span>, <span>Vertex Cover Reconfiguration</span>, and <span>2-SAT Reconfiguration</span>. We highlight that RIH has recently been proven by Hirahara and Ohsaka (STOC 2024) and Karthik C.S. and Manurangsi (2023).</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103733"},"PeriodicalIF":0.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145618296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2026-01-07DOI: 10.1016/j.jcss.2026.103758
Xiaowei Huang , Shiguang Feng , Lvzhou Li
Connectivity is a fundamental structural property of matroids, and has been studied algorithmically over 50 years. In 1974, Cunningham proposed a deterministic algorithm consuming queries to the independence oracle to determine whether a matroid is connected. Since then, no algorithm, not even a random one, has worked better. To the best of our knowledge, the classical query complexity lower bound and the quantum complexity for this problem have not been considered. Thus, in this paper we are devoted to addressing these issues, and our contributions are threefold as follows: (i) First, we prove that the randomized query complexity of determining whether a matroid is connected is and thus the algorithm proposed by Cunningham is optimal in classical computing. (ii) Second, we present a quantum algorithm with queries, which exhibits provable quantum speedups over classical ones. (iii) Third, we prove that any quantum algorithm requires queries, which indicates that quantum algorithms can achieve at most a quadratic speedup over classical ones. Therefore, we have a relatively comprehensive understanding of the potential of quantum computing in determining the connectedness of matroids.
{"title":"Quantum and classical query complexities for determining connectedness of matroids","authors":"Xiaowei Huang , Shiguang Feng , Lvzhou Li","doi":"10.1016/j.jcss.2026.103758","DOIUrl":"10.1016/j.jcss.2026.103758","url":null,"abstract":"<div><div>Connectivity is a fundamental structural property of matroids, and has been studied algorithmically over 50 years. In 1974, Cunningham proposed a deterministic algorithm consuming <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> queries to the independence oracle to determine whether a matroid is connected. Since then, no algorithm, not even a random one, has worked better. To the best of our knowledge, the classical query complexity lower bound and the quantum complexity for this problem have not been considered. Thus, in this paper we are devoted to addressing these issues, and our contributions are threefold as follows: (i) First, we prove that the randomized query complexity of determining whether a matroid is connected is <span><math><mi>Ω</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> and thus the algorithm proposed by Cunningham is optimal in classical computing. (ii) Second, we present a quantum algorithm with <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>)</mo></math></span> queries, which exhibits provable quantum speedups over classical ones. (iii) Third, we prove that any quantum algorithm requires <span><math><mi>Ω</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> queries, which indicates that quantum algorithms can achieve at most a quadratic speedup over classical ones. Therefore, we have a relatively comprehensive understanding of the potential of quantum computing in determining the connectedness of matroids.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103758"},"PeriodicalIF":0.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider algorithms for finding and counting small, fixed graphs in sparse host graphs. In the non-sparse setting, the parameters treedepth and treewidth play a crucial role in fast, constant-space and polynomial-space algorithms respectively. We discover two new parameters that we call matched treedepth and matched treewidth. We show that, for many patterns, finding and counting patterns with low matched treedepth and low matched treewidth can be done asymptotically faster than the existing algorithms when the host graphs are sparse. As an application to finding and counting fixed-size patterns, we discover -time.1 constant-space algorithms for graphs on at most 11 edges and -time, polynomial-space algorithms for graphs on at most 9 edges.2
{"title":"Finding and counting patterns in sparse graphs","authors":"Balagopal Komarath , Anant Kumar , Suchismita Mishra , Aditi Sethia","doi":"10.1016/j.jcss.2025.103728","DOIUrl":"10.1016/j.jcss.2025.103728","url":null,"abstract":"<div><div>We consider algorithms for finding and counting small, fixed graphs in sparse host graphs. In the non-sparse setting, the parameters treedepth and treewidth play a crucial role in fast, constant-space and polynomial-space algorithms respectively. We discover two new parameters that we call matched treedepth and matched treewidth. We show that, for many patterns, finding and counting patterns with low matched treedepth and low matched treewidth can be done asymptotically faster than the existing algorithms when the host graphs are sparse. As an application to finding and counting fixed-size patterns, we discover <span><math><mover><mrow><mi>O</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><msup><mrow><mi>m</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span>-time.<span><span><sup>1</sup></span></span> constant-space algorithms for graphs on at most 11 edges and <span><math><mover><mrow><mi>O</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>-time, polynomial-space algorithms for graphs on at most 9 edges.<span><span><sup>2</sup></span></span></div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103728"},"PeriodicalIF":0.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145618294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2025-11-17DOI: 10.1016/j.jcss.2025.103735
Max A. Alekseyev
We address the problem of finding sets of integers of a given size with a maximum number of pairs summing to powers of 2. By fixing particular pairs, this problem reduces to finding a labeling of the vertices of a given graph with pairwise distinct integers such that the endpoint labels for each edge sum up to a power of 2. We propose an efficient algorithm for this problem, which at its core relies on another algorithm that, given two sets of linear homogeneous polynomials with integer coefficients, computes all variable assignments to powers of 2 that nullify polynomials from the first set but not from the second. With the proposed algorithms, we determine the maximum size of graphs of order n that admit such a labeling for all , and construct the maximum admissible graphs for . We also identify the minimal forbidden subgraphs of order ≤11, whose presence prevents the graphs from having such a labeling.
{"title":"Maximizing the number of integer pairs summing to powers of 2 via graph labeling and solving restricted systems of linear (in)equations","authors":"Max A. Alekseyev","doi":"10.1016/j.jcss.2025.103735","DOIUrl":"10.1016/j.jcss.2025.103735","url":null,"abstract":"<div><div>We address the problem of finding sets of integers of a given size with a maximum number of pairs summing to powers of 2. By fixing particular pairs, this problem reduces to finding a labeling of the vertices of a given graph with pairwise distinct integers such that the endpoint labels for each edge sum up to a power of 2. We propose an efficient algorithm for this problem, which at its core relies on another algorithm that, given two sets of linear homogeneous polynomials with integer coefficients, computes all variable assignments to powers of 2 that nullify polynomials from the first set but not from the second. With the proposed algorithms, we determine the maximum size of graphs of order <em>n</em> that admit such a labeling for all <span><math><mi>n</mi><mo>≤</mo><mn>21</mn></math></span>, and construct the maximum admissible graphs for <span><math><mi>n</mi><mo>≤</mo><mn>20</mn></math></span>. We also identify the minimal forbidden subgraphs of order ≤11, whose presence prevents the graphs from having such a labeling.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103735"},"PeriodicalIF":0.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145618295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号