Information Processing Letters最新文献

{"title":"Free products of semigroups and monoids with a deterministic context-free word problem","authors":"Peter Kostolányi","doi":"10.1016/j.ipl.2024.106541","DOIUrl":"10.1016/j.ipl.2024.106541","url":null,"abstract":"<div><div>The class of all finitely generated semigroups with a deterministic context-free word problem is shown to be closed under free products, answering a question of T. Brough, A. J. Cain, and M. Pfeiffer. On the other hand, it is proved that the class of all finitely generated monoids with a deterministic context-free word problem is not closed under monoid free products.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"188 ","pages":"Article 106541"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142653220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effective data reduction for strongly stable matching in very sparse graphs","authors":"Rosa Wolf,&nbsp;Klaus Heeger ,&nbsp;André Nichterlein","doi":"10.1016/j.ipl.2024.106534","DOIUrl":"10.1016/j.ipl.2024.106534","url":null,"abstract":"<div><div>We provide a linear-time computable problem kernel of linear size for <span>Strongly Stable Roommates</span> parameterized by the feedback edge number of the acceptability graph (which encodes which agents may be matched to each other).</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"188 ","pages":"Article 106534"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An improved spectral lower bound of treewidth","authors":"Tatsuya Gima ,&nbsp;Tesshu Hanaka ,&nbsp;Kohei Noro ,&nbsp;Hirotaka Ono ,&nbsp;Yota Otachi","doi":"10.1016/j.ipl.2024.106536","DOIUrl":"10.1016/j.ipl.2024.106536","url":null,"abstract":"<div><div>We show that for every <em>n</em>-vertex graph with at least one edge, its treewidth is greater than or equal to <span><math><mi>n</mi><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>/</mo><mo>(</mo><mi>Δ</mi><mo>+</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo><mo>−</mo><mn>1</mn></math></span>, where Δ and <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> are the maximum degree and the second smallest Laplacian eigenvalue of the graph, respectively. This lower bound improves the one by Chandran and Subramanian [<em>Inf. Process. Lett.</em>, 2003] and the subsequent one by the authors of the present paper [<em>IEICE Trans. Inf. Syst.</em>, 2024]. The new lower bound is <em>almost</em> 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.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"188 ","pages":"Article 106536"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Covering segments on a line with drones","authors":"Sergey Bereg ,&nbsp;José-Miguel Díaz-Báñez ,&nbsp;Alina Kasiuk ,&nbsp;Miguel-Angel Pérez-Cutiño ,&nbsp;Fabio Rodríguez","doi":"10.1016/j.ipl.2024.106540","DOIUrl":"10.1016/j.ipl.2024.106540","url":null,"abstract":"<div><div>Covering a set of segments in a plane with vehicles of limited autonomy is a problem of practical interest. The limited battery endurance imposes periodical visits to a static base station. Typically, two optimization problems are considered: minimize the number of tours, and minimize the total traveled distance. In a general setting, the problems are NP-hard and in this letter, we study the one-dimensional version. For covering segments on a line, we design efficient solutions for both optimization problems. First, we design a greedy algorithm that is optimal for the first task, and for both tasks when only one segment is considered. Being <em>n</em> and <em>m</em> the number of segments and tours of an optimal solution, respectively, our algorithm runs in <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo>)</mo></math></span> time. For the second criterion, our solution is based on Dynamic Programming and runs in <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>m</mi><mo>)</mo></math></span> time.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"188 ","pages":"Article 106540"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Airports and railways with unsplittable demand","authors":"Hossein Jowhari ,&nbsp;Shamisa Nematollahi","doi":"10.1016/j.ipl.2024.106538","DOIUrl":"10.1016/j.ipl.2024.106538","url":null,"abstract":"<div><div>In the problem of airports and railways with unsplittable demand (ARUD), we are given a complete graph <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> with weights on the vertices <span><math><mi>a</mi><mo>:</mo><mi>V</mi><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>, and the length of the edges <span><math><mi>ℓ</mi><mo>:</mo><mi>V</mi><mo>×</mo><mi>V</mi><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>. Additionally, a positive integer <em>k</em> serves as the capacity parameter. We are also provided with a function <span><math><mi>b</mi><mo>:</mo><mi>V</mi><mo>→</mo><mi>N</mi></math></span> that defines a non-zero demand for each city. The goal is to compute a spanning forest <em>R</em> of <em>G</em> and a subset <span><math><mi>A</mi><mo>⊆</mo><mi>V</mi></math></span> of minimum cost such that each component in <em>R</em> has one open facility and the total demand in each component is at most <em>k</em> (the capacity constraint). The cost of the solution <span><math><mo>(</mo><mi>A</mi><mo>,</mo><mi>R</mi><mo>)</mo></math></span> is defined as <span><math><msub><mrow><mo>∑</mo></mrow><mrow><mi>v</mi><mo>∈</mo><mi>A</mi></mrow></msub><mi>a</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>+</mo><msub><mrow><mo>∑</mo></mrow><mrow><mi>e</mi><mo>∈</mo><mi>E</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></msub><mi>ℓ</mi><mo>(</mo><mi>e</mi><mo>)</mo></math></span>. This problem is a generalization of the Airport and Railways (AR) problem introduced by Adamaszek et al. (STACS 2016). In Adamaszek et al. version, each vertex has a unit demand.</div><div>This paper presents a bi-criteria approximation algorithm for the metric ARUD problem in the sense that the algorithm is allowed to exceed the capacity constraints by <span><math><mi>O</mi><mo>(</mo><mi>k</mi><mo>)</mo></math></span> while the cost of the solution is compared with the cost of an optimal solution that does not violate the capacity constraint. Our approach builds upon an existing approximation algorithm for the metric AR problem, developed by Adamaszek et al. (STACS 2018), and further leverages the well-known rounding algorithm of Shmoys and Tardos for the Generalized Assignment Problem (GAP). Assuming the total demand is polynomially bounded in the number of vertices, our algorithm runs in polynomial time. We also show that it is NP-hard to find an approximate solution for ARUD within any factor without violating the capacity constraints. This is the case even when each demand is polynomially bounded in the number of vertices. Furthermore, we determine the complexity of ARUD for some fixed values of <em>k</em>.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"188 ","pages":"Article 106538"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Algorithms for subgraph complementation to some classes of graphs","authors":"Dhanyamol Antony ,&nbsp;Sagartanu Pal ,&nbsp;R.B. Sandeep","doi":"10.1016/j.ipl.2024.106530","DOIUrl":"10.1016/j.ipl.2024.106530","url":null,"abstract":"<div><p>For a class <span><math><mi>G</mi></math></span> of graphs, the objective of <span>Subgraph Complementation to</span> <span><math><mi>G</mi></math></span> is to find whether there exists a subset <em>S</em> of vertices of the input graph <em>G</em> such that modifying <em>G</em> by complementing the subgraph induced by <em>S</em> results in a graph in <span><math><mi>G</mi></math></span>. We obtain a polynomial-time algorithm for the problem when <span><math><mi>G</mi></math></span> is the class of graphs with minimum degree at least <em>k</em>, for a constant <em>k</em>, answering an open problem by Fomin et al. (Algorithmica, 2020). When <span><math><mi>G</mi></math></span> is the class of graphs without any induced copies of the star graph on <span><math><mi>t</mi><mo>+</mo><mn>1</mn></math></span> vertices (for any constant <span><math><mi>t</mi><mo>≥</mo><mn>3</mn></math></span>) and diamond, we obtain a polynomial-time algorithm for the problem. This is in contrast with a result by Antony et al. (Algorithmica, 2022) that the problem is NP-complete and cannot be solved in subexponential-time (assuming the Exponential Time Hypothesis) when <span><math><mi>G</mi></math></span> is the class of graphs without any induced copies of the star graph on <span><math><mi>t</mi><mo>+</mo><mn>1</mn></math></span> vertices, for every constant <span><math><mi>t</mi><mo>≥</mo><mn>5</mn></math></span>.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"188 ","pages":"Article 106530"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141985069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Luby's MIS algorithms made self-stabilizing","authors":"George Giakkoupis ,&nbsp;Volker Turau ,&nbsp;Isabella Ziccardi","doi":"10.1016/j.ipl.2024.106531","DOIUrl":"10.1016/j.ipl.2024.106531","url":null,"abstract":"<div><p>We reconsider two well-known distributed randomized algorithms computing a maximal independent set, proposed in the seminal work of Luby (1986). We enhance these algorithms such that they become self-stabilizing without sacrificing their run-time, i.e., both stabilize in <span><math><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> synchronous rounds with high probability on any <em>n</em>-node graph. The first algorithm gets along with three states, but needs to know an upper bound on the maximum degree. The second does not need any information about the graph, but uses a number of states that is linear in the node degree. Both algorithms use messages of logarithmic size.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"188 ","pages":"Article 106531"},"PeriodicalIF":0.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020019024000619/pdfft?md5=8797cfe630838abf367b5e1ac7c3484f&pid=1-s2.0-S0020019024000619-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141985068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Is this network proper forest-based?","authors":"Katharina T. Huber ,&nbsp;Leo van Iersel ,&nbsp;Vincent Moulton ,&nbsp;Guillaume E. Scholz","doi":"10.1016/j.ipl.2024.106500","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106500","url":null,"abstract":"<div><p>In evolutionary biology, networks are becoming increasingly used to represent evolutionary histories for species that have undergone non-treelike or reticulate evolution. Such networks are essentially directed acyclic graphs with a leaf set that corresponds to a collection of species, and in which non-leaf vertices with indegree 1 correspond to speciation events and vertices with indegree greater than 1 correspond to reticulate events such as gene transfer. Recently forest-based networks have been introduced, which are essentially (multi-rooted) networks that can be formed by adding some arcs to a collection of phylogenetic trees (or phylogenetic forest), where each arc is added in such a way that its ends always lie in two different trees in the forest. In this paper, we consider the complexity of deciding whether a given network is proper forest-based, that is, whether it can be formed by adding arcs to some underlying phylogenetic forest which contains the same number of trees as there are roots in the network. More specifically, we show that it is NP-complete to decide whether a tree-child network with <em>m</em> roots is proper forest-based, for each <span><math><mi>m</mi><mo>≥</mo><mn>2</mn></math></span>. Moreover, for binary networks the problem remains NP-complete when <span><math><mi>m</mi><mo>≥</mo><mn>3</mn></math></span> but becomes polynomial-time solvable for <span><math><mi>m</mi><mo>=</mo><mn>2</mn></math></span>. We also give a fixed parameter tractable (FPT) algorithm, with parameters the maximum outdegree of a vertex, the number of roots, and the number of indegree 2 vertices, for deciding if a semi-binary network is proper forest-based. A key element in proving our results is a new characterization for when a network with <em>m</em> roots is proper forest-based in terms of certain <em>m</em>-colorings.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106500"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020019024000309/pdfft?md5=6bb24ac246fe9301af0f20ad64b94c09&pid=1-s2.0-S0020019024000309-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140924528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A note on the k-restriction problem","authors":"Jing-You Lin,&nbsp;Shi-Chun Tsai","doi":"10.1016/j.ipl.2024.106515","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106515","url":null,"abstract":"<div><p>Consider a set of demands, each taking length-<em>k</em> strings as input. The <em>k</em>-restriction problem is to construct a small set of length-<em>m</em> strings, such that given any <em>k</em> positions and any demand, there exists a string in the set satisfying the demand at these positions. The <em>k</em>-restriction problem relates to many problems, such as <em>k</em>-independent sets, covering arrays, and many other combinatorial applications. By considering the VC-dimension of demands, we prove bounds independent of the number of demands with the Lovász Local Lemma. As a result, we can prove better bounds for demands with finite VC-dimension.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106515"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141250243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Algorithmic aspects of {Pk}-isolation in graphs and extremal graphs for a {P3}-isolation bound","authors":"Jie Chen ,&nbsp;Yi-Ping Liang ,&nbsp;Cai-Xia Wang ,&nbsp;Shou-Jun Xu","doi":"10.1016/j.ipl.2024.106521","DOIUrl":"10.1016/j.ipl.2024.106521","url":null,"abstract":"<div><p>A subset <em>S</em> of the vertex set of a graph <em>G</em> is an <span><math><mi>F</mi></math></span><em>-isolating set</em> of <em>G</em> if <span><math><mi>G</mi><mo>−</mo><mi>N</mi><mo>[</mo><mi>S</mi><mo>]</mo></math></span> does not contain a copy of a member of <span><math><mi>F</mi></math></span> as a subgraph, where <span><math><mi>F</mi></math></span> is a family of connected graphs and <span><math><mi>N</mi><mo>[</mo><mi>S</mi><mo>]</mo></math></span> is the closed neighborhood of <em>S</em>. The <span><math><mi>F</mi></math></span><em>-isolation number</em> of <em>G</em> is the minimum cardinality of an <span><math><mi>F</mi></math></span>-isolating set of <em>G</em>, denoted by <span><math><mi>ι</mi><mo>(</mo><mi>G</mi><mo>,</mo><mi>F</mi><mo>)</mo></math></span>. Given a graph <em>G</em>, <span><math><mo>{</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>}</mo></math></span>-ISOLATION asks for the size of a smallest <span><math><mo>{</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>}</mo></math></span>-isolating set of <em>G</em> for a fixed positive integer <em>k</em>, where <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> is a path of order <em>k</em>. In this paper, we first show that the decision version of <span><math><mo>{</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>}</mo></math></span>-ISOLATION is NP-complete for chordal graphs and planar graphs. Secondly, we propose a linear time algorithm to compute a smallest <span><math><mo>{</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>}</mo></math></span>-isolating set of a tree. Finally, we solve the problem of characterizing the connected graphs <em>G</em> with <span><math><mi>ι</mi><mo>(</mo><mi>G</mi><mo>,</mo><mo>{</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>}</mo><mo>)</mo><mo>=</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>7</mn></mrow></mfrac><mo>|</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo></math></span>, proposed by Zhang and Wu [Discrete Appl. Math. 304 (2021) 365-374].</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"187 ","pages":"Article 106521"},"PeriodicalIF":0.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141629965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}