{"title":"A linear algorithm for radio k-coloring of powers of paths having small diameters","authors":"Dipayan Chakraborty , Soumen Nandi , Sagnik Sen , D.K. Supraja","doi":"10.1016/j.jcss.2024.103577","DOIUrl":"10.1016/j.jcss.2024.103577","url":null,"abstract":"<div><p>The radio <em>k</em>-chromatic number <span><math><mi>r</mi><msub><mrow><mi>c</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> of a graph <em>G</em> is the minimum integer <em>λ</em> such that there exists a function <span><math><mi>ϕ</mi><mo>:</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>→</mo><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><mi>λ</mi><mo>}</mo></math></span> satisfying <span><math><mo>|</mo><mi>ϕ</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>−</mo><mi>ϕ</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>|</mo><mo>≥</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>−</mo><mi>d</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></span>, where <span><math><mi>d</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></span> denotes the distance between <em>u</em> and <em>v</em>. A considerable amount of attention has been given to find the exact values or providing polynomial time algorithms to determine <span><math><mi>r</mi><msub><mrow><mi>c</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> for several basic graph families such as paths, cycles, trees, and powers of paths, usually for some specific values of <em>k</em>. In this article, we find the exact values of <span><math><mi>r</mi><msub><mrow><mi>c</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> where <em>G</em> is a power of a path with diameter strictly less than <em>k</em>. Our proof readily provides a linear time algorithm for assigning a radio <em>k</em>-coloring of <em>G</em>. Furthermore, our proof technique is a potential tool for solving the same problem for other classes of graphs having “small” diameters.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"147 ","pages":"Article 103577"},"PeriodicalIF":1.1,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142136727","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}
{"title":"On finding short reconfiguration sequences between independent sets","authors":"Akanksha Agrawal , Soumita Hait , Amer E. Mouawad","doi":"10.1016/j.jcss.2024.103578","DOIUrl":"10.1016/j.jcss.2024.103578","url":null,"abstract":"<div><p><span>Token Sliding Optimization</span> asks whether there exists a sequence of at most <em>ℓ</em> steps that transforms independent set <em>S</em> into <em>T</em>, where at each step a token slides to an unoccupied neighboring vertex (while maintaining independence). In <span>Token Jumping Optimization</span>, we are instead allowed to jump from a vertex to any unoccupied vertex. Both problems are known to be <span>FPT</span> when parameterized by <em>ℓ</em> on nowhere dense graphs. In this work, we show that both problems are <span>FPT</span> for parameter <span><math><mi>k</mi><mo>+</mo><mi>ℓ</mi><mo>+</mo><mi>d</mi></math></span> on <em>d</em>-degenerate graphs as well as for parameter <span><math><mo>|</mo><mi>M</mi><mo>|</mo><mo>+</mo><mi>ℓ</mi><mo>+</mo><mi>Δ</mi></math></span> on graphs having a modulator <em>M</em> to maximum degree Δ. We complement these results by showing that for parameter <em>ℓ</em> both problems become hard already on 2-degenerate graphs. Finally, we show that using such families one can obtain a unified algorithm for the standard <span>Token Jumping</span> problem parameterized by <em>k</em> on degenerate and nowhere dense graphs.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"147 ","pages":"Article 103578"},"PeriodicalIF":1.1,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142084354","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}
Guilherme C.M. Gomes , Clément Legrand-Duchesne , Reem Mahmoud , Amer E. Mouawad , Yoshio Okamoto , Vinicius F. dos Santos , Tom C. van der Zanden
{"title":"Minimum separator reconfiguration","authors":"Guilherme C.M. Gomes , Clément Legrand-Duchesne , Reem Mahmoud , Amer E. Mouawad , Yoshio Okamoto , Vinicius F. dos Santos , Tom C. van der Zanden","doi":"10.1016/j.jcss.2024.103574","DOIUrl":"10.1016/j.jcss.2024.103574","url":null,"abstract":"<div><p>We study the problem of reconfiguring <em>s</em>-<em>t</em>-separators on finite simple graphs. We consider several variants of the problem, focusing on the token sliding and jumping models. We begin with a polynomial-time algorithm that computes (if one exists) a shortest sequence of slides and another that decides if a sequence of jumps exists and outputs a witnessing sequence. We also show that deciding if a reconfiguration sequence of at most <em>ℓ</em> jumps exists is an <span><math><mtext>NP</mtext></math></span>-complete problem. To complement this result, we investigate the parameterized complexity of the natural parameterizations of the problem: by the size <em>k</em> of the minimum <em>s</em>-<em>t</em>-separators and by the number of jumps <em>ℓ</em>. We show that the problem is in <span>FPT</span> parameterized by <em>k</em>, but that it does not admit a polynomial kernel unless <span><math><mtext>NP</mtext><mo>⊆</mo><mtext>coNP/poly</mtext></math></span>. Our final result is a kernel with <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> vertices and edges.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"146 ","pages":"Article 103574"},"PeriodicalIF":1.1,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141936525","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}
{"title":"Towards declarative comparabilities: Application to functional dependencies","authors":"Lhouari Nourine , Jean-Marc Petit , Simon Vilmin","doi":"10.1016/j.jcss.2024.103576","DOIUrl":"10.1016/j.jcss.2024.103576","url":null,"abstract":"<div><p>In real life, data are often of poor quality as a result, for instance, of uncertainty, mismeasurements, missing values or bad inputs. This issue hampers an implicit yet crucial operation of every database management system: equality testing. Indeed, equality is, in the end, a context-dependent operation with a plethora of interpretations. In practice, the treatment of different types of equality is left to programmers, who have to struggle with those interpretations in their code. We introduce a lattice-based declarative framework to address this problem. It allows specification of numerous semantics for equality at a high level of abstraction. To go beyond tuple equality, we study functional dependencies (FDs) in the light of our framework. First, we define abstract FDs, generalizing classical FDs. These lead to the consideration of particular interpretations of equality: realities. Building upon realities and possible/certain answers, we introduce possible/certain FDs and give some complexity results.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"146 ","pages":"Article 103576"},"PeriodicalIF":1.1,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141936526","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}
{"title":"Modular SAT-based techniques for reasoning tasks in team semantics","authors":"Arnaud Durand , Juha Kontinen , Jouko Väänänen","doi":"10.1016/j.jcss.2024.103575","DOIUrl":"10.1016/j.jcss.2024.103575","url":null,"abstract":"<div><p>We study the complexity of reasoning tasks for logics in team semantics. Our main focus is on the data complexity of model checking but we also derive new results for logically defined counting and enumeration problems. Our approach is based on modular reductions of these problems into the corresponding problems of various classes of Boolean formulas. We illustrate our approach via several new tractability/intractability results.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"146 ","pages":"Article 103575"},"PeriodicalIF":1.1,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022000024000709/pdfft?md5=257fe45a7b50d68c8b72d3df843b4963&pid=1-s2.0-S0022000024000709-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141936332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}
Nina Klobas , George B. Mertzios , Hendrik Molter , Paul G. Spirakis
{"title":"The complexity of computing optimum labelings for temporal connectivity","authors":"Nina Klobas , George B. Mertzios , Hendrik Molter , Paul G. Spirakis","doi":"10.1016/j.jcss.2024.103564","DOIUrl":"10.1016/j.jcss.2024.103564","url":null,"abstract":"<div><p>A graph is temporally connected if a strict temporal path exists from every vertex <em>u</em> to every other vertex <em>v</em>. This paper studies <em>temporal design</em> problems for undirected temporally connected graphs. Given a connected undirected graph <em>G</em>, the goal is to determine the smallest total number of time-labels <span><math><mo>|</mo><mi>λ</mi><mo>|</mo></math></span> needed to ensure temporal connectivity, where <span><math><mo>|</mo><mi>λ</mi><mo>|</mo></math></span> denotes the sum, over all edges, of the size of the set of labels associated to an edge. The basic problem, called <span>Minimum Labeling</span> (<span>ML</span>) can be solved optimally in polynomial time. We introduce the <span>Min. Aged Labeling</span> (<span>MAL</span>) problem, which involves connecting the graph with an upper-bound on the maximum label, the <span>Min. Steiner Labeling</span> (<span>MSL</span>) problem, focusing on connecting specific important vertices, and the age-restricted version of <span>MSL</span>, <span>Min. Aged Steiner Labeling</span> (<span>MASL</span>). We show that <span>MAL</span> is NP-complete, <span>MASL</span> is W[1]-hard, and while <span>MSL</span> remains NP-hard, it is FPT with respect to the number of terminals.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"146 ","pages":"Article 103564"},"PeriodicalIF":1.1,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S002200002400059X/pdfft?md5=47d92c214e02fc0c658d2c49a1fdf6d8&pid=1-s2.0-S002200002400059X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"The impact of state merging on predictive accuracy in probabilistic tree automata: Dietze's conjecture revisited","authors":"","doi":"10.1016/j.jcss.2024.103563","DOIUrl":"10.1016/j.jcss.2024.103563","url":null,"abstract":"<div><p>Dietze's conjecture concerns the problem of equipping a tree automaton <em>M</em> with weights to make it probabilistic, in such a way that the resulting automaton <em>N</em> predicts a given corpus <span><math><mi>C</mi></math></span> as accurately as possible. The conjecture states that the accuracy cannot increase if the states in <em>M</em> are merged with respect to an equivalence relation ∼ so that the result is a smaller automaton <span><math><msup><mrow><mi>M</mi></mrow><mrow><mo>∼</mo></mrow></msup></math></span>. Put differently, merging states can never improve predictions. This is under the assumption that both <em>M</em> and <span><math><msup><mrow><mi>M</mi></mrow><mrow><mo>∼</mo></mrow></msup></math></span> are bottom-up deterministic and accept every tree in <span><math><mi>C</mi></math></span>. We prove that the conjecture holds, using a construction that turns any probabilistic version <span><math><msup><mrow><mi>N</mi></mrow><mrow><mo>∼</mo></mrow></msup></math></span> of <span><math><msup><mrow><mi>M</mi></mrow><mrow><mo>∼</mo></mrow></msup></math></span> into a probabilistic version <em>N</em> of <em>M</em>, such that <em>N</em> assigns at least as great a weight to each tree in <span><math><mi>C</mi></math></span> as <span><math><msup><mrow><mi>N</mi></mrow><mrow><mo>∼</mo></mrow></msup></math></span> does.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"146 ","pages":"Article 103563"},"PeriodicalIF":1.1,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022000024000588/pdfft?md5=9e1c1d599bbcfc040fd29b857c6c21e8&pid=1-s2.0-S0022000024000588-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141571800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"Corrigendum to “Homomorphism preservation on quasi-wide classes” [J. Comput. Syst. Sci. 76 (5) (2010) 324–332]","authors":"Anuj Dawar","doi":"10.1016/j.jcss.2024.103553","DOIUrl":"https://doi.org/10.1016/j.jcss.2024.103553","url":null,"abstract":"","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"145 ","pages":"Article 103553"},"PeriodicalIF":1.1,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022000024000485/pdfft?md5=958b77feeb0f3875c742d2e66ce417ce&pid=1-s2.0-S0022000024000485-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141297834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}
Zhao Wang , Yaping Mao , Sun-Yuan Hsieh , Ralf Klasing , Yuzhi Xiao
{"title":"The g-extra connectivity of graph products","authors":"Zhao Wang , Yaping Mao , Sun-Yuan Hsieh , Ralf Klasing , Yuzhi Xiao","doi":"10.1016/j.jcss.2024.103552","DOIUrl":"10.1016/j.jcss.2024.103552","url":null,"abstract":"<div><p>Connectivity is one of important parameters for the fault tolerant of an interconnection network. In 1996, Fàbrega and Fiol proposed the concept of <em>g</em>-extra connectivity. A subset of vertices <em>S</em> is said to be a <em>cutset</em> if <span><math><mi>G</mi><mo>−</mo><mi>S</mi></math></span> is not connected. A cutset <em>S</em> is called an <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span><em>-cutset</em>, where <em>g</em> is a non-negative integer, if every component of <span><math><mi>G</mi><mo>−</mo><mi>S</mi></math></span> has at least <span><math><mi>g</mi><mo>+</mo><mn>1</mn></math></span> vertices. If <em>G</em> has at least one <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span>-cutset, the <em>g-extra connectivity</em> of <em>G</em>, denoted by <span><math><msub><mrow><mi>κ</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, is then defined as the minimum cardinality over all <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span>-cutsets of <em>G</em>. In this paper, we first obtain the exact value of <em>g</em>-extra connectivity for the lexicographic product of two general graphs. Next, the upper and lower sharp bounds of <em>g</em>-extra connectivity for the Cartesian product of two general graphs are given. In the end, we apply our results on grid graphs and 2-dimensional generalized hypercubes.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"145 ","pages":"Article 103552"},"PeriodicalIF":1.1,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141195346","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}
Isnard Lopes Costa , Raul Lopes , Andrea Marino , Ana Silva
{"title":"On computing large temporal (unilateral) connected components","authors":"Isnard Lopes Costa , Raul Lopes , Andrea Marino , Ana Silva","doi":"10.1016/j.jcss.2024.103548","DOIUrl":"https://doi.org/10.1016/j.jcss.2024.103548","url":null,"abstract":"<div><p>A temporal (directed) graph is one where edges are available only at specific times during its lifetime, <em>τ</em>. Paths in these graphs are sequences of adjacent edges whose appearing times are either strictly increasing or non-strictly increasing. Classical concepts of connected and unilateral components can be naturally extended to temporal graphs. We address fundamental questions in temporal graphs. (i) What is the complexity of deciding the existence of a component of size <em>k</em>, parameterized by <em>τ</em>, <em>k</em>, and <span><math><mi>k</mi><mo>+</mo><mi>τ</mi></math></span>? The answer depends on the component definition and whether the graph is directed or undirected. (ii) What is the minimum running time to check if a subset of vertices is pairwise reachable? A quadratic-time algorithm exists, but a faster time is unlikely unless <span>SETH</span> fails. (iii) Can we verify if a subset of vertices forms a component in polynomial time? This is <span>NP</span> -complete depending on the temporal component definition.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"144 ","pages":"Article 103548"},"PeriodicalIF":1.1,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141244778","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}