Journal of Computer and System Sciences最新文献

{"title":"Time-sharing scheduling with tolerance capacities","authors":"George Karakostas ,&nbsp;Stavros G. Kolliopoulos","doi":"10.1016/j.jcss.2024.103605","DOIUrl":"10.1016/j.jcss.2024.103605","url":null,"abstract":"<div><div>Motivated by time-sharing systems with deadlines, we introduce the study of the following problem. We are given <em>m</em> machines and <em>n</em> jobs, as well as a set of <em>tolerance capacities</em> <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>≥</mo><mn>0</mn></math></span> for every job <em>j</em> and machine <em>i</em>. Can we assign the jobs so that, if job <em>j</em> ends up on machine <em>i</em>, the total size of jobs that are processed on <em>i</em> is at most <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub></math></span>? We define two natural optimization versions: (i) Maximize the total weight of jobs that can be assigned without violating the tolerance capacities. (ii) Minimize the amount <span><math><mi>ρ</mi><mo>≥</mo><mn>1</mn></math></span> by which capacities have to be scaled so that all jobs can be assigned. For (i), we provide constant-factor approximations even in the presence of additional side-constraints. For (ii), we provide a strong inapproximability result and integrality gap lower bounds for two key relaxations.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"148 ","pages":"Article 103605"},"PeriodicalIF":1.1,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142720552","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":"Embedding hypercubes into torus and Cartesian product of paths and/or cycles for minimizing wirelength","authors":"Zhiyi Tang","doi":"10.1016/j.jcss.2024.103603","DOIUrl":"10.1016/j.jcss.2024.103603","url":null,"abstract":"<div><div>Though embedding problems have been considered for several regular graphs <span><span>[1]</span></span>, <span><span>[2]</span></span>, <span><span>[3]</span></span>, it is still an open problem for hypercube into torus <span><span>[4]</span></span>, <span><span>[2]</span></span>. In the paper, we prove the conjecture mathematically and obtain the minimum wirelength of embedding for hypercube into Cartesian product of paths and/or cycles. In addition, we explain that Gray code embedding is an optimal strategy in such embedding problems.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"148 ","pages":"Article 103603"},"PeriodicalIF":1.1,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142654142","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":"The parameterized complexity of the survivable network design problem","authors":"Andreas Emil Feldmann ,&nbsp;Anish Mukherjee ,&nbsp;Erik Jan van Leeuwen","doi":"10.1016/j.jcss.2024.103604","DOIUrl":"10.1016/j.jcss.2024.103604","url":null,"abstract":"<div><div>In the well-known <span>Survivable Network Design Problem (SNDP)</span>, we are given an undirected graph <em>G</em> with edge costs, a set <em>R</em> of terminal vertices, and an integer demand <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>t</mi></mrow></msub></math></span> for every terminal pair <span><math><mi>s</mi><mo>,</mo><mi>t</mi><mo>∈</mo><mi>R</mi></math></span>. The task is to compute a subgraph <em>H</em> of <em>G</em> of minimum cost, such that for every terminal pair <span><math><mi>s</mi><mo>,</mo><mi>t</mi><mo>∈</mo><mi>R</mi></math></span> there are at least <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>t</mi></mrow></msub></math></span> disjoint paths between <em>s</em> and <em>t</em> in <em>H</em>. Depending on the type of disjointness, we obtain several variants of SNDP that have been widely studied in the literature: if the paths are required to be edge-disjoint we obtain <span>EC-SNDP</span>, while if they must be internally vertex-disjoint we obtain <span>VC-SNDP</span>. Another important case is the element-connectivity variant (<span>LC-SNDP</span>), where the paths must be disjoint on edges and non-terminals, i.e., they may only share terminals. In this work we shed light on the parameterized complexity of the above problems. We consider several natural parameters, which include the solution size <em>ℓ</em>, the sum of demands <em>D</em>, the number of terminals <em>k</em>, and the maximum demand <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>max</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"148 ","pages":"Article 103604"},"PeriodicalIF":1.1,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142703522","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":"Monitoring the edges of product networks using distances","authors":"Wen Li ,&nbsp;Ralf Klasing ,&nbsp;Yaping Mao ,&nbsp;Bo Ning","doi":"10.1016/j.jcss.2024.103602","DOIUrl":"10.1016/j.jcss.2024.103602","url":null,"abstract":"<div><div>Foucaud et al. recently introduced and initiated the study of a new graph-theoretic concept in the area of network monitoring. Let <em>G</em> be a graph with vertex set <span><math><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and edge set <span><math><mi>E</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. For any subset <em>M</em> in <span><math><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and an edge <em>e</em> in <span><math><mi>E</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, let <span><math><mi>P</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>e</mi><mo>)</mo></math></span> be the set of pairs <span><math><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> such that <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>≠</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>G</mi><mo>−</mo><mi>e</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> where <span><math><mi>x</mi><mo>∈</mo><mi>M</mi></math></span> and <span><math><mi>y</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. <em>M</em> is called a <em>distance-edge-monitoring set</em> if every edge <em>e</em> of <em>G</em> is monitored by some vertex of <em>M</em>, that is, the set <span><math><mi>P</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>e</mi><mo>)</mo></math></span> is nonempty. The <em>distance-edge-monitoring number</em> of <em>G</em>, denoted by <span><math><mi>dem</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, is defined as the smallest size of distance-edge-monitoring sets of <em>G</em>. For two graphs <span><math><mi>G</mi><mo>,</mo><mi>H</mi></math></span> of order <span><math><mi>m</mi><mo>,</mo><mi>n</mi></math></span>, respectively, in this paper, we prove that <span><math><mi>max</mi><mo>⁡</mo><mo>{</mo><mi>m</mi><mi>dem</mi><mo>(</mo><mi>H</mi><mo>)</mo><mo>,</mo><mi>n</mi><mi>dem</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>}</mo><mo>≤</mo><mi>dem</mi><mo>(</mo><mi>G</mi><mspace></mspace><mo>□</mo><mspace></mspace><mi>H</mi><mo>)</mo><mo>≤</mo><mi>m</mi><mi>dem</mi><mo>(</mo><mi>H</mi><mo>)</mo><mo>+</mo><mi>n</mi><mi>dem</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>−</mo><mi>dem</mi><mo>(</mo><mi>G</mi><mo>)</mo><mi>dem</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span>, where □ is the Cartesian product operation. Moreover, we characterize the networks attaining the upper and lower bounds and show their applications on some known networks. We also obtain the distance-edge-monitoring numbers of join, corona, cluster, and some specific networks.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"148 ","pages":"Article 103602"},"PeriodicalIF":1.1,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142703524","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":"Algorithms and Turing kernels for detecting and counting small patterns in unit disk graphs","authors":"Jesper Nederlof,&nbsp;Krisztina Szilágyi","doi":"10.1016/j.jcss.2024.103600","DOIUrl":"10.1016/j.jcss.2024.103600","url":null,"abstract":"<div><div>In this paper we investigate the parameterized complexity of counting and detecting small patterns in unit disk graphs: Given an <em>n</em>-vertex unit disk graph <em>G</em> with an embedding of ply <em>p</em> (i.e. <em>G</em> is an intersection graph of closed unit disks, and each point is contained in at most <em>p</em> disks) and a <em>k</em>-vertex unit disk graph <em>P</em>, count the number of (induced) copies of <em>P</em> in <em>G</em>. For general patterns <em>P</em>, we give an <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>O</mi><mo>(</mo><mi>p</mi><mi>k</mi><mo>/</mo><mi>log</mi><mo>⁡</mo><mi>k</mi><mo>)</mo></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 for counting pattern occurrences. We show this is tight, even for ply <span><math><mi>p</mi><mo>=</mo><mn>2</mn></math></span>: any <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>o</mi><mo>(</mo><mi>n</mi><mo>/</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></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 violates the Exponential Time Hypothesis (ETH). Our approach combines tools developed for planar subgraph isomorphism such as ‘efficient inclusion-exclusion’ from Nederlof (2020) <span><span>[15]</span></span>, and ‘isomorphisms checks’ from Bodlaender et al. (2016) <span><span>[5]</span></span> with a different separator hierarchy and a new bound on the number of non-isomorphic separations tailored for unit disk graphs.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"148 ","pages":"Article 103600"},"PeriodicalIF":1.1,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142654144","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":"Backwards-reachability for cooperating multi-pushdown systems","authors":"Chris Köcher ,&nbsp;Dietrich Kuske","doi":"10.1016/j.jcss.2024.103601","DOIUrl":"10.1016/j.jcss.2024.103601","url":null,"abstract":"<div><div>A cooperating multi-pushdown system consists of a tuple of pushdown systems that can delegate the execution of recursive procedures to sub-tuples; control returns to the calling tuple once all sub-tuples finished their task. This allows the concurrent execution since disjoint sub-tuples can perform their task independently. Because of the concrete form of recursive descent into sub-tuples, the content of the multi-pushdown does not form an arbitrary tuple of words, but can be understood as a Mazurkiewicz trace. For such systems, we prove that the backwards reachability relation efficiently preserves recognizability, generalizing a result and proof technique by Bouajjani et al. for single-pushdown systems. It follows that the reachability relation is decidable for cooperating multi-pushdown systems in polynomial time and the same holds, e.g., for safety and liveness properties given by recognizable sets of configurations.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"148 ","pages":"Article 103601"},"PeriodicalIF":1.1,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142654143","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":"On computing optimal temporal branchings and spanning subgraphs","authors":"Daniela Bubboloni ,&nbsp;Costanza Catalano ,&nbsp;Andrea Marino ,&nbsp;Ana Silva","doi":"10.1016/j.jcss.2024.103596","DOIUrl":"10.1016/j.jcss.2024.103596","url":null,"abstract":"<div><div>We extend the concept of out/in-branchings spanning the vertices of a digraph to temporal graphs, which are digraphs where arcs are available only at prescribed times. While the literature has focused on minimum weight/earliest arrival time Temporal Out-Branchings (<span>tob</span>), we solve the problem for other optimization criteria (travel duration, departure time, number of transfers, total waiting time, traveling time). For some criteria we provide a log linear algorithm for computing such branchings, while for others we prove that deciding the existence of a spanning <span>tob</span> is <span>NP</span>-complete. The same results hold for optimal temporal in-branchings. We also investigate the related problem of computing a spanning temporal subgraph with the minimum number of arcs and optimizing a chosen criterion; this problem turns out to be always <span>NP</span>-hard. The hardness results are quite surprising, as computing optimal paths between nodes is always polynomial-time.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"148 ","pages":"Article 103596"},"PeriodicalIF":1.1,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554740","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":"Single-exponential FPT algorithms for enumerating secluded F-free subgraphs and deleting to scattered graph classes","authors":"Bart M.P. Jansen ,&nbsp;Jari J.H. de Kroon ,&nbsp;Michał Włodarczyk","doi":"10.1016/j.jcss.2024.103597","DOIUrl":"10.1016/j.jcss.2024.103597","url":null,"abstract":"<div><div>The celebrated notion of important separators bounds the number of small <span><math><mo>(</mo><mi>S</mi><mo>,</mo><mi>T</mi><mo>)</mo></math></span>-separators in a graph which are ‘farthest from <em>S</em>’ in a technical sense. In this paper, we introduce a generalization of this powerful algorithmic primitive, tailored to undirected graphs, that is phrased in terms of <em>k-secluded</em> vertex sets: sets with an open neighborhood of size at most <em>k</em>. In this terminology, the bound on important separators says that there are at most <span><math><msup><mrow><mn>4</mn></mrow><mrow><mi>k</mi></mrow></msup></math></span> maximal <em>k</em>-secluded connected vertex sets <em>C</em> containing <em>S</em> but disjoint from <em>T</em>. We generalize this statement significantly: even when we demand that <span><math><mi>G</mi><mo>[</mo><mi>C</mi><mo>]</mo></math></span> avoids a finite set <span><math><mi>F</mi></math></span> of forbidden induced subgraphs, the number of such maximal subgraphs is <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>O</mi><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></math></span> and they can be enumerated efficiently. This enumeration algorithm allows us to give improved parameterized algorithms for <span>Connected</span> <em>k</em><span>-Secluded</span> <span><math><mi>F</mi></math></span><span>-Free Subgraph</span> and for deleting into scattered graph classes.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"148 ","pages":"Article 103597"},"PeriodicalIF":1.1,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554741","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":"Parameterized results on acyclic matchings with implications for related problems","authors":"Juhi Chaudhary ,&nbsp;Meirav Zehavi","doi":"10.1016/j.jcss.2024.103599","DOIUrl":"10.1016/j.jcss.2024.103599","url":null,"abstract":"<div><div>A matching <em>M</em> in a graph <em>G</em> is an <em>acyclic matching</em> if the subgraph of <em>G</em> induced by the endpoints of the edges of <em>M</em> is a forest. Given a graph <em>G</em> and <span><math><mi>ℓ</mi><mo>∈</mo><mi>N</mi></math></span>, <span>Acyclic Matching</span> asks whether <em>G</em> has an acyclic matching of <em>size</em> at least <em>ℓ</em>. In this paper, we prove that assuming <span><math><mi>W</mi><mo>[</mo><mn>1</mn><mo>]</mo><mo>⊈</mo><mi>FPT</mi></math></span>, there does not exist any <span><math><mi>FPT</mi></math></span>-approximation algorithm for <span>Acyclic Matching</span> that approximates it within a constant factor when parameterized by <em>ℓ</em>. Our reduction also asserts <span><math><mi>FPT</mi></math></span>-inapproximability for <span>Induced Matching</span> and <span>Uniquely Restricted Matching</span>. We also consider three below-guarantee parameters for <span>Acyclic Matching</span>, viz. <span><math><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mi>ℓ</mi></math></span>, <span><math><mrow><mi>MM</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>−</mo><mi>ℓ</mi></math></span>, and <span><math><mrow><mi>IS</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>−</mo><mi>ℓ</mi></math></span>, where <span><math><mi>n</mi><mo>=</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, <span><math><mi>MM</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is the <em>matching number</em>, and <span><math><mi>IS</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is the <em>independence number</em> of <em>G</em>. Also, we show that <span>Acyclic Matching</span> does not exhibit a polynomial kernel with respect to vertex cover number (or vertex deletion distance to clique) plus the size of the matching unless <span><math><mrow><mi>NP</mi></mrow><mo>⊆</mo><mrow><mi>coNP</mi></mrow><mo>/</mo><mrow><mi>poly</mi></mrow></math></span>.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"148 ","pages":"Article 103599"},"PeriodicalIF":1.1,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530067","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":"Exact and parameterized algorithms for the independent cutset problem","authors":"Johannes Rauch ,&nbsp;Dieter Rautenbach ,&nbsp;Uéverton S. Souza","doi":"10.1016/j.jcss.2024.103598","DOIUrl":"10.1016/j.jcss.2024.103598","url":null,"abstract":"<div><div>The <span>Independent Cutset</span> problem asks whether there is a set of vertices in a given graph that is both independent and a cutset. This problem is <figure><img></figure>-complete even when the input graph is planar and has maximum degree five. We first present a <span><math><msup><mrow><mi>O</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><msup><mrow><mn>1.4423</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span>-time algorithm to compute a minimum independent cutset (if any). Since the property of having an independent cutset is MSO₁-expressible, our main results are concerned with structural parameterizations for the problem considering parameters incomparable with clique-width. We present <figure><img></figure>-time algorithms under the following parameters: the dual of the maximum degree, the dual of the solution size, the size of a dominating set (where a dominating set is given as an additional input), the size of an odd cycle transversal, the distance to chordal graphs, and the distance to <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>5</mn></mrow></msub></math></span>-free graphs. We close by introducing the notion of <em>α</em>-domination, which generalizes key ideas of this article.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"148 ","pages":"Article 103598"},"PeriodicalIF":1.1,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554742","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}