Theoretical Computer Science最新文献

{"title":"On MAX–SAT with cardinality constraint","authors":"Fahad Panolan ,&nbsp;Hannane Yaghoubizade","doi":"10.1016/j.tcs.2024.114971","DOIUrl":"10.1016/j.tcs.2024.114971","url":null,"abstract":"<div><div>We consider the weighted MAX–SAT problem with an additional constraint that <strong>at most</strong> <em>k</em> variables can be set to true. We call this problem <em>k</em><span>–WMAX–SAT</span>. This problem admits a <span><math><mo>(</mo><mn>1</mn><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>e</mi></mrow></mfrac><mo>)</mo></math></span>-factor approximation algorithm in polynomial time [Sviridenko, Algorithmica (2001)] and it is proved that there is no <span><math><mo>(</mo><mn>1</mn><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>e</mi></mrow></mfrac><mo>+</mo><mi>ϵ</mi><mo>)</mo></math></span>-factor approximation algorithm in <span><math><mi>f</mi><mo>(</mo><mi>k</mi><mo>)</mo><mo>⋅</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>o</mi><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></math></span> time for <span>Maximum Coverage</span>, the unweighted monotone version of <em>k</em><span>–WMAX–SAT</span> [Manurangsi, SODA 2020]. Therefore, we study two restricted versions of the problem in the realm of parameterized complexity.<ul><li><span>1.</span><span><div>When the input is an unweighted 2–CNF formula (the problem is called <em>k</em><span>–MAX–2SAT</span>), we design an efficient polynomial-size approximate kernelization scheme. That is, we design a polynomial-time algorithm that given a 2–CNF formula <em>ψ</em> and <span><math><mi>ϵ</mi><mo>&gt;</mo><mn>0</mn></math></span>, compresses the input instance to a 2–CNF formula <span><math><msup><mrow><mi>ψ</mi></mrow><mrow><mo>⋆</mo></mrow></msup></math></span> such that any <em>c</em>-approximate solution of <span><math><msup><mrow><mi>ψ</mi></mrow><mrow><mo>⋆</mo></mrow></msup></math></span> can be converted to a <span><math><mi>c</mi><mo>(</mo><mn>1</mn><mo>−</mo><mi>ϵ</mi><mo>)</mo></math></span>-approximate solution of <em>ψ</em> in polynomial time.</div></span></li><li><span>2.</span><span><div>When the input is a planar CNF formula, i.e., the variable-clause incidence graph is a planar graph, we show the following results:<ul><li><span>•</span><span><div>There is an FPT algorithm for <em>k</em><span>–WMAX–SAT</span> on planar CNF formulas that runs in <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>O</mi><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup><mo>⋅</mo><mo>(</mo><mi>C</mi><mo>+</mo><mi>V</mi><mo>)</mo></math></span> time.</div></span></li><li><span>•</span><span><div>There is a polynomial-time approximation scheme for <em>k</em><span>–WMAX–SAT</span> on planar CNF formulas that runs in time <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>O</mi><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>ϵ</mi></mrow></mfrac><mo>)</mo></mrow></msup><mo>⋅</mo><mi>k</mi><mo>⋅</mo><mo>(</mo><mi>C</mi><mo>+</mo><mi>V</mi><mo>)</mo></math></span>.</div></span></li></ul> The above-mentioned <em>C</em> and <em>V</em> are the number of clauses and variables of the input formula respectively.</div></span></li></ul></div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1025 ","pages":"Article 114971"},"PeriodicalIF":0.9,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656671","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":"Approximating the shortest path problem with scenarios","authors":"Adam Kasperski,&nbsp;Paweł Zieliński","doi":"10.1016/j.tcs.2024.114972","DOIUrl":"10.1016/j.tcs.2024.114972","url":null,"abstract":"<div><div>This paper discusses the shortest path problem in a general directed graph with <em>n</em> nodes and <em>K</em> cost scenarios (objectives). In order to choose a solution, the min-max criterion is applied. The min-max version of the problem is hard to approximate within <span><math><mi>Ω</mi><mo>(</mo><msup><mrow><mi>log</mi></mrow><mrow><mn>1</mn><mo>−</mo><mi>ϵ</mi></mrow></msup><mo>⁡</mo><mi>K</mi><mo>)</mo></math></span> for any <span><math><mi>ϵ</mi><mo>&gt;</mo><mn>0</mn></math></span> unless NP<!--> <span><math><mo>⊆</mo><mtext>DTIME</mtext><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mtext>polylog</mtext><mspace></mspace><mi>n</mi></mrow></msup><mo>)</mo></math></span> even for arc series-parallel graphs and within <span><math><mi>Ω</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>/</mo><mi>log</mi><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> unless NP<!--> <span><math><mo>⊆</mo><mtext>ZPTIME</mtext><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>log</mi><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mi>n</mi></mrow></msup><mo>)</mo></math></span> for acyclic graphs. The best approximation algorithm for the min-max shortest path problem in general graphs, known to date, has an approximation ratio of <em>K</em>. In this paper, an <span><math><mover><mrow><mi>O</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><msqrt><mrow><mi>n</mi></mrow></msqrt><mo>)</mo></math></span> flow LP-based approximation algorithm for min-max shortest path in general graphs is constructed. It is also shown that the approximation ratio obtained is close to an integrality gap of the corresponding flow LP relaxation.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1025 ","pages":"Article 114972"},"PeriodicalIF":0.9,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656151","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":"Retraction notice to “Optimizing Scalability and Availability of Cloud Based Software Services Using Modified Scale Rate Limiting Algorithm” [Theoretical computer science 943 (2023) 230-240]","authors":"V.L. Padma Latha ,&nbsp;N. Sudhakar Reddy ,&nbsp;A. Suresh Babu","doi":"10.1016/j.tcs.2024.114944","DOIUrl":"10.1016/j.tcs.2024.114944","url":null,"abstract":"<div><div>This article has been retracted: please see Elsevier Policy on Article Withdrawal (<span><span>https://www.elsevier.com/locate/withdrawalpolicy</span><svg><path></path></svg></span>).</div><div>This article has been retracted at the request of the Editor-in-Chief of Theoretical Computer Science, Section A.</div><div>The article is a duplicate of a paper that has already been published in Int. J. Nonlinear Anal. Appl., Volume 13 (2022), Issue 2, Pages 1893-1905, <span><span>http://dx.doi.org/10.22075/ijnaa.2022.27403.3588</span><svg><path></path></svg></span>. One of the conditions of submission of a paper for publication is therefore that authors declare explicitly that the paper has not been previously published and is not under consideration for publication elsewhere. As such this article represents a misuse of the scientific publishing system.</div><div>The scientific community takes a very strong view on this matter and apologies are offered to readers of the journal that this was not detected during the submission process.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1024 ","pages":"Article 114944"},"PeriodicalIF":0.9,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142662723","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":"Geography, Kotzig's Nim, and variants","authors":"Srinivas Arun","doi":"10.1016/j.tcs.2024.114957","DOIUrl":"10.1016/j.tcs.2024.114957","url":null,"abstract":"<div><div>Geography is a combinatorial game in which two players take turns moving a token along edges of a directed graph and deleting the vertex they came from. We expand upon work by Fox and Geissler, who classified the computational complexity of determining the winner of various Geography variants given a graph. In particular, we show NP-hardness for undirected partizan Geography with free deletion on bipartite graphs and directed partizan Geography with free deletion on acyclic graphs. In addition, we study Kotzig's Nim, a special case of Geography where the vertices are labeled and moves correspond to additions by fixed amounts. We partially resolve a conjecture by Tan and Ward about games with a certain move set.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1023 ","pages":"Article 114957"},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142654084","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":"Distributed computing in the asynchronous LOCAL model","authors":"Carole Delporte-Gallet,&nbsp;Hugues Fauconnier,&nbsp;Pierre Fraigniaud,&nbsp;Mikaël Rabie","doi":"10.1016/j.tcs.2024.114952","DOIUrl":"10.1016/j.tcs.2024.114952","url":null,"abstract":"<div><div>The <span>LOCAL</span> model is among the main models for studying locality in the framework of distributed network computing. This model is however subject to pertinent criticisms, including the facts that all nodes wake up simultaneously, perform in lock steps, and are failure-free. We show that relaxing these hypotheses to some extent does not hurt local computing. In particular, we show that, for any task <em>T</em> associated to a locally checkable labeling (<span>lcl</span>), if <em>T</em> is solvable in <em>t</em> rounds by a deterministic algorithm in the <span>LOCAL</span> model, then <em>T</em> remains solvable by a deterministic algorithm in <span><math><mi>O</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span> rounds in an asynchronous variant of the <span>LOCAL</span> model whenever <span><math><mi>t</mi><mo>=</mo><mi>O</mi><mo>(</mo><mtext>polylog</mtext><mspace></mspace><mi>n</mi><mo>)</mo></math></span>. This improves the result by Castañeda et al. [TCS, 2019], which was restricted to 3-coloring the rings. More generally, the main contribution of this paper is to show that, perhaps surprisingly, asynchrony and failures in the computations do not restrict the power of the <span>LOCAL</span> model, as long as the communications remain synchronous and failure-free. To this end, this paper introduces a new distributed renaming technique to provide nodes with consistent identifiers.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1025 ","pages":"Article 114952"},"PeriodicalIF":0.9,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656202","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":"Structural parameterizations of vertex integrity","authors":"Tatsuya Gima ,&nbsp;Tesshu Hanaka ,&nbsp;Yasuaki Kobayashi ,&nbsp;Ryota Murai ,&nbsp;Hirotaka Ono ,&nbsp;Yota Otachi","doi":"10.1016/j.tcs.2024.114954","DOIUrl":"10.1016/j.tcs.2024.114954","url":null,"abstract":"<div><div>The graph parameter <em>vertex integrity</em> measures how vulnerable a graph is to a removal of a small number of vertices. More precisely, a graph with small vertex integrity admits a small number of vertex removals to make the remaining connected components small. In this paper, we initiate a systematic study of structural parameterizations of the problem of computing the unweighted/weighted vertex integrity. As structural graph parameters, we consider well-known parameters such as clique-width, treewidth, pathwidth, treedepth, modular-width, neighborhood diversity, twin cover number, and cluster vertex deletion number. We show several positive and negative results and present sharp complexity contrasts. We also show that the vertex integrity can be approximated within an <span><math><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mrow><mi>opt</mi></mrow><mo>)</mo></math></span> factor.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1024 ","pages":"Article 114954"},"PeriodicalIF":0.9,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586214","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":"Instance-optimal information-based voting","authors":"Flavio Chierichetti","doi":"10.1016/j.tcs.2024.114945","DOIUrl":"10.1016/j.tcs.2024.114945","url":null,"abstract":"&lt;div&gt;&lt;div&gt;The classical Condorcet Jury Theorem considers a voting scenario in which there exists a candidate whose election would be ideal for each voter; each voter, though, has only a limited understanding of the world and is thus unable to determine exactly who this candidate is. The main question in this scenario is whether the voters, acting individually, can cast their ballots so that the unknown optimal candidate wins the election, and the welfare of the group of voters is maximized.&lt;/div&gt;&lt;div&gt;In this setting, each candidate is represented by a known probability distribution over signals about the world that the voters can perceive, that is, over bits. One of these candidates is chosen (secretively, by an adversary) to be the &lt;em&gt;ideal&lt;/em&gt; candidate. Afterwards, each voter samples this unknown candidate's distribution once and casts a ballot with the hope that the unknown ideal candidate wins the election.&lt;/div&gt;&lt;div&gt;In this paper, we consider the famous Condorcet voting system, as well as some of its variants. First, we give a positive answer to an open question of Chierichetti and Kleinberg &lt;span&gt;&lt;span&gt;[8]&lt;/span&gt;&lt;/span&gt;, and show that, with Condorcet voting, there exists a uniform voting strategy that makes the group of voters succeed with probability &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; provided that &lt;span&gt;&lt;math&gt;&lt;mi&gt;Θ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;tv&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;ln&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; voters take part in the election — here, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;tv&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is the minimum total variation distance between the distributions of two candidates.&lt;/div&gt;&lt;div&gt;We also give a uniform voting strategy for the Copeland voting system (a variant of Condorcet) that makes the group succeed with probability &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mi&gt;Θ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;ln&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; voters, where &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is the minimum Hellinger distance between the distributions. Our uniform Copeland strategy, then, is an &lt;em&gt;instance-optimal&lt;/em&gt; hypothesis testing algorithm: constants aside, the strategy is as efficient as the optimal omniscient algorithm which determines the unknown candidate after having directly observed each of the signals perceived by the voters. Then, we “derandomize” our uniform Copeland strategy, and obtain a Condorcet strategy that achieves instance-optimality at the cost of losing uniformity; finally, we prove that this loss of uniformity is necessary: no uniform Co","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1024 ","pages":"Article 114945"},"PeriodicalIF":0.9,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586213","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":"Parking problem by oblivious mobile robots in infinite grids","authors":"Abhinav Chakraborty ,&nbsp;Krishnendu Mukhopadhyaya","doi":"10.1016/j.tcs.2024.114953","DOIUrl":"10.1016/j.tcs.2024.114953","url":null,"abstract":"<div><div>In this paper, the parking problem of a swarm of mobile robots has been studied. The robots are deployed at the nodes of an infinite grid, which has a subset of prefixed nodes marked as <em>parking nodes</em>. A parking node <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> has a capacity of <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>, which is given as an input and represents the number of robots it is capable of accommodating. As a solution to the parking problem, in the final configuration, robots need to partition themselves into groups so that each parking node contains a number of robots that are equal to the capacity of the node. It is assumed that the number of robots in the initial configuration equals the sum of the capacities of the parking nodes. The robots are assumed to be autonomous, anonymous, homogeneous, identical and oblivious. They operate under an asynchronous scheduler. They do not have any agreement on the coordinate axes, nor do they agree on a common chirality. All the initial configurations for which the problem is unsolvable have been identified. A deterministic distributed algorithm has been proposed for the remaining configurations, ensuring the solvability of the problem.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1023 ","pages":"Article 114953"},"PeriodicalIF":0.9,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142653124","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":"Double declined subnetwork reliability analysis in bubble-sort networks under node fault model","authors":"Kaiyue Meng,&nbsp;Yuxing Yang","doi":"10.1016/j.tcs.2024.114941","DOIUrl":"10.1016/j.tcs.2024.114941","url":null,"abstract":"<div><div>The <em>n</em>-dimensional bubble-sort network <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> is a competitive interconnection network that could be used to construct large-scale multiprocessor computer systems. Let <em>p</em> be the reliability of each node in <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> and let <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msub><mo>(</mo><mi>p</mi><mo>)</mo></math></span> be the <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msub></math></span>-subnetwork reliability (i.e., double declined subnetwork reliability) in <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> under the equiprobability node fault model. In this paper, the bounds on <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msub><mo>(</mo><mi>p</mi><mo>)</mo></math></span> are derived for <span><math><mi>n</mi><mo>≥</mo><mn>4</mn></math></span>, and an algorithm is given to further verify the accuracy of the lower and upper bounds. The MTTFs that maintain the healthy state of different numbers of disjoint <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msub></math></span>'s in <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> under different partition patterns are calculated. Simulations are also carried out to verify the MTTFs. Both the theoretical result and the simulating result show that using the flexible partition pattern will make the network more reliable in the sense of double declined subnetwork availability.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1023 ","pages":"Article 114941"},"PeriodicalIF":0.9,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553641","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":"Algebraic properties and transformations of monographs","authors":"Thierry Boy de la Tour","doi":"10.1016/j.tcs.2024.114939","DOIUrl":"10.1016/j.tcs.2024.114939","url":null,"abstract":"<div><div>Monographs are graph-like structures with directed edges of unlimited length that are freely adjacent to each other. The standard nodes are represented as edges of length zero. They can be drawn in a way consistent with standard graphs and many others, like E-graphs or ∞-graphs. The category of monographs share many properties with the categories of graph structures (algebras of monadic many-sorted signatures, equivalent to presheaf toposes), except that there is no terminal monograph. It is universal in the sense that its slice categories (or categories of typed monographs) are equivalent to the categories of graph structures. Type monographs thus emerge as a natural way of specifying graph structures. A detailed analysis of single and double pushout transformations of monographs is provided, and a notion of attributed typed monographs generalizing typed attributed E-graphs is analyzed w.r.t. attribute-preserving transformations.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1024 ","pages":"Article 114939"},"PeriodicalIF":0.9,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553817","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}