Theoretical Computer Science最新文献

{"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}

{"title":"Priority algorithms with advice for disjoint path allocation problems","authors":"Hans-Joachim Böckenhauer ,&nbsp;Fabian Frei ,&nbsp;Silvan Horvath","doi":"10.1016/j.tcs.2024.114942","DOIUrl":"10.1016/j.tcs.2024.114942","url":null,"abstract":"<div><div>We analyze the Disjoint Path Allocation problem (DPA) in the priority framework. Motivated by the problem of traffic regulation in communication networks, DPA consists of allocating edge-disjoint paths in a graph. Like an online algorithm, a priority algorithm receives its input sequentially and must output irrevocable decisions for individual input items before having seen the entire input. However, in contrast to the online setting, a priority algorithm may choose an order on the set of all possible input items and the actual input is then presented according to this order. A priority algorithm is thus a natural model for the intuitively well-understood concept of a greedy algorithm.</div><div>Mainly motivated by their application for proving lower bounds, we also consider priority algorithms with advice, thus measuring the necessary amount of information about the yet unknown parts of the input.</div><div>Besides considering the classical variant of the DPA problem on paths and the related problem of Length-Weighted DPA, we mainly focus on DPA on trees. We show asymptotically matching upper and lower bounds on the advice necessary for optimality in LWDPA and generalize the known optimality result for DPA on paths to trees with maximal degree at most 3. On trees with higher maximal degree, we prove matching upper and lower bounds on the approximation ratio in the advice-free priority setting as well as upper and lower bounds on the advice necessary to achieve optimality.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1021 ","pages":"Article 114942"},"PeriodicalIF":0.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554209","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":"Euclidean division by d in base b","authors":"Jean-Éric Pin","doi":"10.1016/j.tcs.2024.114937","DOIUrl":"10.1016/j.tcs.2024.114937","url":null,"abstract":"<div><div>Let <span><math><mi>b</mi><mo>⩾</mo><mn>2</mn></math></span> be an integer. For each positive integer <em>d</em>, let <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>d</mi><mo>,</mo><mi>b</mi></mrow></msub></math></span> be the Euclidean division by <em>d</em> in base <em>b</em>, that is, the function which associates to a word <em>u</em> in <span><math><msup><mrow><mo>{</mo><mn>0</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>b</mi><mo>−</mo><mn>1</mn><mo>}</mo></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>, representing an integer <em>n</em> in base <em>b</em>, the unique word of the same length as <em>u</em> representing the quotient of the division of <em>n</em> by <em>d</em>. We describe the pure sequential transducer realizing this function and analyze the algebraic structure of its syntactic monoid. We compute its size, describe its Green's relations and its minimum ideal. As a consequence, we show that it is a group if and only if <em>d</em> and <em>b</em> are coprime numbers, it is a <em>p</em>-group if and only if <em>d</em> is a power of <em>p</em> and <em>b</em> is congruent to 1 modulo <em>p</em> and it is an aperiodic monoid if and only if <em>d</em> divides some power of <em>b</em>. The uniform continuity of <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>d</mi><mo>,</mo><mi>b</mi></mrow></msub></math></span> for the pro-group metric was studied by Reutenauer and Schützenberger in 1995. We launch a similar study for the uniform continuity of <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>d</mi><mo>,</mo><mi>b</mi></mrow></msub></math></span> with respect to the pro-<em>p</em> metric, where <em>p</em> is a prime number.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1024 ","pages":"Article 114937"},"PeriodicalIF":0.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553818","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":"Restricted holant dichotomy on domain sizes 3 and 4","authors":"Yin Liu,&nbsp;Austen Z. Fan,&nbsp;Jin-Yi Cai","doi":"10.1016/j.tcs.2024.114931","DOIUrl":"10.1016/j.tcs.2024.114931","url":null,"abstract":"<div><div><span><math><msup><mrow><mi>Holant</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>f</mi><mo>)</mo></math></span> denotes a class of counting problems specified by a constraint function <em>f</em>. We prove complexity dichotomy theorems for <span><math><msup><mrow><mi>Holant</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>f</mi><mo>)</mo></math></span> in two settings: (1) <em>f</em> is any symmetric arity-3 real-valued function on input of domain size 3. (2) <em>f</em> is any symmetric arity-3 <span><math><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></span>-valued function on input of domain size 4.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1023 ","pages":"Article 114931"},"PeriodicalIF":0.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553640","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":"Comparison of machine learning algorithms for classification of Big Data sets","authors":"Barkha Singh,&nbsp;Sreedevi Indu,&nbsp;Sudipta Majumdar","doi":"10.1016/j.tcs.2024.114938","DOIUrl":"10.1016/j.tcs.2024.114938","url":null,"abstract":"<div><div>This article analyzes and compares various Quantum machine learning algorithms on big data. The main contribution of this article is to provide a new machine-learning approach using Quantum computing for big data analysis with features of robust, novel, and effective Quantum computing. This work proposes a global Quantum feature extraction technique for large-scale image classification based on Schmidt decomposition for the first time. Additionally, a new version of the Quantum learning algorithm is presented, which uses the features of Hamming distance to classify images. With the help of algorithm analysis and experimental findings from the benchmark database Caltech 101, a successful method for large-scale image classification is developed and put forth in the context of big data. The proposed model yields an average accuracy of 98% with the proposed enhanced Quantum classifier, QeSVM classifier, swarm particle optimizer with Twin wave SVM, QPSO-TWSVM, and other Q-CNN models on different Big Data sets.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1024 ","pages":"Article 114938"},"PeriodicalIF":0.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586215","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":"No six-cell neighborhood cellular automaton solves the parity problem","authors":"Anna Nenca ,&nbsp;Barbara Wolnik ,&nbsp;Bernard De Baets","doi":"10.1016/j.tcs.2024.114923","DOIUrl":"10.1016/j.tcs.2024.114923","url":null,"abstract":"<div><div>The parity problem is one of the best-known classification problems studied to examine the computational abilities of cellular automata. In this inverse problem, one is looking for a cellular automaton that can classify each initial configuration into one of two classes according to its parity. In the case of deterministic one-dimensional cellular automata, there exists a local rule that effectively solves the parity problem, but it is unknown whether it is the simplest possible rule. Specifically, it is known that a cellular automaton with a nine-cell neighborhood can solve the parity problem, whereas no cellular automaton with a five-cell neighborhood is capable of doing so. These findings have remained unimproved for the past 10 years. In this paper, we present novel tools that allow to narrow down the existing gap. With the help of these tools, we are able to demonstrate that there is no cellular automaton with a six-cell neighborhood capable of solving the parity problem.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1021 ","pages":"Article 114923"},"PeriodicalIF":0.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554208","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":"Constructing red-black spanners for mixed-charging vehicular networks","authors":"Sergey Bereg ,&nbsp;Yuya Higashikawa ,&nbsp;Naoki Katoh ,&nbsp;Junichi Teruyama ,&nbsp;Yuki Tokuni ,&nbsp;Binhai Zhu","doi":"10.1016/j.tcs.2024.114932","DOIUrl":"10.1016/j.tcs.2024.114932","url":null,"abstract":"<div><div>Motivated by the recent trend of increasing number of e-cars and hybrid cars, we investigate the problem of building a red-black spanner for a mixed-charging vehicular network. In such a network, we have two kinds of gas/charging stations: electric (black) and the traditional gas (red) stations. Our requirement is that one cannot connect two gas stations directly in the spanner (i.e., no red-red edge), and the goal is to build a linear-size spanner with a bounded stretch factor under this requirement. (In 2-d, it can be shown that a spanner with an optimal stretch factor could have a quadratic size and if one is constrained to build the spanner purely from a given road network then it is impossible to obtain a bounded stretch factor.) Our main results are summarized as follows.<ul><li><span>1.</span><span><div>In 1-d, a linear-size red-black spanner is built to satisfy the ‘no red-red edge’ requirement which achieves the optimal stretch factor.</div></span></li><li><span>2.</span><span><div>In 2-d and under the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> metric, we build a linear-size red-black spanner satisfying the ‘no red-red edge’ requirement which achieves a stretch factor of 1.998.</div></span></li><li><span>3.</span><span><div>In 2-d and under the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> metric, a linear-size red-black spanner is built to satisfy the ‘no red-red edge’ requirement which achieves a stretch factor of 3.613.</div></span></li></ul></div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1023 ","pages":"Article 114932"},"PeriodicalIF":0.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553639","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":"Parameterized complexity of vertex splitting to pathwidth at most 1","authors":"Jakob Baumann,&nbsp;Matthias Pfretzschner,&nbsp;Ignaz Rutter","doi":"10.1016/j.tcs.2024.114928","DOIUrl":"10.1016/j.tcs.2024.114928","url":null,"abstract":"<div><div>Motivated by the planarization of 2-layered straight-line drawings, we consider the problem of modifying a graph such that the resulting graph has pathwidth at most 1. The problem <span>Pathwidth-One Vertex Explosion</span> (<span>POVE</span>) asks whether such a graph can be obtained using at most <em>k</em> vertex explosions, where a <em>vertex explosion</em> replaces a vertex <em>v</em> by <span><math><mi>deg</mi><mo>⁡</mo><mo>(</mo><mi>v</mi><mo>)</mo></math></span> degree-1 vertices, each incident to exactly one edge that was originally incident to <em>v</em>. For <span>POVE</span>, we give an FPT algorithm with running time <span><math><mi>O</mi><mo>(</mo><msup><mrow><mn>4</mn></mrow><mrow><mi>k</mi></mrow></msup><mo>⋅</mo><mi>m</mi><mo>)</mo></math></span> and an <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> kernel, thereby improving over the <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>6</mn></mrow></msup><mo>)</mo></math></span>-kernel by Ahmed et al. <span><span>[2]</span></span> in a more general setting. Similarly, a <em>vertex split</em> replaces a vertex <em>v</em> by two distinct vertices <span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> and distributes the edges originally incident to <em>v</em> arbitrarily to <span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. Analogously to <span>POVE</span>, we define the problem variant <span>Pathwidth-One Vertex Splitting</span> (<span>POVS</span>) that uses the split operation instead of vertex explosions. Here we obtain a linear kernel and an algorithm with running time <span><math><mi>O</mi><mo>(</mo><msup><mrow><mo>(</mo><mn>6</mn><mi>k</mi><mo>+</mo><mn>12</mn><mo>)</mo></mrow><mrow><mi>k</mi></mrow></msup><mo>⋅</mo><mi>m</mi><mo>)</mo></math></span>. This answers an open question by Ahmed et al. <span><span>[2]</span></span>.</div><div>Finally, we consider the problem Π<span>-VertexSplitting</span> (Π<span>-VS</span>), which generalizes the problem <span>POVS</span> and asks whether a given graph can be turned into a graph of a specific graph class Π using at most <em>k</em> vertex splits. For graph classes Π that can be defined in monadic second-order graph logic (MSO₂), we show that the problem Π<span>-VS</span> can be expressed as an MSO₂ formula, resulting in an FPT algorithm for Π<span>-VS</span> parameterized by <em>k</em> if Π additionally has bounded treewidth. We obtain the same result for the problem variant using vertex explosions.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1021 ","pages":"Article 114928"},"PeriodicalIF":0.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554211","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":"MODRED: A code-based non-interactive key exchange protocol","authors":"Junling Pei,&nbsp;Fang-Wei Fu","doi":"10.1016/j.tcs.2024.114943","DOIUrl":"10.1016/j.tcs.2024.114943","url":null,"abstract":"<div><div>How to construct a non-interactive key exchange (NIKE) protocol based on coding theory is an opening problem. In this paper, we propose the first code-based NIKE protocol MODRED, whose security relies on the hardness of the Restricted Syndrome Decoding (R-SD) problem and its variant. A non-interactive error reconciliation mechanism is presented and applied to MODRED, which enables the two sides of communication to “approximately agree” on the shared key. This is of great significance because it may lead to a more generic framework construction. Furthermore, our proposal is competitive and practical. We provide an initial choice of parameters for MODRED, tailored to 120-bit post-quantum security level, yielding the public keys of less than 1.2 MBs.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1021 ","pages":"Article 114943"},"PeriodicalIF":0.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554253","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":"An approximate cost recovery scheme for the k-product facility location game with penalties","authors":"Xiaowei Li,&nbsp;Xiwen Lu","doi":"10.1016/j.tcs.2024.114933","DOIUrl":"10.1016/j.tcs.2024.114933","url":null,"abstract":"<div><div>This paper considers a variant of the classic facility location game called the <em>k</em>-product facility location game with penalties. In this game, each facility can only produce at most one kind of product and each customer must be supplied with <em>k</em> different products or be rejected by paying the penalty cost. The authors propose a 2-approximate cross-monotonic cost-sharing scheme for the game when <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span>, and a (<span><math><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mi>k</mi><mo>−</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>)-approximate cross-monotonic cost-sharing scheme when <span><math><mi>k</mi><mo>≥</mo><mn>3</mn></math></span>, respectively. Furthermore, the lower bound is obtained for the <em>k</em>-product facility location game with penalties.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1021 ","pages":"Article 114933"},"PeriodicalIF":0.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554148","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}