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A signature scheme constructed from zero knowledge argument of knowledge for the subgraph isomorphism problem
IF 0.9 4区 计算机科学
Theoretical Computer Science Pub Date : 2025-03-08 DOI: 10.1016/j.tcs.2025.115180
Chii Liang Ng , Denis C.K. Wong , Gek L. Chia , Bok Min Goi , Wai Kong Lee , Wun She Yap
{"title":"A signature scheme constructed from zero knowledge argument of knowledge for the subgraph isomorphism problem","authors":"Chii Liang Ng ,&nbsp;Denis C.K. Wong ,&nbsp;Gek L. Chia ,&nbsp;Bok Min Goi ,&nbsp;Wai Kong Lee ,&nbsp;Wun She Yap","doi":"10.1016/j.tcs.2025.115180","DOIUrl":"10.1016/j.tcs.2025.115180","url":null,"abstract":"<div><div>In this paper, we propose an honest-verifier zero knowledge argument of knowledge for subgraph isomorphism and convert it into a signature scheme by using the well-known Fiat-Shamir transformation. Our protocol generalizes the famous Blum's zero knowledge proof for graph Hamiltonicity, but with a major difference: we additionally commit to the permuted subgraph isomorphism during commitment phase. This modification is made to satisfy a property called “quantum computationally unique response”, which ensures that an efficient quantum adversary cannot distinguish whether the superposition of the response is measured. This property is utilized to prove that the resulting signature scheme achieves EUF-CMA security in the quantum random oracle model.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1038 ","pages":"Article 115180"},"PeriodicalIF":0.9,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600868","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}
引用次数: 0
Some new results on equitable tree-coloring parameters of graphs
IF 0.9 4区 计算机科学
Theoretical Computer Science Pub Date : 2025-03-07 DOI: 10.1016/j.tcs.2025.115178
Bei Niu
{"title":"Some new results on equitable tree-coloring parameters of graphs","authors":"Bei Niu","doi":"10.1016/j.tcs.2025.115178","DOIUrl":"10.1016/j.tcs.2025.115178","url":null,"abstract":"<div><div>Equitable tree-coloring addresses a structure decomposition problem in communication networks while considering security aspects. Specifically, an equitable tree-<em>t</em>-coloring of a graph is a vertex <em>t</em>-coloring such that each color class induces a forest and the size of any two color classes differs by at most one. This paper demonstrated if <em>G</em> is an equitably tree-<em>t</em>-colorable graph and <em>H</em> is an arbitrary graph with less than 2<em>t</em> vertices (<span><math><mi>n</mi><mo>&lt;</mo><mn>2</mn><mi>t</mi></math></span>), it is possible to construct an equitable tree-<em>t</em>-coloring of the corona product graph <span><math><mi>G</mi><mo>∘</mo><mi>H</mi></math></span> in cubic time. Additionally, the equitable tree-coloring of the extended corona product formed by combining graphs <em>G</em> and <em>H</em> has also been investigated.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1037 ","pages":"Article 115178"},"PeriodicalIF":0.9,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143579121","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}
引用次数: 0
Move-optimal arbitrary pattern formation by mobile robots on rectangular grid using near-optimal spatial area
IF 0.9 4区 计算机科学
Theoretical Computer Science Pub Date : 2025-03-07 DOI: 10.1016/j.tcs.2025.115179
Avisek Sharma , Satakshi Ghosh , Pritam Goswami , Buddhadeb Sau
{"title":"Move-optimal arbitrary pattern formation by mobile robots on rectangular grid using near-optimal spatial area","authors":"Avisek Sharma ,&nbsp;Satakshi Ghosh ,&nbsp;Pritam Goswami ,&nbsp;Buddhadeb Sau","doi":"10.1016/j.tcs.2025.115179","DOIUrl":"10.1016/j.tcs.2025.115179","url":null,"abstract":"<div><div>Arbitrary pattern formation (APF) is a well-studied problem in swarm robotics. To the best of our knowledge, the problem has been considered in two different settings: one in a euclidean plane and another in an infinite grid. This work deals with the problem in an infinite rectangular grid setting. The previous works in literature dealing with the APF problem in an infinite grid had a fundamental issue. These deterministic algorithms use a lot of spatial area in the grid to solve the problem, mainly to maintain the asymmetry of the configuration and avoid any collision. These solution techniques cannot be useful if there is a spatial constraint in the application field. In this work, we consider luminous robots (each robot equipped with a light that can take three colors) to avoid symmetry, but we carefully designed a deterministic algorithm that solves the APF problem using the minimal required spatial area in the grid if the initial pattern is asymmetric. The robots are autonomous, identical, and anonymous, and they operate in Look-Compute-Move cycles under a fully-asynchronous scheduler. The APF algorithm proposed in <span><span>[1]</span></span> by Bose et al. can be modified using luminous robots so that it uses minimal spatial area, but that algorithm is not move-optimal. The algorithm proposed in this paper not only uses minimal spatial area but is also asymptotically move-optimal.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1038 ","pages":"Article 115179"},"PeriodicalIF":0.9,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143609682","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}
引用次数: 0
Solving NP-hard problems on GaTEx graphs: Linear-time algorithms for perfect orderings, cliques, colorings, and independent sets
IF 0.9 4区 计算机科学
Theoretical Computer Science Pub Date : 2025-03-07 DOI: 10.1016/j.tcs.2025.115157
Marc Hellmuth , Guillaume E. Scholz
{"title":"Solving NP-hard problems on GaTEx graphs: Linear-time algorithms for perfect orderings, cliques, colorings, and independent sets","authors":"Marc Hellmuth ,&nbsp;Guillaume E. Scholz","doi":"10.1016/j.tcs.2025.115157","DOIUrl":"10.1016/j.tcs.2025.115157","url":null,"abstract":"<div><div>The class of <span>Ga</span>lled-<span>T</span>ree <span>Ex</span>plainable (<span>GaTEx</span>) graphs has recently been discovered as a natural generalization of cographs. Cographs are precisely those graphs that can be uniquely represented by a rooted tree where the leaves correspond to the vertices of the graph. As a generalization, <span>GaTEx</span> graphs are precisely those that can be uniquely represented by a particular rooted acyclic network, called a galled-tree.</div><div>This paper explores the use of galled-trees to solve combinatorial problems on <span>GaTEx</span> graphs that are, in general, NP-hard. We demonstrate that finding a maximum clique, an optimal vertex coloring, a perfect order, as well as a maximum independent set in <span>GaTEx</span> graphs can be efficiently done in linear time. The key idea behind the linear-time algorithms is to utilize the galled-trees that explain the <span>GaTEx</span> graphs as a guide for computing the respective cliques, colorings, perfect orders, or independent sets.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1037 ","pages":"Article 115157"},"PeriodicalIF":0.9,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143579122","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}
引用次数: 0
Kolmogorov-Loveland betting strategies lose the Betting game on open sets
IF 0.9 4区 计算机科学
Theoretical Computer Science Pub Date : 2025-03-07 DOI: 10.1016/j.tcs.2025.115177
Tomislav Petrović
{"title":"Kolmogorov-Loveland betting strategies lose the Betting game on open sets","authors":"Tomislav Petrović","doi":"10.1016/j.tcs.2025.115177","DOIUrl":"10.1016/j.tcs.2025.115177","url":null,"abstract":"<div><div>Whether Kolmogorov-Loveland randomness (KLR) is the same as Martin-Löf randomness (MLR) is a major open problem in the study of algorithmic randomness. More general classes of betting strategies than Kolmogorov-Loveland ones have been studied in <span><span>[8]</span></span>, <span><span>[13]</span></span>, <span><span>[12]</span></span>. In each case it was proven that the class induces a notion of randomness equivalent to MLR. In all of those proofs, it was shown that the class contains a finite set of betting strategies such that for any given bound, when betting on a binary sequence contained in an effective open set of small enough measure, at least one of the betting strategies in the set earns capital larger than the bound. We show that the class of Kolmogorov-Loveland betting strategies does not have this property.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1037 ","pages":"Article 115177"},"PeriodicalIF":0.9,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600729","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}
引用次数: 0
Reconfigurable routing in data center networks
IF 0.9 4区 计算机科学
Theoretical Computer Science Pub Date : 2025-03-06 DOI: 10.1016/j.tcs.2025.115154
David C. Kutner, Iain A. Stewart
{"title":"Reconfigurable routing in data center networks","authors":"David C. Kutner,&nbsp;Iain A. Stewart","doi":"10.1016/j.tcs.2025.115154","DOIUrl":"10.1016/j.tcs.2025.115154","url":null,"abstract":"<div><div>A hybrid network is a static (electronic) network that is augmented with optical switches. The Reconfigurable Routing Problem (RRP) in hybrid networks is the problem of finding settings for the optical switches augmenting a static network so as to achieve optimal delivery of some given workload. The problem has previously been studied in various scenarios with both tractability and NP-hardness results obtained. However, the data center and interconnection networks to which the problem is most relevant are almost always such that the static network is highly structured (and often node-symmetric) whereas all previous results assume that the static network can be arbitrary (which makes existing computational hardness results less technologically relevant and also easier to obtain). In this paper, and for the first time, we prove various intractability results for RRP where the underlying static network is highly structured, for example consisting of a hypercube, and also extend some existing tractability results.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1038 ","pages":"Article 115154"},"PeriodicalIF":0.9,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143609681","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}
引用次数: 0
The exact spanning ratio of the parallelogram Delaunay graph
IF 0.9 4区 计算机科学
Theoretical Computer Science Pub Date : 2025-03-05 DOI: 10.1016/j.tcs.2025.115152
Prosenjit Bose , Jean-Lou De Carufel , Sandrine Njoo
{"title":"The exact spanning ratio of the parallelogram Delaunay graph","authors":"Prosenjit Bose ,&nbsp;Jean-Lou De Carufel ,&nbsp;Sandrine Njoo","doi":"10.1016/j.tcs.2025.115152","DOIUrl":"10.1016/j.tcs.2025.115152","url":null,"abstract":"<div><div>Finding the exact spanning ratio of a Delaunay graph has been one of the longstanding open problems in Computational Geometry. Currently there are only four convex shapes for which the exact spanning ratio of their Delaunay graph is known: the equilateral triangle, the square, the regular hexagon and the rectangle. We add a fifth convex shape by proving the exact spanning ratio of the parallelogram Delaunay graph. The worst-case spanning ratio is <em>exactly</em><span><span><span><math><mfrac><mrow><msqrt><mrow><mn>2</mn></mrow></msqrt><msqrt><mrow><mn>1</mn><mo>+</mo><msup><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>2</mn><mi>A</mi><mi>cos</mi><mo>⁡</mo><mo>(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo><mo>+</mo><mo>(</mo><mi>A</mi><mo>+</mo><mi>cos</mi><mo>⁡</mo><mo>(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo><mo>)</mo><msqrt><mrow><mn>1</mn><mo>+</mo><msup><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>2</mn><mi>A</mi><mi>cos</mi><mo>⁡</mo><mo>(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></mrow></msqrt></mrow></msqrt></mrow><mrow><mi>sin</mi><mo>⁡</mo><mo>(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></mrow></mfrac><mo>,</mo></math></span></span></span> where <em>A</em> is the aspect ratio and <span><math><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is the non-obtuse angle of the parallelogram.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1037 ","pages":"Article 115152"},"PeriodicalIF":0.9,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600730","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}
引用次数: 0
Compact zero-knowledge arguments for Blum integers
IF 0.9 4区 计算机科学
Theoretical Computer Science Pub Date : 2025-03-05 DOI: 10.1016/j.tcs.2025.115155
Jules Maire , Damien Vergnaud
{"title":"Compact zero-knowledge arguments for Blum integers","authors":"Jules Maire ,&nbsp;Damien Vergnaud","doi":"10.1016/j.tcs.2025.115155","DOIUrl":"10.1016/j.tcs.2025.115155","url":null,"abstract":"<div><div>We present a communication-efficient zero-knowledge argument of knowledge for the factorization of Blum integers, a special class of integers of the form <span><math><mi>n</mi><mo>=</mo><mi>p</mi><mi>q</mi></math></span>, where <em>p</em> and <em>q</em> are distinct prime numbers satisfying <span><math><mi>p</mi><mo>≡</mo><mi>q</mi><mo>≡</mo><mn>3</mn><mspace></mspace><mrow><mi>mod</mi></mrow><mspace></mspace><mn>4</mn></math></span> and <span><math><mi>p</mi><mo>≃</mo><mi>q</mi><mo>≃</mo><msqrt><mrow><mi>n</mi></mrow></msqrt></math></span>. Existing protocols for proving such statements often incur significant communication costs, especially when demonstrating that <em>p</em> and <em>q</em> are of nearly equal size.</div><div>We leverage the MPC-in-the-head paradigm, a cryptographic technique that transforms secure multi-party computation protocols into efficient zero-knowledge proof systems. In our protocol, the prover uses additive sharing of <em>p</em> and <em>q</em> over the integers. This approach simplifies proving the size relationship <span><math><mi>p</mi><mo>≃</mo><mi>q</mi><mo>≃</mo><msqrt><mrow><mi>n</mi></mrow></msqrt></math></span> and the congruence <span><math><mi>p</mi><mo>≡</mo><mi>q</mi><mo>≡</mo><mn>3</mn><mspace></mspace><mrow><mi>mod</mi></mrow><mspace></mspace><mn>4</mn></math></span> without requiring costly range proofs. To verify the primality of <em>p</em> and <em>q</em>, we employ the Boneh-Franklin biprimality test.</div><div>Our protocol achieves a significant reduction in communication complexity. For a 2048-bit integer <em>n</em> and 128-bit security, we construct an argument as small as 6.3 KB, with prover and verifier computational costs comparable to existing protocols that require over 131 KB.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1038 ","pages":"Article 115155"},"PeriodicalIF":0.9,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600869","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}
引用次数: 0
Closure and decision properties for higher-dimensional automata
IF 0.9 4区 计算机科学
Theoretical Computer Science Pub Date : 2025-03-03 DOI: 10.1016/j.tcs.2025.115156
Amazigh Amrane , Hugo Bazille , Uli Fahrenberg , Krzysztof Ziemiański
{"title":"Closure and decision properties for higher-dimensional automata","authors":"Amazigh Amrane ,&nbsp;Hugo Bazille ,&nbsp;Uli Fahrenberg ,&nbsp;Krzysztof Ziemiański","doi":"10.1016/j.tcs.2025.115156","DOIUrl":"10.1016/j.tcs.2025.115156","url":null,"abstract":"<div><div>We report some further developments regarding the language theory of higher-dimensional automata (HDAs). Regular languages of HDAs are sets of finite interval partially ordered multisets (pomsets) with interfaces. We show a pumping lemma which allows us to expose a class of non-regular languages. Concerning decision and closure properties, we show that inclusion of regular languages is decidable (hence is emptiness), and that intersections of regular languages are again regular. Yet complements of regular languages are not always regular. We introduce a width-bounded complement and show that width-bounded complements of regular languages are again regular.</div><div>We also study determinism and ambiguity. We show that it is decidable whether a regular language is accepted by a deterministic HDA and that there exist regular languages with unbounded ambiguity. Finally, we characterize one-letter deterministic languages in terms of ultimately periodic functions.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1036 ","pages":"Article 115156"},"PeriodicalIF":0.9,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143549042","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}
引用次数: 0
Ordinal maximin guarantees for group fair division
IF 0.9 4区 计算机科学
Theoretical Computer Science Pub Date : 2025-03-03 DOI: 10.1016/j.tcs.2025.115151
Pasin Manurangsi , Warut Suksompong
{"title":"Ordinal maximin guarantees for group fair division","authors":"Pasin Manurangsi ,&nbsp;Warut Suksompong","doi":"10.1016/j.tcs.2025.115151","DOIUrl":"10.1016/j.tcs.2025.115151","url":null,"abstract":"<div><div>We investigate fairness in the allocation of indivisible items among groups of agents using the notion of maximin share (MMS). While previous work has shown that no nontrivial multiplicative MMS approximation can be guaranteed in this setting for general group sizes, we demonstrate that ordinal relaxations are much more useful. For example, we show that if <em>n</em> agents are distributed equally across <em>g</em> groups, there exists a 1-out-of-<em>k</em> MMS allocation for <span><math><mi>k</mi><mo>=</mo><mi>O</mi><mo>(</mo><mi>g</mi><mi>log</mi><mo>⁡</mo><mo>(</mo><mi>n</mi><mo>/</mo><mi>g</mi><mo>)</mo><mo>)</mo></math></span>, while if all but a constant number of agents are in the same group, we obtain <span><math><mi>k</mi><mo>=</mo><mi>O</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>. We also establish the tightness of these bounds and provide non-asymptotic results for the case of two groups. Our proofs leverage connections to combinatorial covering designs.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1036 ","pages":"Article 115151"},"PeriodicalIF":0.9,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143549054","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}
引用次数: 0
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