International Journal of Foundations of Computer Science最新文献

{"title":"Edge-Disjoint Hamiltonian Cycles in Balanced Hypercubes with Applications to Fault-Tolerant Data Broadcasting","authors":"Shuai Liu, Yan Wang, Jianxi Fan, Baolei Cheng","doi":"10.1142/s0129054124500047","DOIUrl":"https://doi.org/10.1142/s0129054124500047","url":null,"abstract":"<p>The existence of multiple edge-disjoint Hamiltonian cycles (EDHCs for short) is a desirable property of interconnection networks. These parallel cycles can provide an advantage for algorithms that require a ring structure. Additionally, EDHCs can enhance all-to-all data broadcasting and edge fault tolerance in network communications. In this paper, we investigate the construction of EDHCs in the balanced hypercube, which is a variant of the hypercube with many attractive properties, such as strong connectivity, regularity, and symmetry. In particular, each processor in the balanced hypercube has a backup processor that shares the common neighbors, enabling fault tolerance and efficient system reconfiguration. In 2019, Lü <i>et al.</i> provided an algorithm to construct two EDHCs in an <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi></math></span><span></span>-dimensional balanced hypercube <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>B</mi><msub><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span><span></span> for <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi><mo>≥</mo><mn>2</mn></math></span><span></span>. We further study this topic and give some construction schemes to construct <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mn>2</mn></mrow><mrow><mo stretchy=\"false\">⌊</mo><msub><mrow><mo>log</mo></mrow><mrow><mn>2</mn></mrow></msub><mi>n</mi><mo stretchy=\"false\">⌋</mo></mrow></msup></math></span><span></span> EDHCs in <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>B</mi><msub><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span><span></span> for <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi><mo>≥</mo><mn>2</mn></math></span><span></span>. Since <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mi>B</mi><msub><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span><span></span> is <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mn>2</mn><mi>n</mi></math></span><span></span>-regular, our result is optimal for <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi><mo>=</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>r</mi></mrow></msup></math></span><span></span> (<span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><mi>r</mi><mo>≥</mo><mn>1</mn></math></span><span></span>). In addition, we simulate the fault-tolerant data broadcasting through these parallel cycles as transmission channels.</p>","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140630649","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":"Algorithmic Aspects of Outer-Independent Double Roman Domination in Graphs","authors":"Amit Sharma, P. Venkata Subba Reddy, S. Arumugam, Jakkepalli Pavan Kumar","doi":"10.1142/s0129054124500059","DOIUrl":"https://doi.org/10.1142/s0129054124500059","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; be graph. For any function &lt;span&gt;&lt;math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mo stretchy=\"false\"&gt;{&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo stretchy=\"false\"&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;, let &lt;span&gt;&lt;math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo stretchy=\"false\"&gt;{&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;, &lt;span&gt;&lt;math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;. The function &lt;span&gt;&lt;math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; is called an outer-independent double Roman dominating function (OIDRDF) if the following conditions are satisfied.&lt;/p&gt;&lt;table border=\"0\" list-type=\"order\" width=\"95%\"&gt;&lt;tr&gt;&lt;td valign=\"top\"&gt;&lt;sup&gt;(i)&lt;/sup&gt;&lt;/td&gt;&lt;td colspan=\"5\" valign=\"top\"&gt;&lt;p&gt;If &lt;span&gt;&lt;math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;, then &lt;span&gt;&lt;math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;mo stretchy=\"false\"&gt;∩&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; or &lt;span&gt;&lt;math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;mo stretchy=\"false\"&gt;∩&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td valign=\"top\"&gt;&lt;sup&gt;(ii)&lt;/sup&gt;&lt;/td&gt;&lt;td colspan=\"5\" valign=\"top\"&gt;&lt;p&gt;If &lt;span&gt;&lt;math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;, then &lt;span&gt;&lt;math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;mo stretchy=\"false\"&gt;∩&lt;/mo&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo stretchy=\"false\"&gt;∪&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td valign=\"top\"&gt;&lt;sup&gt;(iii)&lt;/sup&gt;&lt;/td&gt;&lt;td colspan=\"5\" valign=\"top\"&gt;&lt;p&gt;&lt;span&gt;&lt;math altimg=\"eq-00011.gif\" display=\"inline\" overflow=","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":"26 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316560","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":"A Note of Reliability Analysis of SM-λ in Folded-Crossed Hypercube with Conditional Faults","authors":"Jinjie Ma, Mingzu Zhang, Chenxi Li, Hengji Qiao, Yang Fan","doi":"10.1142/s0129054124500035","DOIUrl":"https://doi.org/10.1142/s0129054124500035","url":null,"abstract":"&lt;p&gt;The fault tolerance of an interconnection network of parallel and distributed systems can be evaluated by various topological parameters of its underlying graph &lt;span&gt;&lt;math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;, with strong Menger edge connectivity being a vital parameter in this regard. A connected graph &lt;span&gt;&lt;math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; is called strongly Menger edge connected (SM-&lt;span&gt;&lt;math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;) if it connects any pair of vertices &lt;span&gt;&lt;math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; and &lt;span&gt;&lt;math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; with &lt;span&gt;&lt;math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mo&gt;min&lt;/mo&gt;&lt;mo stretchy=\"false\"&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;mo stretchy=\"false\"&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; number of edge-disjoint paths. Under the uniform distribution of faults in a large interconnection network, it is improbable that each faulty edge incident to a vertex will occur simultaneously. Thus, &lt;span&gt;&lt;math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;-strongly Menger edge connected of order &lt;span&gt;&lt;math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; was introduced in 2018 by He &lt;i&gt;et al.&lt;/i&gt; Here, &lt;span&gt;&lt;math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; is called as &lt;span&gt;&lt;math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;-strongly Menger edge connected of order &lt;span&gt;&lt;math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;, if &lt;span&gt;&lt;math altimg=\"eq-00014.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;−&lt;/mo&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; remains SM-&lt;span&gt;&lt;math altimg=\"eq-00015.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math altimg=\"eq-00016.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; is an arbitrary edge set in a graph &lt;span&gt;&lt;math altimg=\"eq-00017.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; with &lt;span&gt;&lt;math altimg=\"eq-00018.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; and the minimum degree of the remaining graph &lt;span&gt;&lt;math altimg=\"eq-00019.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;mo stretchy=\"fal","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":"56 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140196741","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":"Non-Adaptive and Adaptive Two-Sided Search with Fast Objects","authors":"Alexey Lebedev, Christian Deppe","doi":"10.1142/s0129054124500023","DOIUrl":"https://doi.org/10.1142/s0129054124500023","url":null,"abstract":"<p>In 1946, Koopman introduced a two-sided search model. In this model, a searched object is active and can move, at most, one step after each test. We analyze the model of a combinatorial two-sided search by allowing more moves of the searched object after each test. We give strategies and show that they are optimal. We consider adaptive and non-adaptive strategies. We show the surprising result that with the combinatorial two-sided search on a path graph, the optimal non-adaptive search needs the same number of tests as the corresponding adaptive strategy does. The strategy obtained can also be used as an encoding strategy to sent the position of a moving element through a transmission channel.</p>","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":"271 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140045330","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":"Smooth Subsum Search A Heuristic for Practical Integer Factorization","authors":"Markus Hittmeir","doi":"10.1142/s0129054123500296","DOIUrl":"https://doi.org/10.1142/s0129054123500296","url":null,"abstract":"<p>The two currently fastest general-purpose integer factorization algorithms are the Quadratic Sieve and the Number Field Sieve. Both techniques are used to find so-called smooth values of certain polynomials, i.e., values that factor completely over a set of small primes (the factor base). As the names of the methods suggest, a sieving procedure is used for the task of quickly identifying smooth values among the candidates in a certain range. While the Number Field Sieve is asymptotically faster, the Quadratic Sieve is still considered the most efficient factorization technique for numbers up to around 100 digits. In this paper, we challenge the Quadratic Sieve by presenting a novel approach based on representing smoothness candidates as sums that are always divisible by several of the primes in the factor base. The resulting values are generally smaller than those considered in the Quadratic Sieve, increasing the likelihood of them being smooth. Using the fastest implementations of the Self-initializing Quadratic Sieve in Python as benchmarks, a Python implementation of our approach runs consistently 5 to 7 times faster for numbers with 45–100 digits, and around 10 times faster for numbers with 30–40 digits. We discuss several avenues for further improvements and applications of the technique.</p>","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":"4311 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140045282","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":"A Verifiable Multi-Secret Sharing Scheme Based on ℓ-Intersection Pair of Cyclic Codes","authors":"Md Ajaharul Hossain, Ramakrishna Bandi","doi":"10.1142/s0129054123500284","DOIUrl":"https://doi.org/10.1142/s0129054123500284","url":null,"abstract":"A verifiable multi-secret sharing (VMSS) scheme addresses various security issues, helping in cheating detection and cheater identification. The dimension of the intersection of a given pair of cyclic codes over a finite field [Formula: see text] is represented by [Formula: see text]. In this paper, we propose a VMSS scheme based on an [Formula: see text]-intersection pair of cyclic codes. The proposed scheme is very useful for sharing a large number of secrets. If [Formula: see text] is the number of secrets in a threshold [Formula: see text] scheme, then for [Formula: see text], the computational complexity and the public values required in the reconstruction phase are much less compared to many existing schemes in the literature. Overall, the proposed scheme comprises nearly all the features, like being verifiable, testing participants’ integrity, checking Verifier frauds, and most importantly, it is of multi-use type.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":"4 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139209229","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":"Tree-Based Generation of Restricted Graph Languages","authors":"Henrik Björklund, Johanna Björklund, Petter Ericson","doi":"10.1142/s0129054123480106","DOIUrl":"https://doi.org/10.1142/s0129054123480106","url":null,"abstract":"Order-preserving DAG grammars (OPDGs) is a formalism for representing languages of structurally restricted graphs. As demonstrated in [17], they are sufficiently expressive to model abstract meaning representations in natural language processing, a graph-based form of semantic representation in which nodes encode objects and edges relations. At the same time, they can be parsed in [Formula: see text], where [Formula: see text] and [Formula: see text] are the sizes of the grammar and the input graph, respectively. In this work, we provide an initial algebra semantic for OPDGs, which allows us to view them as regular tree grammars under an equivalence theory. This makes it possible to transfer results from the field of formal tree languages to the domain of OPDGs, both in the unweighted and the weighted case. In particular, we show that deterministic OPDGs can be minimised efficiently, and that they are learnable under the “minimal adequeate teacher” paradigm, that is, by querying an oracle for equivalence between languages, and membership of individual graphs. To conclude, we demonstrate that the languages generated by OPDGs are definable in monadic second-order logic.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":"86 10","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139240397","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":"Author Index Volume 34 (2023)","authors":"","doi":"10.1142/s0129054123990010","DOIUrl":"https://doi.org/10.1142/s0129054123990010","url":null,"abstract":"","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":"102 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139257455","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 Minimum k-Tree Cover of a Connected Graph Inspired by the Multi-Ferry Routing in Delay Tolerant Networks","authors":"Fujita Satoshi","doi":"10.1142/s0129054123500235","DOIUrl":"https://doi.org/10.1142/s0129054123500235","url":null,"abstract":"In this paper, we consider the problem of covering the vertex set of a given graph by [Formula: see text] trees so as to minimize the maximum weight of the trees, as a subproblem of the multi-ferry scheduling problem proposed by Zhao and Ammar. After pointing out that the approximation ratio of a greedy scheme based on the Kruskal’s algorithm is provably bad, we show that the approximation ratio cannot be better than 3/2 for [Formula: see text] even when the edge selection criterion is modified so as to minimize the increase in the maximum weight in the collection of trees. We then propose two polynomial-time algorithms with a guaranteed approximation ratio. The first algorithm achieves 3-approximation for the class of graphs in which the edge weights satisfy the triangle inequality. The second algorithm achieves 4-approximation for any connected graph with arbitrary edge weights.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":"62 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139270076","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":"Weighted Linear Dynamic Logic","authors":"Manfred Droste, Gustav Grabolle, George Rahonis","doi":"10.1142/s0129054123480088","DOIUrl":"https://doi.org/10.1142/s0129054123480088","url":null,"abstract":"<p>We introduce a weighted linear dynamic logic (weighted LDL for short) and show the expressive equivalence of its formulas to weighted rational expressions. This adds a new characterization for recognizable series to the fundamental Schützenberger theorem. Surprisingly, the equivalence does not require any restriction to our weighted LDL. Our results hold over arbitrary (resp. totally complete) semirings for finite (resp. infinite) words. As a consequence, the equivalence problem for weighted LDL formulas over fields is decidable in doubly exponential time. In contrast to classical logics, we show that our weighted LDL is expressively incomparable to weighted LTL for finite words. We determine a fragment of the weighted LTL such that series over finite and infinite words definable by LTL formulas in this fragment are definable also by weighted LDL formulas. This is an extended version of [17].</p>","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":"38 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140075369","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}