Theoretical Computer Science最新文献

{"title":"Discriminating code and set cover with k-bend paths","authors":"Yu Yang,&nbsp;Cai-Xia Wang,&nbsp;Shou-Jun Xu","doi":"10.1016/j.tcs.2025.115458","DOIUrl":"10.1016/j.tcs.2025.115458","url":null,"abstract":"<div><div>In this paper, we explore geometric discriminating code and set cover problems with <em>k</em>-bend paths. We first demonstrate that both the discriminating code problem and the set cover problem with unit 0-bend paths are NP-hard. Additionally, we establish that the set cover problem is NP-hard with unit 1-bend paths restricted to type ⌜, where horizontal segments intersect a vertical line and vertical segments intersect a horizontal line. Furthermore, we show that the discriminating code problem remains NP-hard with unit 1-bend paths of type ⌜, where all vertical segments intersect a horizontal line. Finally, we provide approximation algorithms for these two problems, specifically for 0-bend paths of uniform length and for 1-bend paths of type ⌜, where all horizontal and vertical segments are of equal length.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115458"},"PeriodicalIF":0.9,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144633893","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":"Path cover using only short paths","authors":"Mingyang Gong ,&nbsp;Guangting Chen ,&nbsp;Zhi-Zhong Chen ,&nbsp;Guohui Lin ,&nbsp;Riki Uchida","doi":"10.1016/j.tcs.2025.115455","DOIUrl":"10.1016/j.tcs.2025.115455","url":null,"abstract":"<div><div>We study a variant of the well-known <em>Path Cover</em> problem where the candidate paths in a solution have orders up to a fixed integer <em>k</em>. In Path Cover, one finds a minimum number of vertex-disjoint paths in an input graph to cover all the vertices; in our variant, not all paths but only those short ones, i.e., containing up to <em>k</em> vertices, can be used as candidates. The problem is NP-hard when <span><math><mi>k</mi><mo>≥</mo><mn>3</mn></math></span>; in the literature, there exist quite a number of approximation algorithms, especially for small <em>k</em>'s. We present an improved <span><math><mfrac><mrow><mi>k</mi></mrow><mrow><mn>3</mn></mrow></mfrac></math></span>-approximation algorithm for <span><math><mi>k</mi><mo>∈</mo><mo>{</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>8</mn><mo>}</mo></math></span>, an improved <span><math><mfrac><mrow><mn>55</mn></mrow><mrow><mn>31</mn></mrow></mfrac></math></span>-approximation algorithm for <span><math><mi>k</mi><mo>=</mo><mn>5</mn></math></span>, and an improved <span><math><mfrac><mrow><mn>8</mn></mrow><mrow><mn>5</mn></mrow></mfrac></math></span>-approximation algorithm for <span><math><mi>k</mi><mo>=</mo><mn>4</mn></math></span>. The novelty inside these improved algorithms is observing a close connection between an optimal path cover and a certain polynomial-time computed edge set.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115455"},"PeriodicalIF":0.9,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614657","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 finite axiomatisability of weak bisimulation-based congruences","authors":"Luca Aceto ,&nbsp;Valentina Castiglioni ,&nbsp;Anna Ingólfsdóttir ,&nbsp;Bas Luttik","doi":"10.1016/j.tcs.2025.115453","DOIUrl":"10.1016/j.tcs.2025.115453","url":null,"abstract":"<div><div>We study the axiomatisability of CCS parallel composition operator modulo weak bisimulation-based congruences. Specifically, we prove that all congruences that are coarser than rooted branching bisimilarity, and finer than rooted weak bisimilarity, do not admit a finite equational axiomatisation over the recursion, restriction, and relabelling free fragment of CCS.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115453"},"PeriodicalIF":0.9,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614827","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":"On the Weisfeiler algorithm of depth-1 stabilization","authors":"Gang Chen ,&nbsp;Qing Ren ,&nbsp;Ilia Ponomarenko","doi":"10.1016/j.tcs.2025.115460","DOIUrl":"10.1016/j.tcs.2025.115460","url":null,"abstract":"<div><div>An origin of the multidimensional Weisfeiler-Leman algorithm goes back to a refinement procedure of deep stabilization, introduced by B. Weisfeiler in a paper included in the collective monograph “On construction and identification of graphs” (1976). This procedure is recursive and the recursion starts from an algorithm of depth-1 stabilization, which has never been discussed in the literature.</div><div>A goal of the present paper is to show that a simplified algorithm of the depth-1 stabilization has the same power as the 3-dimensional Weisfeiler-Leman algorithm. It is proved that the class of coherent configurations obtained as the output of this simplified algorithm coincides with the class introduced earlier by the third author. As an application we also prove that if there exist at least two nonisomorphic projective planes of order <em>q</em>, then the Weisfeiler-Leman dimension of the incidence graph of any projective plane of order <em>q</em> is at least 4.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115460"},"PeriodicalIF":0.9,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614826","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":"Modular soundness checking of feature model evolution plans","authors":"Crystal Chang Din ,&nbsp;Charaf Eddine Dridi ,&nbsp;Ida Sandberg Motzfeldt ,&nbsp;Violet Ka I Pun ,&nbsp;Volker Stolz ,&nbsp;Ingrid Chieh Yu","doi":"10.1016/j.tcs.2025.115451","DOIUrl":"10.1016/j.tcs.2025.115451","url":null,"abstract":"<div><div>Feature model evolution plans (FMEPs) describe how feature models for software product lines (SPLs) evolve over time. While different feature models can exist for different points in time over the lifetime of the product line, an FMEP describes how to compute a feature model for a given time point. SPLs capitalise on the variability and reusability of the software through combining optional and mandatory features. As business requirements change over time, FMEPs should support intermediate update. A plan hence contains updates to an initial model by adding, deleting, moving or changing elements at different points in time, in line with the evolving business requirements on the SPL, potentially affecting feature models that should be derived in the future from the plan.</div><div>A recurring challenge in maintaining FMEPs is that updates may lead to inconsistent intermediate feature models, most notably so-called paradoxes. A paradox may not materialise at the first point in time an update on the plan is performed to obtain a particular feature model, but may only in combination with a later modification prescribed by the plan create a structurally invalid model. Correspondingly, a single modification to a plan may require multiple checks over the liftetime of the affected elements to rule out paradoxes.</div><div>Current approaches require the analysis from the point in time an update is applied to an FMEP throughout the entire lifetime of the plan. In this paper, we define a so-called interval-based feature model (IBFM) to represent FMEPs, with a precise definition of spatial and temporal scopes that narrow the time interval and the sub-models that an update can affect. We propose a rule system for updating IBFMs, and also prove the soundness of the proposed rules and show their modularity, i.e., that each rule operates strictly within its temporal and spatial scopes. We have conducted a detailed evaluation on our modular approach and present the experimental results, which show that we outperform an existing linear approach.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115451"},"PeriodicalIF":0.9,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632958","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":"Broadening the applicability of local completeness analysis with intensional and extensional guarantees","authors":"Flavio Ascari ,&nbsp;Roberto Bruni ,&nbsp;Roberta Gori","doi":"10.1016/j.tcs.2025.115452","DOIUrl":"10.1016/j.tcs.2025.115452","url":null,"abstract":"<div><div>Local Completeness Logic (LCL) is a proof system for program analysis rooted in abstract interpretation. The program semantics is under-approximated by any provable postcondition, like incorrectness logic does, but it is also over-approximated by a (locally) <em>complete</em> abstraction of such a postcondition, like Hoare logic does. Therefore, <em>any derivable triple</em> will either prove the program to be correct or unveil true bugs. While the completeness of a program's function with respect to an abstract domain is inherently <em>extensional</em>, LCL's rules demand the preservation of local completeness throughout the abstract interpreter's computations. This characteristic renders LCL analysis <em>intensional</em>, meaning it depends on the way the program is written. Consequently, LCL proof system may not derive all the valid triples. This paper addresses this discrepancy by: 1) designing new rules that allow one to perform part of the intensional analysis in different (complete) abstract domains whenever necessary; and 2) to compare their expressiveness. Notably, some of these new rules enable the derivation of all extensionally valid triples, thereby decoupling the set of provable properties from the way the program is written.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115452"},"PeriodicalIF":0.9,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632959","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":"Partial permutations comparison, maintenance and applications","authors":"Avivit Levy ,&nbsp;Ely Porat ,&nbsp;B. Riva Shalom","doi":"10.1016/j.tcs.2025.115433","DOIUrl":"10.1016/j.tcs.2025.115433","url":null,"abstract":"<div><div>This paper studies <em>partial permutations</em> and their use in algorithmic tasks. A <em>partial permutation</em> over Σ is a bijection <span><math><msub><mrow><mi>π</mi></mrow><mrow><mi>p</mi><mi>a</mi><mi>r</mi></mrow></msub><mo>:</mo><msub><mrow><mi>Σ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>↦</mo><msub><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> mapping a subset <span><math><msub><mrow><mi>Σ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>⊂</mo><mi>Σ</mi></math></span> to a subset <span><math><msub><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⊂</mo><mi>Σ</mi></math></span>, where <span><math><mo>|</mo><msub><mrow><mi>Σ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>|</mo><mo>=</mo><mo>|</mo><msub><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>|</mo></math></span> (<span><math><mo>|</mo><mi>Σ</mi><mo>|</mo></math></span> denotes the size of a set Σ). Intuitively, two partial permutations <em>agree</em> if their mapping pairs do not form <em>conflicts</em>. We formally define this notion enabling a consistent as well as informatively rich comparison between partial permutations. We define the <em>Partial Permutations Agreement</em> problem (PPA), as follows. Given two sets <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> of partial permutations over alphabet Σ, each of size <em>n</em>, output a pair (<span><math><msub><mrow><mi>π</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>π</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>)</mo></math></span>, where <span><math><msub><mrow><mi>π</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>∈</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>π</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>∈</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>π</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> <em>agrees</em> with <span><math><msub><mrow><mi>π</mi></mrow><mrow><mi>j</mi></mrow></msub></math></span>, if exists. We study the existence of a data structure for efficiently maintaining a dynamic set of partial permutations enabling to retrieve agreement of partial permutations giving both negative and positive results. As applications we point out: (1) fruitful/futile methods for efficient genes sequences comparison in database, (2) an automatic color transformation data augmentation technique for image processing through neural networks, (3) negatively answer a recently posed open question on the strict parameterized dictionary matching with one gap (PDMOG) problem over general dictionary alphabets.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115433"},"PeriodicalIF":0.9,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144596499","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":"Bit-array-based alternatives to HyperLogLog","authors":"Svante Janson ,&nbsp;Jérémie Lumbroso ,&nbsp;Robert Sedgewick","doi":"10.1016/j.tcs.2025.115450","DOIUrl":"10.1016/j.tcs.2025.115450","url":null,"abstract":"<div><div>We present a family of algorithms for the problem of estimating the number of distinct items in an input stream that are simple to implement and are appropriate for practical applications. Our algorithms are a logical extension of the series of algorithms developed by Flajolet and his coauthors starting in 1983 that culminated in the widely used <span>HyperLogLog</span> algorithm. These algorithms divide the input stream into <em>M</em> substreams and lead to a time-accuracy tradeoff where a small number of bits per substream are saved to achieve a relative accuracy proportional to <span><math><mn>1</mn><mo>/</mo><msqrt><mrow><mi>M</mi></mrow></msqrt></math></span>. Our algorithms use just one or two bits per substream. Their effectiveness is demonstrated by a proof of approximate normality, with explicit expressions for standard errors that inform parameter settings and allow proper quantitative comparisons with other methods. Performance hypotheses are validated through experiments using a realistic input stream, with the general conclusion that our algorithms are significantly more accurate than <span>HyperLogLog</span> when using the same amount of memory, and they use significantly less memory than <span>HyperLogLog</span> to achieve a given accuracy.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115450"},"PeriodicalIF":0.9,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144596498","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":"Algorithms for Shortest Path Tour Problem","authors":"Yucen Gao ,&nbsp;Zhuoran Li ,&nbsp;Jingyu He ,&nbsp;Jun Fang ,&nbsp;Hui Gao ,&nbsp;Xiaofeng Gao ,&nbsp;Guihai Chen","doi":"10.1016/j.tcs.2025.115428","DOIUrl":"10.1016/j.tcs.2025.115428","url":null,"abstract":"<div><div>Carpooling route planning becomes an important problem with the growth of low-carbon traffic systems. When each passenger has multiple potential pick-up/drop-off locations, the problem will be more challenging. In the paper, we discussed a simplified carpooling route planning problem, namely the Shortest Path Tour Problem (SPTP), whose aim is to find a single-origin single-destination shortest path through an ordered sequence of disjoint node subsets. We propose Stage Dijkstra and Global Dijkstra algorithms to find the optimal shortest path, with the time complexity of <span><math><mi>O</mi><mo>(</mo><mi>l</mi><mo>(</mo><mi>n</mi><mo>+</mo><mi>m</mi><mo>)</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> and <span><math><mi>O</mi><mo>(</mo><mi>l</mi><mo>(</mo><mi>n</mi><mo>+</mo><mi>m</mi><mo>)</mo><mi>log</mi><mo>⁡</mo><mo>(</mo><mi>l</mi><mi>n</mi><mo>)</mo><mo>)</mo></math></span> respectively, where <em>l</em> represents the number of node subsets. To the best of our knowledge, <span><math><mi>O</mi><mo>(</mo><mi>l</mi><mo>(</mo><mi>n</mi><mo>+</mo><mi>m</mi><mo>)</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> is the best time complexity of the exact algorithms for SPTP. Besides, the Stage Dijkstra and Global Dijkstra algorithms both have the linear space complexity, which is highly suitable for resource-constrained environments. Experiments conducted on large-scale road networks and synthetic datasets demonstrate the effectiveness and efficiency of our proposed algorithms in terms of running time and memory consumption.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115428"},"PeriodicalIF":0.9,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144596497","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":"Joint bidding in ad auctions","authors":"Yuchao Ma ,&nbsp;Weian Li ,&nbsp;Wanzhi Zhang ,&nbsp;Yahui Lei ,&nbsp;Zhicheng Zhang ,&nbsp;Qi Qi ,&nbsp;Qiang Liu ,&nbsp;Xingxing Wang","doi":"10.1016/j.tcs.2025.115449","DOIUrl":"10.1016/j.tcs.2025.115449","url":null,"abstract":"<div><div>In traditional advertising auctions, commodity suppliers as advertisers compete for adverting positions to display commodities. As e-commerce platforms become more prevalent, offline retailers are also opening online virtual shops, and retailers are starting to pay a fee for extra exposure of their shops. This has led to situations where a single commodity may be sponsored by both the retailer and the supplier, offering opportunities for more profit. In order to explore this novel advertising pattern, we propose a new model called the joint advertising system (JAS), where retailers and suppliers jointly bid for advertising positions. In the context of this realistic scenario, conventional mechanisms such as GFP, GSP and Myerson auction cannot be applied directly. Besides, the VCG mechanism results in negative revenue in JAS. To solve this issue, we modify the payment rule of VCG to create a revised VCG mechanism that guarantees incentive compatible, individually rational and weakly budget-balanced. Additionally, we leverage the structure of the affine maximizer auction (AMA) and the technique of automated mechanism design to train joint AMA. Finally, we conduct several experiments to demonstrate the performance of the joint AMA. It turns out that our mechanism maintains good economic properties and outperforms other mechanisms in various settings.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115449"},"PeriodicalIF":0.9,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614658","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}