Information and Computation最新文献

{"title":"Exact counting of subtrees with diameter no more than d in trees: A generating function approach","authors":"Yu Yang ,&nbsp;Bang-Bang Jin ,&nbsp;Xiaoming Sun ,&nbsp;Xiao-Dong Zhang ,&nbsp;Bo Li ,&nbsp;Kai Zhao ,&nbsp;Hua Wang","doi":"10.1016/j.ic.2025.105353","DOIUrl":"10.1016/j.ic.2025.105353","url":null,"abstract":"<div><div>Network motifs, regarded as fundamental building blocks, offer crucial insights into the structure and function of complex networks, with broad applications across disciplines including sociology, computer science, bioinformatics, chemoinformatics, and pharmaceutics. However, the identification of network motifs remains a significant and computationally challenging problem. Among various motifs, subtree enumeration has garnered substantial attention in recent years, particularly due to its relevance in network science and bioinformatics. For an <em>n</em>-vertex tree <em>T</em>, by introducing novel generating functions with <span><math><mo>(</mo><mi>d</mi><mo>+</mo><mn>2</mn><mo>)</mo></math></span> variables, we propose an innovative algorithm for the exact enumeration of <em>T</em>'s subtrees rooted at fixed vertex <em>v</em>, where the distance between <em>v</em> and the farthest leaf is <span><math><mi>k</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>d</mi></math></span>, and the distance between any two leaves is no more than <em>d</em>. Building on this algorithm, we develop novel recursive algorithms for exact enumerating various diameter no more than <em>d</em> subtrees (abbreviated as DNMT-<em>d</em> subtrees) of <em>T</em>. As applications, we apply these algorithms to derive the number of DNMT-<em>d</em> subtrees in a full binary tree <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>h</mi></mrow></msub></math></span> with <span><math><mi>h</mi><mo>≥</mo><mn>2</mn></math></span> levels, and briefly discuss the density of DNMT-<em>d</em> subtrees in general trees. Our research generalizes the work of Frank Ruskey on Listing and Counting Subtrees of a Tree in 1981 and makes it a special case of our study where <em>d</em> equals the diameter of the tree <em>T</em>. Moreover, the proposed <span><math><mi>O</mi><mo>(</mo><mi>d</mi><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> algorithms introduce new approaches for enumerating subtrees under diameter constraints and lay the groundwork for counting diameter-constrained subgraphs (motifs) in complex networks.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"307 ","pages":"Article 105353"},"PeriodicalIF":1.0,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048821","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":"Two-state spin systems with negative interactions","authors":"Yumou Fei ,&nbsp;Leslie Ann Goldberg ,&nbsp;Pinyan Lu","doi":"10.1016/j.ic.2025.105340","DOIUrl":"10.1016/j.ic.2025.105340","url":null,"abstract":"<div><div>We study the approximability of computing the partition functions of two-state spin systems. The problem is parameterized by a <span><math><mn>2</mn><mo>×</mo><mn>2</mn></math></span> symmetric matrix. Previous results on this problem were restricted either to the case where the matrix has non-negative entries, or to the case where the diagonal entries are equal, i.e. Ising models. In this paper, we study the generalization to arbitrary <span><math><mn>2</mn><mo>×</mo><mn>2</mn></math></span> interaction matrices with real entries. We show that in some regions of the parameter space, it's #P-hard to even determine the sign of the partition function, while in other regions there are fully polynomial approximation schemes for the partition function. Our results reveal several new computational phase transitions.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"307 ","pages":"Article 105340"},"PeriodicalIF":1.0,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144907971","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":"The g-good-neighbor diagnosability of product networks under the PMC model","authors":"Zhao Wang ,&nbsp;Yaping Mao ,&nbsp;Sun-Yuan Hsieh ,&nbsp;Ralf Klasing","doi":"10.1016/j.ic.2025.105341","DOIUrl":"10.1016/j.ic.2025.105341","url":null,"abstract":"<div><div>The concept of neighbor connectivity originated from the assessment of the subversion of espionage networks caused by underground resistance movements, and it has now been applied to measure the disruption of networks caused by cascading failures through neighbors. In this paper, we give two necessary and sufficient conditions of the existence of <em>g</em>-good-neighbor diagnosability. We introduce a new concept called <em>g</em>-good neighbor cut-component number (gc number for short), which has close relation with <em>g</em>-good-neighbor diagnosability. Sharp lower and upper bounds of the gc number of general graphs in terms of the <em>g</em>-good neighbor connectivity have been proposed, which provide a formula to compute the <em>g</em>-good-neighbor diagnosability for general graphs (therefore for Cartesian product graphs). As their applications, we get the exact values or bounds for the gc numbers and <em>g</em>-good-neighbor diagnosability of grid, torus networks and generalized cubes.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"307 ","pages":"Article 105341"},"PeriodicalIF":1.0,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144913409","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":"Decision problems for systems of language equations and inequations","authors":"Alexander Okhotin","doi":"10.1016/j.ic.2025.105344","DOIUrl":"10.1016/j.ic.2025.105344","url":null,"abstract":"<div><div>Systems of language equations <span><math><mi>φ</mi><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>=</mo><mi>ψ</mi><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span> and inequations <span><math><mi>φ</mi><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>≠</mo><mi>ψ</mi><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span> are studied, where <em>φ</em> and <em>ψ</em> may contain Boolean operations and concatenation. It is proved that the problem whether such a system has a solution is <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>0</mn></mrow></msubsup></math></span>-complete in the arithmetical hierarchy (cf. the earlier studied case of equations only, where it is co-r.e.-complete), the problem whether it has a unique solution is in <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mn>3</mn></mrow><mrow><mn>0</mn></mrow></msubsup><mo>∩</mo><msubsup><mrow><mi>Π</mi></mrow><mrow><mn>3</mn></mrow><mrow><mn>0</mn></mrow></msubsup></math></span>, and is both <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>0</mn></mrow></msubsup></math></span>-hard and <span><math><msubsup><mrow><mi>Π</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>0</mn></mrow></msubsup></math></span>-hard, existence of a finite or regular solution is an r.e.-complete problem, while testing whether a system has finitely many solutions is <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mn>3</mn></mrow><mrow><mn>0</mn></mrow></msubsup></math></span>-complete. Furthermore, it is shown that the class of languages representable by unique solutions of such systems is exactly the class of recursive sets, but decision procedures for the set cannot be algorithmically constructed out of a system. All results hold already for equations over a unary alphabet.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"307 ","pages":"Article 105344"},"PeriodicalIF":1.0,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144907970","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":"Towards a theoretical understanding of why local search works for clustering with fair-center representation","authors":"Zhen Zhang ,&nbsp;Junfeng Yang ,&nbsp;Limei Liu ,&nbsp;Xuesong Xu ,&nbsp;Guozhen Rong ,&nbsp;Qilong Feng","doi":"10.1016/j.ic.2025.105343","DOIUrl":"10.1016/j.ic.2025.105343","url":null,"abstract":"<div><div>The representative <em>k</em>-median problem generalizes the classical clustering formulations in that it partitions the data points into <em>ℓ</em> disjoint demographic groups and imposes a lower-bound constraint on the number of opened facilities from each group, such that all the groups are fairly represented by the opened facilities. Due to its simplicity, the local-search heuristic, which iteratively swaps a bounded number of closed facilities for the same number of opened ones to improve the solution, has been frequently used in the representative <em>k</em>-median problem. It is known that the local-search heuristic, when restricted to constant-size swaps, yields a constant-factor approximation if <span><math><mi>ℓ</mi><mo>=</mo><mn>2</mn></math></span>, and has an unbounded approximation ratio if <em>ℓ</em> is super-constant. However, for any constant <span><math><mi>ℓ</mi><mo>&gt;</mo><mn>2</mn></math></span>, the existence of a constant-factor approximation under constant-size swaps remained an open question for a long time. In response to this question, we demonstrate that the local-search heuristic guarantees a <span><math><mo>(</mo><mn>4</mn><mi>ℓ</mi><mo>+</mo><mn>5</mn><mo>)</mo></math></span>-approximation when up to <span><math><mi>ℓ</mi><mo>(</mo><mi>ℓ</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span> facilities are allowed to be swapped in each iteration, thus providing an affirmative answer to the question.</div><div>Our main technical contribution is a novel approach for theoretically analyzing the local-search heuristic, which bounds its approximation ratio by linearly combining the clustering cost increases induced by a set of hierarchically organized swaps. Our techniques also generalize to the <em>k</em>-means clustering formulation and reveal similar approximation guarantees for the local-search heuristic.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"307 ","pages":"Article 105343"},"PeriodicalIF":1.0,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144904104","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":"The Billaud Conjecture for alphabet size 4","authors":"Szymon Łopaciuk ,&nbsp;Daniel Reidenbach","doi":"10.1016/j.ic.2025.105342","DOIUrl":"10.1016/j.ic.2025.105342","url":null,"abstract":"<div><div>The Billaud Conjecture, first stated in 1993, is a fundamental problem on finite words and their heirs, i.e., the words obtained by a projection deleting a single letter. The conjecture states that every morphically primitive word, i.e., a word that is not a fixed point of any non-identity morphism, has at least one morphically primitive heir. The correctness of the conjecture has so far been established in a few special cases, which mainly restrict the alphabet size. In this paper we give a proof for the next such case, i.e., for alphabet size 4.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"307 ","pages":"Article 105342"},"PeriodicalIF":1.0,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144922507","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":"Existential and universal width of alternating finite automata","authors":"Yo-Sub Han ,&nbsp;Sungmin Kim ,&nbsp;Sang-Ki Ko ,&nbsp;Kai Salomaa","doi":"10.1016/j.ic.2025.105337","DOIUrl":"10.1016/j.ic.2025.105337","url":null,"abstract":"<div><div>The existential width of an alternating finite automaton (AFA) <em>A</em> on a string <em>w</em> is, roughly speaking, the number of nondeterministic choices that <em>A</em> uses in an accepting computation on <em>w</em> that uses least nondeterminism. The universal width of <em>A</em> on string <em>w</em> is the least number of parallel branches an accepting computation of <em>A</em> on <em>w</em> needs to have. The existential or universal width of <em>A</em> is said to be finite if it is bounded for all accepted strings. We show that finiteness of existential and universal width of an AFA is decidable and at least PSPACE-hard. We consider the problem of deciding whether the existential or universal width is bounded by a given integer. We show that the problem is PSPACE-complete for AFAs where the number of transitions defined for a given universal state and input symbol is bounded by a constant.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"306 ","pages":"Article 105337"},"PeriodicalIF":1.0,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144841623","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":"Complexity of exclusive nondeterministic finite automata","authors":"Martin Kutrib,&nbsp;Andreas Malcher,&nbsp;Matthias Wendlandt","doi":"10.1016/j.ic.2025.105336","DOIUrl":"10.1016/j.ic.2025.105336","url":null,"abstract":"<div><div>Exclusive nondeterministic finite automata (XNFA) are nondeterministic finite automata with an exclusive-or-like acceptance condition. An input is accepted if there is exactly one accepting path in its computation tree. If there are none or more than one accepting paths, the input is rejected. It turns out that, from a descriptional complexity point of view, XNFAs differ significantly from the known types of finite automata. In particular the state costs for the simulation of an XNFA by a DFA are <span><math><msup><mrow><mn>3</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>−</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>+</mo><mn>1</mn></math></span> states, while the costs for simulating an XNFA by an NFA are <span><math><mi>n</mi><mo>⋅</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span> states. Both bounds are also shown to be tight. On the other hand, NFAs may have advantages in comparison to XNFAs. For the simulation of an NFA by an XNFA, a tight bound of <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>−</mo><mn>1</mn></math></span> states is given. Finally, we investigate the computational complexity of different decision problems for XNFAs and it turns out that emptiness, universality, inclusion, and equivalence are <span>PSPACE</span>-complete.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"306 ","pages":"Article 105336"},"PeriodicalIF":1.0,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144864286","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":"Concept analysis approach for graphs","authors":"Mengyao Zhao ,&nbsp;Yanhui Zhai ,&nbsp;Deyu Li","doi":"10.1016/j.ic.2025.105338","DOIUrl":"10.1016/j.ic.2025.105338","url":null,"abstract":"<div><div>Graphs possess the ability to model complex systems in the real world, leading to their widespread application in fields such as social network analysis and recommendation systems. However, one of the major challenges in processing graph data lies in the inherent structural complexity of graphs. Consequently, extracting meaningful structural information from graph data has become a significant area of research. Formal Concept Analysis provides a method for expressing and analyzing algebraic structures by constructing concept lattices, which can effectively uncover complex structures within data. This paper proposes a concept analysis approach for graph data, revealing the relationship between graph structures and their corresponding concepts. Initially, the paper focuses on the connected components of disconnected graphs, exploring their specific representations in their respective concept lattices, and demonstrating that each connected component corresponds to a connected equivalence class within its associated lattice. Subsequently, the paper investigates the correspondence between graph structures of connected components and their associated concepts, identifying the concepts corresponding to cliques and to non-clique connected subgraphs. The findings indicate that these graph structures can be reconstructed through their corresponding concepts, thereby transforming operations on graph structures into operations on concepts and offering a novel perspective on graph structure manipulation. Finally, the paper analyzes the correspondence between concepts in concept lattices and graph structures, revealing the rationale behind concept construction. The results show that the concepts are closely related to a special class of graph structures, namely maximal star-clique graphs.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"306 ","pages":"Article 105338"},"PeriodicalIF":1.0,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144864287","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":"Relations between equation automata and follow automata","authors":"Ping Lu ,&nbsp;Haiming Chen","doi":"10.1016/j.ic.2025.105333","DOIUrl":"10.1016/j.ic.2025.105333","url":null,"abstract":"<div><div>This paper focuses on the relations between two small automata, <em>i.e.,</em> the equation automaton and the follow automaton, which are both quotients of the position automaton. Ilie and Yu had pointed out that a rigorous analysis of their relations is necessary but difficult. We aim to tackle this problem. We first provide a sufficient condition for the equation automaton to be a quotient of the follow automaton, and then show that there exist different conditions under which the relations between these two automata vary.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"306 ","pages":"Article 105333"},"PeriodicalIF":1.0,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896338","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}