Theoretical Computer Science最新文献

Opinion maximization in social networks via link recommendation

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2025-02-03 DOI: 10.1016/j.tcs.2025.115090

Liwang Zhu , Zhongzhi Zhang

{"title":"Opinion maximization in social networks via link recommendation","authors":"Liwang Zhu , Zhongzhi Zhang","doi":"10.1016/j.tcs.2025.115090","DOIUrl":"10.1016/j.tcs.2025.115090","url":null,"abstract":"<div><div>We study a variation of the Friedkin-Johnsen model for opinion dynamics in a leader-follower social network with n nodes and m edges, where the node set is partitioned into three subsets: set of leader nodes with opinion 1, set of leaders with opinion 0, and set of follower nodes. We give an explicit expression for the steady-state opinion vector in terms of some related matrices and the initial opinion vector, and interpret the equilibrium opinion vector as the weighted average of the initial opinions for all nodes with the weights being the escape probabilities of a defining random walk. We then pose an opinion maximization problem of recommending k new edges between 1-leader and follower nodes so that the equilibrium overall opinion is maximized. We show that the objective function is monotone and submodular, and propose a simple greedy algorithm with an approximation factor <math><mo>(</mo><mn>1</mn><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>e</mi></mrow></mfrac><mo>)</mo></math> that approximately solves the problem in cubic running time. To speed up the computation, we also provide a fast algorithm with an approximation ratio <math><mo>(</mo><mn>1</mn><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>e</mi></mrow></mfrac><mo>−</mo><mi>ϵ</mi><mo>)</mo></math> and computation complexity <math><mover><mrow><mi>O</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><mi>m</mi><mi>k</mi><msup><mrow><mi>ϵ</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>)</mo></math> for any <math><mi>ϵ</mi><mo>></mo><mn>0</mn></math>, where the <math><mover><mrow><mi>O</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><mo>⋅</mo><mo>)</mo></math> notation suppresses the <math><mrow><mi>poly</mi></mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math> factors. Extensive experiments on both real social networks with real opinions and datasets with synthetic opinions demonstrate that our algorithms are effective, efficient, and scale well to large social networks.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1033 ","pages":"Article 115090"},"PeriodicalIF":0.9,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143348192","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

Finding a minimum spanning tree with a small non-terminal set

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2025-01-31 DOI: 10.1016/j.tcs.2025.115092

Tesshu Hanaka , Yasuaki Kobayashi

{"title":"Finding a minimum spanning tree with a small non-terminal set","authors":"Tesshu Hanaka , Yasuaki Kobayashi","doi":"10.1016/j.tcs.2025.115092","DOIUrl":"10.1016/j.tcs.2025.115092","url":null,"abstract":"<div><div>In this paper, we study the problem of finding a minimum weight spanning tree that contains each vertex in a given subset <math><msub><mrow><mi>V</mi></mrow><mrow><mi>NT</mi></mrow></msub></math> of vertices as an internal vertex. This problem, called Minimum Weight Non-Terminal Spanning Tree, includes s-t Hamiltonian Path as a special case, and hence it is NP-hard. In this paper, we first observe that Non-Terminal Spanning Tree, the unweighted counterpart of Minimum Weight Non-Terminal Spanning Tree, is already NP-hard on some special graph classes. Moreover, it is W[1]-hard when parameterized by clique-width. In contrast, we give a 3k-vertex kernel and <math><msup><mrow><mi>O</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>k</mi></mrow></msup><mo>)</mo></math>-time algorithm, where k is the size of non-terminal set <math><msub><mrow><mi>V</mi></mrow><mrow><mi>NT</mi></mrow></msub></math>. The latter algorithm can be extended to Minimum Weight Non-Terminal Spanning Tree with the restriction that each edge has a polynomially bounded integral weight. We also show that Minimum Weight Non-Terminal Spanning Tree is fixed-parameter tractable parameterized by the number of edges in the subgraph induced by the non-terminal set <math><msub><mrow><mi>V</mi></mrow><mrow><mi>NT</mi></mrow></msub></math>, extending the fixed-parameter tractability of Minimum Weight Non-Terminal Spanning Tree to a more general case. Finally, we give several results for structural parameterization.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1033 ","pages":"Article 115092"},"PeriodicalIF":0.9,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143332660","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

On the geometric red-blue set cover problem

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2025-01-30 DOI: 10.1016/j.tcs.2025.115089

Raghunath Reddy Madireddy , Subhas C. Nandy , Supantha Pandit

{"title":"On the geometric red-blue set cover problem","authors":"Raghunath Reddy Madireddy , Subhas C. Nandy , Supantha Pandit","doi":"10.1016/j.tcs.2025.115089","DOIUrl":"10.1016/j.tcs.2025.115089","url":null,"abstract":"<div><div>Using various geometric objects, we study variations of the geometric Red-Blue Set Cover (RBSC) problem in <math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math>. Here, given two sets R and B of points, called red and blue points, respectively, and a set O of objects, the objective is to compute a subset <math><msup><mrow><mi>O</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>⊆</mo><mi>O</mi></math> of objects such that <math><msup><mrow><mi>O</mi></mrow><mrow><mo>′</mo></mrow></msup></math> covers all the blue points in B and covers the minimum number of red points in R. We show that the RBSC problem with intervals on the real line is polynomial-time solvable. In <math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math>, the problem admits a polynomial-time algorithm for a particular case of axis-parallel lines when no two lines intersect at a red point. However, if the objects are horizontal lines and vertical segments, the problem becomes <math><mi>NP</mi></math>-hard. It remains <math><mi>NP</mi></math>-hard for axis-parallel unit length segments distributed arbitrarily in the plane. The problem is <math><mi>NP</mi></math>-hard for the axis-parallel rectangles even when (i) each rectangle in O is anchored at one of the given two parallel lines, and (ii) a horizontal line intersects all the rectangles in O.</div><div>We show a variation of RBSC, called Special Red Blue Set Cover (SPECIAL-RBSC), to be <math><mi>APX</mi></math>-hard. Next, we use this result to show <math><mi>APX</mi></math>-hardness of the following geometric variations of RBSC problem in <math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math> where the objects are (i) axis-parallel rectangles containing the origin, (ii) axis-parallel strips, (iii) axis-parallel rectangles that are intersecting exactly zero or four times, (iv) axis-parallel line segments, and (v) downward shadows of line segments, by providing the encoding of these problems as the Special Red Blue Set Cover problem. These <math><mi>APX</mi></math>-hardness results are in the same line of work by Chan and Grant (2014), who provided the <math><mi>APX</mi></math>-hardness results for the geometric set cover problem for the above classes of objects.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1033 ","pages":"Article 115089"},"PeriodicalIF":0.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143332657","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

Self-masking for hardening inversions

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2025-01-30 DOI: 10.1016/j.tcs.2025.115094

Paweł Cyprys , Shlomi Dolev , Shlomo Moran

{"title":"Self-masking for hardening inversions","authors":"Paweł Cyprys , Shlomi Dolev , Shlomo Moran","doi":"10.1016/j.tcs.2025.115094","DOIUrl":"10.1016/j.tcs.2025.115094","url":null,"abstract":"<div><div>The question of whether one-way functions (i.e., functions that are easy to compute but hard to invert) exist is arguably one of the central problems in complexity theory, both from theoretical and practical aspects. While proving that such functions exist could be hard, there were quite a few attempts to provide functions that are one way “in practice”, namely, they are easy to compute, but there are no known polynomial time algorithms that compute their (generalized) inverse (or that computing their inverse is as hard as notoriously difficult tasks, like factoring very large integers).</div><div>In this paper, we introduce the self-masking technique, which converts polynomial time computable functions to functions that are likely to be harder to invert. The technique is first defined for univalent functions (note that one way functions that are univalent are basic ingredients for cryptographic protocols). Informally, a self masked version of a univalent function f, denoted <math><mo>[</mo><mi>f</mi><mo>]</mo></math>, replaces two masking substrings of <math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> by their XOR. The masking substrings are critical if <math><mo>[</mo><mi>f</mi><mo>]</mo></math> remains univalent (w.h.p.). Thus, when the masking substrings are critical, inverting <math><mrow><mo>[</mo><mi>f</mi><mo>]</mo></mrow><mo>(</mo><mi>x</mi><mo>)</mo></math> is at least as hard as reconstructing the masking substrings from their XOR.</div><div>We apply this technique to functions based on variants of the subset sum problem and obtain functions that resist known techniques for inverting the original, unmasked functions (see, e.g., [13]). Applications of this technique to other functions, as well as its extension to multivalent functions, are also discussed.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1032 ","pages":"Article 115094"},"PeriodicalIF":0.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143301914","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

Diagonal of pseudoinverse of graph Laplacian: Fast estimation and exact results

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2025-01-30 DOI: 10.1016/j.tcs.2025.115102

Zenan Lu , Wanyue Xu , Zhongzhi Zhang

{"title":"Diagonal of pseudoinverse of graph Laplacian: Fast estimation and exact results","authors":"Zenan Lu , Wanyue Xu , Zhongzhi Zhang","doi":"10.1016/j.tcs.2025.115102","DOIUrl":"10.1016/j.tcs.2025.115102","url":null,"abstract":"<div><div>The diagonal entries of the pseudoinverse of the Laplacian matrix of a graph appear in many important practical applications since they contain much information about the graph, and many relevant quantities can be expressed in terms of them, such as the Kirchhoff index and current flow centrality. However, a naïve approach for computing the diagonal of a matrix inverse has cubic computational complexity in terms of the matrix dimension, which is not acceptable for large graphs with millions of nodes. Thus, rigorous solutions to the diagonal of the Laplacian matrices for general graphs, even for particular graphs are much less. In this paper, we propose a theoretically guaranteed estimation algorithm, which approximates all diagonal entries of the pseudoinverse of a graph Laplacian in nearly linear time with respect to the number of edges in the graph. We execute extensive experiments on real-life networks, which indicate that our algorithm is both efficient and accurate. Also, we determine exact expressions for the diagonal elements of pseudoinverse of the Laplacian matrices for Koch networks and uniform recursive trees, and compare them with those obtained by our approximation algorithm. Finally, we use our algorithm to evaluate the Kirchhoff index of three deterministic model networks, for which the Kirchhoff index can be rigorously determined. These results further show the effectiveness and efficiency of our algorithm.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1032 ","pages":"Article 115102"},"PeriodicalIF":0.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143302053","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

A subquadratic certification scheme for P5-free graphs

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2025-01-29 DOI: 10.1016/j.tcs.2025.115091

Nicolas Bousquet , Sébastien Zeitoun

引用次数: 0

How to avoid the commuting conversions of IPC

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2025-01-29 DOI: 10.1016/j.tcs.2025.115101

José Espírito Santo , Gilda Ferreira

{"title":"How to avoid the commuting conversions of IPC","authors":"José Espírito Santo , Gilda Ferreira","doi":"10.1016/j.tcs.2025.115101","DOIUrl":"10.1016/j.tcs.2025.115101","url":null,"abstract":"<div><div>Since the observation in 2006 that it is possible to embed IPC into the atomic polymorphic λ-calculus (a predicative fragment of system F with universal instantiations restricted to atomic formulas) different such embeddings appeared in the literature. All of them comprise the Russell-Prawitz translation of formulas, but have different strategies for the translation of proofs. Although these embeddings preserve proof identity, all fail in delivering preservation of reduction steps. In fact, they translate the commuting conversions of IPC to β-equality, or to other kinds of reduction or equality generated by new principles added to system F. The cause for this is the generation of redexes by the translation itself. In this paper, we present an embedding of IPC into atomic system F, still based on the same translation of formulas, but which maps commuting conversions to syntactic identity, while simulating the other kinds of reduction steps present in IPC by βη-reduction. In this sense the translation achieves a truly commuting-conversion-free image of IPC in atomic system F.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1033 ","pages":"Article 115101"},"PeriodicalIF":0.9,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143359060","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

A linkable ring signature scheme with unconditional anonymity in the standard model

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2025-01-29 DOI: 10.1016/j.tcs.2025.115093

Keisuke Hara

{"title":"A linkable ring signature scheme with unconditional anonymity in the standard model","authors":"Keisuke Hara","doi":"10.1016/j.tcs.2025.115093","DOIUrl":"10.1016/j.tcs.2025.115093","url":null,"abstract":"<div><div>Ring signatures allow a user to sign messages as a member of a set of users, which is called a ring. This primitive ensures that anybody can check that one of the members in a ring generate a signature, but cannot detect which member does. Linkable ring signature is a novel extension of ring signature in the sense that anyone can verify whether two signatures were generated by the same user or not. One of the desirable features on (linkable) ring signature is unconditional anonymity which provides signers everlasting anonymity. In 2014, Liu, Au, Susilo, and Zhou proposed the first linkable ring signature scheme with unconditional anonymity. Their scheme is only secure in the random oracle model and leaves to construct a scheme in the standard model as an open problem. In this paper, we solve their open problem and propose the first linkable ring signature scheme with unconditional anonymity in the standard model. Our scheme is constructed based on a non-interactive proof of knowledge, a (standard) signature scheme, a commitment scheme, and a vector commitment scheme with specializable universal common reference string.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1033 ","pages":"Article 115093"},"PeriodicalIF":0.9,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143332658","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

Independent sets of maximum weight beyond claw-free graphs and related problems

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2025-01-29 DOI: 10.1016/j.tcs.2025.115103

Andreas Brandstädt , Vadim Lozin , Raffaele Mosca

{"title":"Independent sets of maximum weight beyond claw-free graphs and related problems","authors":"Andreas Brandstädt , Vadim Lozin , Raffaele Mosca","doi":"10.1016/j.tcs.2025.115103","DOIUrl":"10.1016/j.tcs.2025.115103","url":null,"abstract":"<div><div>The maximum weight independent set problem (WIS), which is known to be generally NP-hard, admits polynomial-time solutions when restricted to graphs in some special classes. In particular, due to the celebrated Edmonds' matching algorithm, WIS is solvable in polynomial time in the class of line graphs. This solution was extended to claw-free graphs and then further to fork-free graphs and to tclaw-free graphs, where tclaw is the graph consisting of t disjoint copies of the claw. The solution for tclaw-free graphs was obtained by generalizing Farber's approach to solve the problem for <math><mi>t</mi><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow></msub></math>-free graphs. In the present paper, we elaborate this approach further to develop a polynomial-time algorithm to solve the problem in the class of fork+tclaw-free graphs, generalizing both fork-free graphs and tclaw-free graphs, and in the class of <math><msub><mrow><mi>P</mi></mrow><mrow><mn>5</mn></mrow></msub><mo>+</mo><mi>t</mi></math>claw-free graphs. We then apply the latter result to solve the more general problem of finding a d-regular induced subgraph of maximum weight in the class of <math><msub><mrow><mi>P</mi></mrow><mrow><mn>5</mn></mrow></msub><mo>+</mo><mi>t</mi><msub><mrow><mi>P</mi></mrow><mrow><mn>3</mn></mrow></msub></math>-free graphs in polynomial time for any natural d and t, extending some of the previously known solutions.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1032 ","pages":"Article 115103"},"PeriodicalIF":0.9,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143301915","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

Linear Programming complementation

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2025-01-29 DOI: 10.1016/j.tcs.2025.115087

Maximilien Gadouleau , George B. Mertzios , Viktor Zamaraev

{"title":"Linear Programming complementation","authors":"Maximilien Gadouleau , George B. Mertzios , Viktor Zamaraev","doi":"10.1016/j.tcs.2025.115087","DOIUrl":"10.1016/j.tcs.2025.115087","url":null,"abstract":"<div><div>In this paper we introduce a new operation for Linear Programming (LP), called LP complementation, which resembles many properties of LP duality. Given a maximisation (resp. minimisation) LP P, we define its complement Q as a specific minimisation (resp. maximisation) LP which has the same objective function as P. Our central result is the LP complementation theorem, that relates the optimal value <figure><img></figure> of P and the optimal value <figure><img></figure> of its complement by <figure><img></figure>. The LP complementation operation can be applied if and only if P has an optimum value greater than 1.</div><div>To illustrate this, we first apply LP complementation to hypergraphs. For any hypergraph H, we review the four classical LPs, namely covering <math><mi>K</mi><mo>(</mo><mi>H</mi><mo>)</mo></math>, packing <math><mi>P</mi><mo>(</mo><mi>H</mi><mo>)</mo></math>, matching <math><mi>M</mi><mo>(</mo><mi>H</mi><mo>)</mo></math>, and transversal <math><mi>T</mi><mo>(</mo><mi>H</mi><mo>)</mo></math>. For every hypergraph <math><mi>H</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math>, we call <figure><img></figure> the complement of H. For each of the above four LPs, we relate the optimal values of the LP for the dual hypergraph <figure><img></figure> to that of the complement hypergraph <figure><img></figure> (e.g. <figure><img></figure>).</div><div>We then apply LP complementation to fractional graph theory. We prove that the LP for the fractional in-dominating number of a digraph D is the complement of the LP for the fractional total out-dominating number of the digraph complement <figure><img></figure> of D. Furthermore we apply the hypergraph complementation theorem to matroids. We establish that the fractional matching number of a matroid coincide with its edge toughness.</div><div>As our last application of LP complementation, we introduce the natural problem Vertex Cover with Budget (VCB): for a graph <math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math> and a positive integer b, what is the maximum number <math><msub><mrow><mi>t</mi></mrow><mrow><mi>b</mi></mrow></msub></math> of vertex covers <math><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>S</mi></mrow><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi>b</mi></mrow></msub></mrow></msub></math> of G, such that every vertex <math><mi>v</mi><mo>∈</mo><mi>V</mi></math> appears in at most b vertex covers? The integer b can be viewed as a “budget” that we can spend on each vertex and, given this budget, we aim to cover all edges","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1032 ","pages":"Article 115087"},"PeriodicalIF":0.9,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143301909","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