Theory of Computing Systems最新文献_第4页

Rational Index of Languages Defined by Grammars with Bounded Dimension of Parse Trees 解析树维度有界的语法所定义语言的有理索引

IF 0.5 4区计算机科学

Theory of Computing Systems Pub Date : 2023-12-20 DOI: 10.1007/s00224-023-10159-3

Ekaterina Shemetova, Alexander Okhotin, Semyon Grigorev

{"title":"Rational Index of Languages Defined by Grammars with Bounded Dimension of Parse Trees","authors":"Ekaterina Shemetova, Alexander Okhotin, Semyon Grigorev","doi":"10.1007/s00224-023-10159-3","DOIUrl":"https://doi.org/10.1007/s00224-023-10159-3","url":null,"abstract":"The rational index (rho _L) of a language L is an integer function, where (rho _L(n)) is the maximum length of the shortest string in (L cap R), over all regular languages R recognized by n-state nondeterministic finite automata (NFA). This paper investigates the rational index of languages defined by grammars with bounded parse tree dimension: this is a numerical measure of the amount of branching in a tree (with trees in a linear grammar having dimension 1). For context-free grammars, a grammar with tree dimension bounded by d has rational index at most (O(n^{2d})), and it is known from the literature that there exists a grammar with rational index (Theta (n^{2d})). In this paper, it is shown that for multi-component grammars with at most k components (k-MCFG) and with a tree dimension bounded by d, the rational index is at most (O(n^{2kd})), where the constant depends on the grammar, and there exists such a grammar with rational index (frac{k}{2^{kd^2 - kd -2k -1} cdot (8k+1)^{2kd}} n^{2kd}). Also, for the case of ordinary context-free grammars, a more precise lower bound (frac{1}{2^{d^2 + d - 3} 3^{2d}} n^{2d}) is established.","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":"10 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138818090","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

Improved Bounds for Matching in Random-Order Streams 随机排序流中匹配的改进边界

IF 0.5 4区计算机科学

Theory of Computing Systems Pub Date : 2023-12-12 DOI: 10.1007/s00224-023-10155-7

Aaron Bernstein

{"title":"Improved Bounds for Matching in Random-Order Streams","authors":"Aaron Bernstein","doi":"10.1007/s00224-023-10155-7","DOIUrl":"https://doi.org/10.1007/s00224-023-10155-7","url":null,"abstract":"We study the problem of computing an approximate maximum cardinality matching in the semi-streaming model when edges arrive in a random order. In the semi-streaming model, the edges of the input graph (G = (V,E)) are given as a stream (e_1, ldots , e_m), and the algorithm is allowed to make a single pass over this stream while using (O(ntext {polylog}(n))) space ((m = |E|) and (n = |V|)). If the order of edges is adversarial, a simple single-pass greedy algorithm yields a 1/2-approximation in O(n) space; achieving a better approximation in adversarial streams remains an elusive open question. A line of recent work shows that one can improve upon the 1/2-approximation if the edges of the stream arrive in a random order. The state of the art for this model is two-fold: Assadi et al. [SODA 2019] show how to compute a (frac{2}{3}) ((sim .66))-approximate matching, but the space requirement is (O(n^{1.5}text {polylog}(n))). Very recently, Farhadi et al. [SODA 2020] presented an algorithm with the desired space usage of (O(ntext {polylog}(n))), but a worse approximation ratio of (frac{6}{11}) ((sim .545)), or (frac{3}{5}) ((=.6)) in bipartite graphs. In this paper, we present an algorithm that computes a (frac{2}{3}(sim .66))-approximate matching using only (O(nlog (n))) space, improving upon both results above. We also note that for adversarial streams, a lower bound of Kapralov [SODA 2013] shows that any algorithm that achieves a (1-frac{1}{e})((sim .63))-approximation requires ((n^{1+Omega (1/log log (n))})) space; recent follow-up work by the same author improved this lower bound to (1+ln (2) sim .59) [SODA 2021]. As a consequence, both our result and the earlier result of Farhadi et al. prove that the problem of computing a maximum matching is strictly easier in random-order streams than in adversarial ones.","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":"31 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138573618","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

Beyond the Existential Theory of the Reals 超越现实存在论

IF 0.5 4区计算机科学

Theory of Computing Systems Pub Date : 2023-12-12 DOI: 10.1007/s00224-023-10151-x

Marcus Schaefer, Daniel Štefankovič

引用次数: 0

Upper Bounds on Communication in Terms of Approximate Rank 近似等级的通信上限

IF 0.5 4区计算机科学

Theory of Computing Systems Pub Date : 2023-12-12 DOI: 10.1007/s00224-023-10158-4

Anna Gál, Ridwan Syed

引用次数: 0

A Closer Look at the Expressive Power of Logics Based on Word Equations 近距离观察基于文字等式的逻辑表达能力

IF 0.5 4区计算机科学

Theory of Computing Systems Pub Date : 2023-12-11 DOI: 10.1007/s00224-023-10154-8

Joel Day, Vijay Ganesh, Nathan Grewal, Matthew Konefal, Florin Manea

{"title":"A Closer Look at the Expressive Power of Logics Based on Word Equations","authors":"Joel Day, Vijay Ganesh, Nathan Grewal, Matthew Konefal, Florin Manea","doi":"10.1007/s00224-023-10154-8","DOIUrl":"https://doi.org/10.1007/s00224-023-10154-8","url":null,"abstract":"Word equations are equations (alpha doteq beta ) where (alpha ) and (beta ) are words consisting of letters from some alphabet (Sigma ) and variables from a set X. Recently, there has been substantial interest in the context of string solving in logics combining word equations with other kinds of constraints on words such as (regular) language membership (regular constraints) and arithmetic over string lengths (length constraints). We consider the expressive power of such logics by looking at the set of all values a single variable might take as part of a satisfying assignment for a given formula. Hence, each formula-variable pair defines a formal language, and each logic defines a class of formal languages. We consider logics arising from combining word equations with either length constraints, regular constraints, or both. We also consider word equations with visibly pushdown language membership constraints as a generalisation of the combination of regular and length constraints. We show that word equations with visibly pushdown membership constraints are sufficient to express all recursively enumerable languages and hence satisfiability is undecidable in this case. We then establish a strict hierarchy involving the other combinations. We also provide a complete characterisation of when a thin regular language is expressible by word equations (alone) and some further partial results for regular languages in the general case.","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":"1052 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138566860","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

Subquadratic-time Algorithm for the Diameter and all Eccentricities on Median Graphs 中位数图上直径和所有偏心率的次二次时间算法

IF 0.5 4区计算机科学

Theory of Computing Systems Pub Date : 2023-12-04 DOI: 10.1007/s00224-023-10153-9

Pierre Bergé, Guillaume Ducoffe, Michel Habib

{"title":"Subquadratic-time Algorithm for the Diameter and all Eccentricities on Median Graphs","authors":"Pierre Bergé, Guillaume Ducoffe, Michel Habib","doi":"10.1007/s00224-023-10153-9","DOIUrl":"https://doi.org/10.1007/s00224-023-10153-9","url":null,"abstract":"On sparse graphs, Roditty and Williams [2013] proved that no (varvec{O(n^{2-varepsilon })})-time algorithm achieves an approximation factor smaller than (varvec{frac{3}{2}}) for the diameter problem unless SETH fails. In this article, we solve an open question formulated in the literature: can we use the structural properties of median graphs to break this global quadratic barrier? We propose the first combinatorial algorithm computing exactly all eccentricities of a median graph in truly subquadratic time. Median graphs constitute the family of graphs which is the most studied in metric graph theory because their structure represents many other discrete and geometric concepts, such as CAT(0) cube complexes. Our result generalizes a recent one, stating that there is a linear-time algorithm for all eccentricities in median graphs with bounded dimension (varvec{d}), i.e. the dimension of the largest induced hypercube. This prerequisite on (varvec{d}) is not necessary anymore to determine all eccentricities in subquadratic time. The execution time of our algorithm is (varvec{O(n^{1.6456}log ^{O(1)} n)}). We provide also some satellite outcomes related to this general result. In particular, restricted to simplex graphs, this algorithm enumerates all eccentricities with a quasilinear running time. Moreover, an algorithm is proposed to compute exactly all reach centralities in time (varvec{O(2^{3d}nlog ^{O(1)}n)}).","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":"150 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138542830","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 Partial Vertex Cover Problem in Bipartite Graphs - a Parameterized Perspective 二部图的部分顶点覆盖问题——一个参数化的透视

IF 0.5 4区计算机科学

Theory of Computing Systems Pub Date : 2023-12-01 DOI: 10.1007/s00224-023-10152-w

Vahan Mkrtchyan, Garik Petrosyan, K. Subramani, Piotr Wojciechowski

{"title":"On the Partial Vertex Cover Problem in Bipartite Graphs - a Parameterized Perspective","authors":"Vahan Mkrtchyan, Garik Petrosyan, K. Subramani, Piotr Wojciechowski","doi":"10.1007/s00224-023-10152-w","DOIUrl":"https://doi.org/10.1007/s00224-023-10152-w","url":null,"abstract":"In this paper, we examine variants of the partial vertex cover problem from the perspective of parameterized algorithms. Recall that in the classical vertex cover problem (VC), we are given a graph (mathbf{G = langle V, E rangle }) and a number k and asked if we can cover all of the edges in (textbf{E}), using at most k vertices from (textbf{V}). The partial vertex cover problem (PVC) is a more general version of the VC problem in which we are given an additional parameter (k'). We then ask the question of whether at least (k') of the edges in (textbf{E}) can be covered using at most k vertices from (textbf{V}). Note that the VC problem is a special case of the PVC problem when (k'=|textbf{E}|). In this paper, we study the weighted generalizations of the PVC problem. This is called the weighted partial vertex cover problem (WPVC). In the WPVC problem, we are given two parameters R and L, associated respectively with the vertex set (textbf{V}) and edge set (textbf{E}) of the graph (textbf{G}) respectively. Additionally, we are given non-negative integral weight functions for the vertices and the edges. The goal then is to cover edges of total weight at least L, using vertices of total weight at most R. This paper studies several variants of the PVC and WPVC problems and establishes new results from the perspective of fixed-parameter tractability and W[1]-hardness. We also introduce a new problem called the partial vertex cover with matching constraints and show that it is Fixed-Parameter Tractable (FPT) for a certain class of graphs. Finally, we show that the WPVC problem is APX-complete for bipartite graphs.","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":"5 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138524057","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

Disentangling the Computational Complexity of Network Untangling 解缠网络解缠的计算复杂度

4区计算机科学

Theory of Computing Systems Pub Date : 2023-11-14 DOI: 10.1007/s00224-023-10150-y

Vincent Froese, Pascal Kunz, Philipp Zschoche

引用次数: 0

Stability, Vertex Stability, and Unfrozenness for Special Graph Classes 特殊图类的稳定性、顶点稳定性和非冻结性

4区计算机科学

Theory of Computing Systems Pub Date : 2023-11-07 DOI: 10.1007/s00224-023-10149-5

Frank Gurski, Jörg Rothe, Robin Weishaupt

{"title":"Stability, Vertex Stability, and Unfrozenness for Special Graph Classes","authors":"Frank Gurski, Jörg Rothe, Robin Weishaupt","doi":"10.1007/s00224-023-10149-5","DOIUrl":"https://doi.org/10.1007/s00224-023-10149-5","url":null,"abstract":"Abstract Frei et al. (J. Comput. Syst. Sci. 123 , 103–121, 2022) show that the stability, vertex stability, and unfrozenness problems with respect to certain graph parameters are complete for $$varvec{Theta _{2}^{textrm{P}}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msubsup> <mml:mi>Θ</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mtext>P</mml:mtext> </mml:msubsup> </mml:mrow> </mml:math> , the class of problems solvable in polynomial time by parallel access to an NP oracle. They studied the common graph parameters $$varvec{alpha }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> </mml:math> (the independence number), $$varvec{beta }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>β</mml:mi> </mml:mrow> </mml:math> (the vertex cover number), $$varvec{omega }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>ω</mml:mi> </mml:mrow> </mml:math> (the clique number), and $$varvec{chi }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>χ</mml:mi> </mml:mrow> </mml:math> (the chromatic number). We complement their approach by providing polynomial-time algorithms solving these problems for special graph classes, namely for graphs with bounded tree-width or bounded clique-width. In order to improve these general time bounds even further, we then focus on trees, forests, bipartite graphs, and co-graphs.","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":"58 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135476611","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

Quantum Algorithm for Lexicographically Minimal String Rotation 字典最小字符串旋转的量子算法

4区计算机科学

Theory of Computing Systems Pub Date : 2023-10-24 DOI: 10.1007/s00224-023-10146-8

Qisheng Wang, Mingsheng Ying

{"title":"Quantum Algorithm for Lexicographically Minimal String Rotation","authors":"Qisheng Wang, Mingsheng Ying","doi":"10.1007/s00224-023-10146-8","DOIUrl":"https://doi.org/10.1007/s00224-023-10146-8","url":null,"abstract":"Abstract Lexicographically minimal string rotation (LMSR) is a problem to find the minimal one among all rotations of a string in the lexicographical order, which is widely used in equality checking of graphs, polygons, automata and chemical structures. In this paper, we propose an $$O(n^{3/4})$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>n</mml:mi> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>/</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> quantum query algorithm for LMSR. In particular, the algorithm has average-case query complexity $$O(sqrt{n} log n)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msqrt> <mml:mi>n</mml:mi> </mml:msqrt> <mml:mo>log</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , which is shown to be asymptotically optimal up to a polylogarithmic factor, compared to its $$Omega left( sqrt{n/log n}right) $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>Ω</mml:mi> <mml:mfenced> <mml:msqrt> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>/</mml:mo> <mml:mo>log</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:msqrt> </mml:mfenced> </mml:mrow> </mml:math> lower bound. Furthermore, we show that our quantum algorithm outperforms any (classical) randomized algorithms in both worst and average cases. As an application, it is used in benzenoid identification and disjoint-cycle automata minimization.","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":"144 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135273543","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: 5