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FPT Approximation and Subexponential Algorithms for Covering Few or Many Edges 覆盖少边或多边的FPT逼近和亚指数算法
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-08-29 DOI: 10.4230/LIPIcs.MFCS.2023.46
F. Fomin, P. Golovach, Tanmay Inamdar, Tomohiro Koana
{"title":"FPT Approximation and Subexponential Algorithms for Covering Few or Many Edges","authors":"F. Fomin, P. Golovach, Tanmay Inamdar, Tomohiro Koana","doi":"10.4230/LIPIcs.MFCS.2023.46","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2023.46","url":null,"abstract":"We study the textsc{$alpha$-Fixed Cardinality Graph Partitioning ($alpha$-FCGP)} problem, the generic local graph partitioning problem introduced by Bonnet et al. [Algorithmica 2015]. In this problem, we are given a graph $G$, two numbers $k,p$ and $0leqalphaleq 1$, the question is whether there is a set $Ssubseteq V$ of size $k$ with a specified coverage function $cov_{alpha}(S)$ at least $p$ (or at most $p$ for the minimization version). The coverage function $cov_{alpha}(cdot)$ counts edges with exactly one endpoint in $S$ with weight $alpha$ and edges with both endpoints in $S$ with weight $1 - alpha$. $alpha$-FCGP generalizes a number of fundamental graph problems such as textsc{Densest $k$-Subgraph}, textsc{Max $k$-Vertex Cover}, and textsc{Max $(k,n-k)$-Cut}. A natural question in the study of $alpha$-FCGP is whether the algorithmic results known for its special cases, like textsc{Max $k$-Vertex Cover}, could be extended to more general settings. One of the simple but powerful methods for obtaining parameterized approximation [Manurangsi, SOSA 2019] and subexponential algorithms [Fomin et al. IPL 2011] for textsc{Max $k$-Vertex Cover} is based on the greedy vertex degree orderings. The main insight of our work is that the idea of greed vertex degree ordering could be used to design fixed-parameter approximation schemes (FPT-AS) for $alpha>0$ and the subexponential-time algorithms for the problem on apex-minor free graphs for maximization with $alpha>1/3$ and minimization with $alpha<1/3$.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133686875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamic constant time parallel graph algorithms with sub-linear work 具有次线性功的动态常数时间并行图算法
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-07-19 DOI: 10.48550/arXiv.2307.10107
Jonas Schmidt, T. Schwentick
{"title":"Dynamic constant time parallel graph algorithms with sub-linear work","authors":"Jonas Schmidt, T. Schwentick","doi":"10.48550/arXiv.2307.10107","DOIUrl":"https://doi.org/10.48550/arXiv.2307.10107","url":null,"abstract":"The paper proposes dynamic parallel algorithms for connectivity and bipartiteness of undirected graphs that require constant time and $O(n^{1/2+epsilon})$ work on the CRCW PRAM model. The work of these algorithms almost matches the work of the $O(log n)$ time algorithm for connectivity by Kopelowitz et al. (2018) on the EREW PRAM model and the time of the sequential algorithm for bipartiteness by Eppstein et al. (1997). In particular, we show that the sparsification technique, which has been used in both mentioned papers, can in principle also be used for constant time algorithms in the CRCW PRAM model, despite the logarithmic depth of sparsification trees.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126657195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Polynomial-Delay Enumeration of Large Maximal Common Independent Sets in Two Matroids 两个拟阵中极大公独立集的多项式-延迟枚举
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-07-18 DOI: 10.48550/arXiv.2307.08948
Yasuaki Kobayashi, Kazuhiro Kurita, Kunihiro Wasa
{"title":"Polynomial-Delay Enumeration of Large Maximal Common Independent Sets in Two Matroids","authors":"Yasuaki Kobayashi, Kazuhiro Kurita, Kunihiro Wasa","doi":"10.48550/arXiv.2307.08948","DOIUrl":"https://doi.org/10.48550/arXiv.2307.08948","url":null,"abstract":"Finding a maximum cardinality common independent set in two matroids (also known as Matroid Intersection) is a classical combinatorial optimization problem, which generalizes several well-known problems, such as finding a maximum bipartite matching, a maximum colorful forest, and an arborescence in directed graphs. Enumerating all maximal common independent sets in two (or more) matroids is a classical enumeration problem. In this paper, we address an ``intersection'' of these problems: Given two matroids and a threshold $tau$, the goal is to enumerate all maximal common independent sets in the matroids with cardinality at least $tau$. We show that this problem can be solved in polynomial delay and polynomial space. We also discuss how to enumerate all maximal common independent sets of two matroids in non-increasing order of their cardinalities.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132472086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On the Expressive Power of Regular Expressions with Backreferences 带反向引用的正则表达式的表达能力
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-07-13 DOI: 10.48550/arXiv.2307.08531
Taisei Nogami, Tachio Terauchi
{"title":"On the Expressive Power of Regular Expressions with Backreferences","authors":"Taisei Nogami, Tachio Terauchi","doi":"10.48550/arXiv.2307.08531","DOIUrl":"https://doi.org/10.48550/arXiv.2307.08531","url":null,"abstract":"A rewb is a regular expression extended with a feature called backreference. It is broadly known that backreference is a practical extension of regular expressions, and is supported by most modern regular expression engines, such as those in the standard libraries of Java, Python, and more. Meanwhile, indexed languages are the languages generated by indexed grammars, a formal grammar class proposed by A.V.Aho. We show that these two models' expressive powers are related in the following way: every language described by a rewb is an indexed language. As the smallest formal grammar class previously known to contain rewbs is the class of context sensitive languages, our result strictly improves the known upper-bound. Moreover, we prove the following two claims: there exists a rewb whose language does not belong to the class of stack languages, which is a proper subclass of indexed languages, and the language described by a rewb without a captured reference is in the class of nonerasing stack languages, which is a proper subclass of stack languages. Finally, we show that the hierarchy investigated in a prior study, which separates the expressive power of rewbs by the notion of nested levels, is within the class of nonerasing stack languages.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133518133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Entropic Risk for Turn-Based Stochastic Games 回合制随机博弈的熵风险
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-07-13 DOI: 10.48550/arXiv.2307.06611
C. Baier, K. Chatterjee, Tobias Meggendorfer, Jakob Piribauer
{"title":"Entropic Risk for Turn-Based Stochastic Games","authors":"C. Baier, K. Chatterjee, Tobias Meggendorfer, Jakob Piribauer","doi":"10.48550/arXiv.2307.06611","DOIUrl":"https://doi.org/10.48550/arXiv.2307.06611","url":null,"abstract":"Entropic risk (ERisk) is an established risk measure in finance, quantifying risk by an exponential re-weighting of rewards. We study ERisk for the first time in the context of turn-based stochastic games with the total reward objective. This gives rise to an objective function that demands the control of systems in a risk-averse manner. We show that the resulting games are determined and, in particular, admit optimal memoryless deterministic strategies. This contrasts risk measures that previously have been considered in the special case of Markov decision processes and that require randomization and/or memory. We provide several results on the decidability and the computational complexity of the threshold problem, i.e. whether the optimal value of ERisk exceeds a given threshold. In the most general case, the problem is decidable subject to Shanuel's conjecture. If all inputs are rational, the resulting threshold problem can be solved using algebraic numbers, leading to decidability via a polynomial-time reduction to the existential theory of the reals. Further restrictions on the encoding of the input allow the solution of the threshold problem in NP$cap$coNP. Finally, an approximation algorithm for the optimal value of ERisk is provided.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132289986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 Finite Variable-Occurrence Fragment of the Calculus of Relations with Bounded Dot-Dagger Alternation 有界点-匕首交替关系演算的有限变现片段
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-07-11 DOI: 10.48550/arXiv.2307.05046
Yoshiki Nakamura
{"title":"On the Finite Variable-Occurrence Fragment of the Calculus of Relations with Bounded Dot-Dagger Alternation","authors":"Yoshiki Nakamura","doi":"10.48550/arXiv.2307.05046","DOIUrl":"https://doi.org/10.48550/arXiv.2307.05046","url":null,"abstract":"We introduce the $k$-variable-occurrence fragment, which is the set of terms having at most $k$ occurrences of variables. We give a sufficient condition for the decidability of the equational theory of the $k$-variable-occurrence fragment using the finiteness of a monoid. As a case study, we prove that for Tarski's calculus of relations with bounded dot-dagger alternation (an analogy of quantifier alternation in first-order logic), the equational theory of the $k$-variable-occurrence fragment is decidable for each $k$.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"128 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128171319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximating the Value of Energy-Parity Objectives in Simple Stochastic Games 简单随机对策中能量平价目标值的逼近
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-07-11 DOI: 10.48550/arXiv.2307.05762
Mohan Dantam, Richard Mayr
{"title":"Approximating the Value of Energy-Parity Objectives in Simple Stochastic Games","authors":"Mohan Dantam, Richard Mayr","doi":"10.48550/arXiv.2307.05762","DOIUrl":"https://doi.org/10.48550/arXiv.2307.05762","url":null,"abstract":"We consider simple stochastic games $mathcal G$ with energy-parity objectives, a combination of quantitative rewards with a qualitative parity condition. The Maximizer tries to avoid running out of energy while simultaneously satisfying a parity condition. We present an algorithm to approximate the value of a given configuration in 2-NEXPTIME. Moreover, $varepsilon$-optimal strategies for either player require at most $O(2EXP(|{mathcal G}|)cdotlog(frac{1}{varepsilon}))$ memory modes.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115081402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Tight Algorithmic Applications of Clique-Width Generalizations 团宽推广的严密算法应用
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-07-10 DOI: 10.48550/arXiv.2307.04628
V. Chekan, Stefan Kratsch
{"title":"Tight Algorithmic Applications of Clique-Width Generalizations","authors":"V. Chekan, Stefan Kratsch","doi":"10.48550/arXiv.2307.04628","DOIUrl":"https://doi.org/10.48550/arXiv.2307.04628","url":null,"abstract":"In this work, we study two natural generalizations of clique-width introduced by Martin F\"urer. Multi-clique-width (mcw) allows every vertex to hold multiple labels [ITCS 2017], while for fusion-width (fw) we have a possibility to merge all vertices of a certain label [LATIN 2014]. F\"urer has shown that both parameters are upper-bounded by treewidth thus making them more appealing from an algorithmic perspective than clique-width and asked for applications of these parameters for problem solving. First, we determine the relation between these two parameters by showing that $operatorname{mcw} leq operatorname{fw} + 1$. Then we show that when parameterized by multi-clique-width, many problems (e.g., Connected Dominating Set) admit algorithms with the same running time as for clique-width despite the exponential gap between these two parameters. For some problems (e.g., Hamiltonian Cycle) we show an analogous result for fusion-width: For this we present an alternative view on fusion-width by introducing so-called glue-expressions which might be interesting on their own. All algorithms obtained in this work are tight up to (Strong) Exponential Time Hypothesis.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128213920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Deciding Predicate Logical Theories of Real-Valued Functions 确定实值函数的谓词逻辑理论
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-06-28 DOI: 10.48550/arXiv.2306.16505
Stefan Ratschan
{"title":"Deciding Predicate Logical Theories of Real-Valued Functions","authors":"Stefan Ratschan","doi":"10.48550/arXiv.2306.16505","DOIUrl":"https://doi.org/10.48550/arXiv.2306.16505","url":null,"abstract":"The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that reason about real-valued functions. This paper defines a first-order predicate language for reasoning about multi-dimensional smooth real-valued functions and their derivatives, and demonstrates that - despite the obvious undecidability barriers - certain positive decidability results for such a language are indeed possible.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117022932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Separating Automatic Relations 分离自动关系
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-05-15 DOI: 10.48550/arXiv.2305.08727
Pablo Barcel'o, Diego Figueira, Rémi Morvan
{"title":"Separating Automatic Relations","authors":"Pablo Barcel'o, Diego Figueira, Rémi Morvan","doi":"10.48550/arXiv.2305.08727","DOIUrl":"https://doi.org/10.48550/arXiv.2305.08727","url":null,"abstract":"We study the separability problem for automatic relations (i.e., relations on finite words definable by synchronous automata) in terms of recognizable relations (i.e., finite unions of products of regular languages). This problem takes as input two automatic relations $R$ and $R'$, and asks if there exists a recognizable relation $S$ that contains $R$ and does not intersect $R'$. We show this problem to be undecidable when the number of products allowed in the recognizable relation is fixed. In particular, checking if there exists a recognizable relation $S$ with at most $k$ products of regular languages that separates $R$ from $R'$ is undecidable, for each fixed $k geq 2$. Our proofs reveal tight connections, of independent interest, between the separability problem and the finite coloring problem for automatic graphs, where colors are regular languages.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129070501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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