International Symposium on Mathematical Foundations of Computer Science最新文献_第2页

Solving irreducible stochastic mean-payoff games and entropy games by relative Krasnoselskii-Mann iteration 用相对Krasnoselskii-Mann迭代求解不可约随机均值-收益对策和熵对策

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-05-03 DOI: 10.48550/arXiv.2305.02458

M. Akian, S. Gaubert, Ulysse Naepels, Basile Terver

{"title":"Solving irreducible stochastic mean-payoff games and entropy games by relative Krasnoselskii-Mann iteration","authors":"M. Akian, S. Gaubert, Ulysse Naepels, Basile Terver","doi":"10.48550/arXiv.2305.02458","DOIUrl":"https://doi.org/10.48550/arXiv.2305.02458","url":null,"abstract":"We analyse an algorithm solving stochastic mean-payoff games, combining the ideas of relative value iteration and of Krasnoselskii-Mann damping. We derive parameterized complexity bounds for several classes of games satisfying irreducibility conditions. We show in particular that an $epsilon$-approximation of the value of an irreducible concurrent stochastic game can be computed in a number of iterations in $O(|logepsilon|)$ where the constant in the $O(cdot)$ is explicit, depending on the smallest non-zero transition probabilities. This should be compared with a bound in $O(|epsilon|^{-1}|log(epsilon)|)$ obtained by Chatterjee and Ibsen-Jensen (ICALP 2014) for the same class of games, and to a $O(|epsilon|^{-1})$ bound by Allamigeon, Gaubert, Katz and Skomra (ICALP 2022) for turn-based games. We also establish parameterized complexity bounds for entropy games, a class of matrix multiplication games introduced by Asarin, Cervelle, Degorre, Dima, Horn and Kozyakin. We derive these results by methods of variational analysis, establishing contraction properties of the relative Krasnoselskii-Mann iteration with respect to Hilbert's semi-norm.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115312836","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

Speed Me up if You Can: Conditional Lower Bounds on Opacity Verification 如果可以，请加快速度:不透明度验证的条件下界

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-04-19 DOI: 10.48550/arXiv.2304.09920

Jivr'i Balun, Tomas Masopust, Petr Osivcka

引用次数: 0

Dichotomies for Maximum Matching Cut: H-Freeness, Bounded Diameter, Bounded Radius 最大匹配切割的二分类:h自由度，有界直径，有界半径

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-04-03 DOI: 10.48550/arXiv.2304.01099

Felicia Lucke, D. Paulusma, B. Ries

{"title":"Dichotomies for Maximum Matching Cut: H-Freeness, Bounded Diameter, Bounded Radius","authors":"Felicia Lucke, D. Paulusma, B. Ries","doi":"10.48550/arXiv.2304.01099","DOIUrl":"https://doi.org/10.48550/arXiv.2304.01099","url":null,"abstract":"The (Perfect) Matching Cut problem is to decide if a graph $G$ has a (perfect) matching cut, i.e., a (perfect) matching that is also an edge cut of $G$. Both Matching Cut and Perfect Matching Cut are known to be NP-complete, leading to many complexity results for both problems on special graph classes. A perfect matching cut is also a matching cut with maximum number of edges. To increase our understanding of the relationship between the two problems, we introduce the Maximum Matching Cut problem. This problem is to determine a largest matching cut in a graph. We generalize and unify known polynomial-time algorithms for Matching Cut and Perfect Matching Cut restricted to graphs of diameter at most $2$ and to $(P_6 + sP_2)$-free graphs. We also show that the complexity of Maximum Matching Cut} differs from the complexities of Matching Cut and Perfect Matching Cut by proving NP-hardness of Maximum Matching Cut for $2P_3$-free quadrangulated graphs of diameter 3 and radius 2 and for subcubic line graphs of triangle-free graphs. In this way, we obtain full dichotomies of Maximum Matching Cut for graphs of bounded diameter, bounded radius and $H$-free graphs.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133985453","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: 2

Locality Theorems in Semiring Semantics 半环语义中的局部性定理

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-03-22 DOI: 10.48550/arXiv.2303.12627

Clotilde Biziere, E. Grädel, Matthias Naaf

引用次数: 1

Descriptive complexity for distributed computing with circuits 带有电路的分布式计算的描述复杂性

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-03-08 DOI: 10.48550/arXiv.2303.04735

Veeti Ahvonen, Damian Heiman, L. Hella, Antti Kuusisto

引用次数: 1

Ordinal measures of the set of finite multisets 有限多集集合的序数测度

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-02-20 DOI: 10.48550/arXiv.2302.09881

Isa Vialard

引用次数: 0

Parameterized Max Min Feedback Vertex Set 参数化的最大最小反馈顶点集

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-02-19 DOI: 10.48550/arXiv.2302.09604

M. Lampis, N. Melissinos, Manolis Vasilakis

引用次数: 2

Distributed CONGEST Algorithm for Finding Hamiltonian Paths in Dirac Graphs and Generalizations Dirac图中寻找哈密顿路径的分布式CONGEST算法及其推广

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-02-01 DOI: 10.48550/arXiv.2302.00742

Noy Biton, R. Levi, Moti Medina

{"title":"Distributed CONGEST Algorithm for Finding Hamiltonian Paths in Dirac Graphs and Generalizations","authors":"Noy Biton, R. Levi, Moti Medina","doi":"10.48550/arXiv.2302.00742","DOIUrl":"https://doi.org/10.48550/arXiv.2302.00742","url":null,"abstract":"We study the problem of finding a Hamiltonian cycle under the promise that the input graph has a minimum degree of at least $n/2$, where $n$ denotes the number of vertices in the graph. The classical theorem of Dirac states that such graphs (a.k.a. Dirac graphs) are Hamiltonian, i.e., contain a Hamiltonian cycle. Moreover, finding a Hamiltonian cycle in Dirac graphs can be done in polynomial time in the classical centralized model. This paper presents a randomized distributed CONGEST algorithm that finds w.h.p. a Hamiltonian cycle (as well as maximum matching) within $O(log n)$ rounds under the promise that the input graph is a Dirac graph. This upper bound is in contrast to general graphs in which both the decision and search variants of Hamiltonicity require $tilde{Omega}(n^2)$ rounds, as shown by Bachrach et al. [PODC'19]. In addition, we consider two generalizations of Dirac graphs: Ore graphs and Rahman-Kaykobad graphs [IPL'05]. In Ore graphs, the sum of the degrees of every pair of non-adjacent vertices is at least $n$, and in Rahman-Kaykobad graphs, the sum of the degrees of every pair of non-adjacent vertices plus their distance is at least $n+1$. We show how our algorithm for Dirac graphs can be adapted to work for these more general families of graphs.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127768389","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

Isometric Path Complexity of Graphs 图的等距路径复杂度

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-12-31 DOI: 10.4230/LIPIcs.MFCS.2023.32

Dibyayan Chakraborty, Jérémie Chalopin, Florent Foucaud, Y. Vaxès

{"title":"Isometric Path Complexity of Graphs","authors":"Dibyayan Chakraborty, Jérémie Chalopin, Florent Foucaud, Y. Vaxès","doi":"10.4230/LIPIcs.MFCS.2023.32","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2023.32","url":null,"abstract":"A set $S$ of isometric paths of a graph $G$ is\"$v$-rooted\", where $v$ is a vertex of $G$, if $v$ is one of the end-vertices of all the isometric paths in $S$. The isometric path complexity of a graph $G$, denoted by $ipco(G)$, is the minimum integer $k$ such that there exists a vertex $vin V(G)$ satisfying the following property: the vertices of any isometric path $P$ of $G$ can be covered by $k$ many $v$-rooted isometric paths. First, we provide an $O(n^2 m)$-time algorithm to compute the isometric path complexity of a graph with $n$ vertices and $m$ edges. Then we show that the isometric path complexity remains bounded for graphs in three seemingly unrelated graph classes, namely, hyperbolic graphs, (theta, prism, pyramid)-free graphs, and outerstring graphs. Hyperbolic graphs are extensively studied in Metric Graph Theory. The class of (theta, prism, pyramid)-free graphs are extensively studied in Structural Graph Theory, e.g. in the context of the Strong Perfect Graph Theorem. The class of outerstring graphs is studied in Geometric Graph Theory and Computational Geometry. Our results also show that the distance functions of these (structurally) different graph classes are more similar than previously thought. There is a direct algorithmic consequence of having small isometric path complexity. Specifically, we show that if the isometric path complexity of a graph $G$ is bounded by a constant, then there exists a polynomial-time constant-factor approximation algorithm for ISOMETRIC PATH COVER, whose objective is to cover all vertices of a graph with a minimum number of isometric paths. This applies to all the above graph classes.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"98 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123175926","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

Support Size Estimation: The Power of Conditioning 支持大小估计:调节的力量

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-11-22 DOI: 10.48550/arXiv.2211.11967

Diptarka Chakraborty, Gunjan Kumar, Kuldeep S. Meel

{"title":"Support Size Estimation: The Power of Conditioning","authors":"Diptarka Chakraborty, Gunjan Kumar, Kuldeep S. Meel","doi":"10.48550/arXiv.2211.11967","DOIUrl":"https://doi.org/10.48550/arXiv.2211.11967","url":null,"abstract":"We consider the problem of estimating the support size of a distribution $D$. Our investigations are pursued through the lens of distribution testing and seek to understand the power of conditional sampling (denoted as COND), wherein one is allowed to query the given distribution conditioned on an arbitrary subset $S$. The primary contribution of this work is to introduce a new approach to lower bounds for the COND model that relies on using powerful tools from information theory and communication complexity. Our approach allows us to obtain surprisingly strong lower bounds for the COND model and its extensions. 1) We bridge the longstanding gap between the upper ($O(log log n + frac{1}{epsilon^2})$) and the lower bound $Omega(sqrt{log log n})$ for COND model by providing a nearly matching lower bound. Surprisingly, we show that even if we get to know the actual probabilities along with COND samples, still $Omega(log log n + frac{1}{epsilon^2 log (1/epsilon)})$ queries are necessary. 2) We obtain the first non-trivial lower bound for COND equipped with an additional oracle that reveals the conditional probabilities of the samples (to the best of our knowledge, this subsumes all of the models previously studied): in particular, we demonstrate that $Omega(log log log n + frac{1}{epsilon^2 log (1/epsilon)})$ queries are necessary.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133399332","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: 2