International Symposium on Mathematical Foundations of Computer Science最新文献_第5页

Independent set reconfiguration on directed graphs 有向图上的独立集重构

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-03-25 DOI: 10.48550/arXiv.2203.13435

Takehiro Ito, Yuni Iwamasa, Yasuaki Kobayashi, Yu Nakahata, Y. Otachi, Masahiro Takahashi, Kunihiro Wasa

{"title":"Independent set reconfiguration on directed graphs","authors":"Takehiro Ito, Yuni Iwamasa, Yasuaki Kobayashi, Yu Nakahata, Y. Otachi, Masahiro Takahashi, Kunihiro Wasa","doi":"10.48550/arXiv.2203.13435","DOIUrl":"https://doi.org/10.48550/arXiv.2203.13435","url":null,"abstract":"Directed Token Sliding asks, given a directed graph and two sets of pairwise non-adjacent vertices, whether one can reach from one set to the other by repeatedly applying a local operation that exchanges a vertex in the current set with one of its out-neighbors, while keeping the nonadjacency. It can be seen as a reconﬁguration process where a token is placed on each vertex in the current set, and the local operation slides a token along an arc respect-ing its direction. Previously, such a problem was extensively studied on undirected graphs, where the edges have no directions and thus the local operation is symmetric. Directed Token Sliding is a generalization of its undirected variant since an undirected edge can be simulated by two arcs of opposite directions. In this paper, we initiate the algorithmic study of Directed Token Sliding . We ﬁrst observe that the problem is PSPACE-complete even if we forbid parallel arcs in opposite directions and that the problem on directed acyclic graphs is NP-complete and W[1]-hard parameterized by the size of the sets in consideration. We then show our main result: a linear-time algorithm for the problem on directed graphs whose underlying undirected graphs are trees, which are called polytrees. Such a result is also known for the undirected variant of the problem on trees [Demaine et al. TCS 2015], but the techniques used here are quite diﬀerent because of the asymmetric nature of the directed problem. We present a characterization of yes-instances based on the existence of a certain set of directed paths, and then derive simple equivalent conditions from it by some observations, which admits an eﬃcient algorithm. For the polytree case, we also present a quadratic-time algorithm that outputs, if the input is a yes-instance, one of the shortest reconﬁguration sequences.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114691571","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: 3

On the Skolem Problem for Reversible Sequences 关于可逆序列的Skolem问题

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-03-14 DOI: 10.48550/arXiv.2203.07061

George Kenison

引用次数: 1

CNF Encodings of Parity 校验校验的CNF编码

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-03-02 DOI: 10.48550/arXiv.2203.01082

G. Emdin, A. Kulikov, Ivan Mihajlin, Nikita Slezkin

引用次数: 0

Algebraic Representations of Unique Bipartite Perfect Matching 唯一二部完美匹配的代数表示

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-03-02 DOI: 10.48550/arXiv.2203.01071

Gal Beniamini

引用次数: 1

The complexity of computing optimum labelings for temporal connectivity 计算时间连通性的最佳标签的复杂性

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-02-11 DOI: 10.4230/LIPIcs.MFCS.2022.62

Nina Klobas, G. Mertzios, Hendrik Molter, P. Spirakis

{"title":"The complexity of computing optimum labelings for temporal connectivity","authors":"Nina Klobas, G. Mertzios, Hendrik Molter, P. Spirakis","doi":"10.4230/LIPIcs.MFCS.2022.62","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2022.62","url":null,"abstract":"A graph is temporally connected if there exists a strict temporal path, i.e. a path whose edges have strictly increasing labels, from every vertex $u$ to every other vertex $v$. In this paper we study temporal design problems for undirected temporally connected graphs. The basic setting of these optimization problems is as follows: given a connected undirected graph $G$, what is the smallest number $|lambda|$ of time-labels that we need to add to the edges of $G$ such that the resulting temporal graph $(G,lambda)$ is temporally connected? As it turns out, this basic problem, called MINIMUM LABELING (ML), can be optimally solved in polynomial time. However, exploiting the temporal dimension, the problem becomes more interesting and meaningful in its following variations, which we investigate in this paper. First we consider the problem MIN. AGED LABELING (MAL) of temporally connecting the graph when we are given an upper-bound on the allowed age (i.e. maximum label) of the obtained temporal graph $(G,lambda)$. Second we consider the problem MIN. STEINER LABELING (MSL), where the aim is now to have a temporal path between any pair of\"terminals\"vertices which lie in a subset $Rsubseteq V$. This relaxed problem resembles STEINER TREE in static graphs. However, due to the requirement of strictly increasing labels in a temporal path, STEINER TREE is not a special case of MSL. Finally we consider the age-restricted version of MSL, namely MIN. AGED STEINER LABELING (MASL). Our main results are threefold: we prove that (i) MAL becomes NP-complete on undirected graphs, while (ii) MASL becomes W[1]-hard with respect to the number $|R|$ of terminals. On the other hand we prove that (iii) although the age-unrestricted problem MSL is NP-hard, it is in FPT with respect to the number $|R|$ of terminals. That is, adding the age restriction, makes the above problems strictly harder.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116969324","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: 5

On the Identity Problem for Unitriangular Matrices of Dimension Four 关于四维酉角矩阵的恒等问题

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-02-10 DOI: 10.4230/LIPIcs.MFCS.2022.43

Rui-Tao Dong

引用次数: 4

Tree exploration in dual-memory model 双内存模型中的树探索

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-12-26 DOI: 10.4230/LIPIcs.MFCS.2022.22

Dominik Bojko, Karol Gotfryd, D. Kowalski, Dominik Pajak

{"title":"Tree exploration in dual-memory model","authors":"Dominik Bojko, Karol Gotfryd, D. Kowalski, Dominik Pajak","doi":"10.4230/LIPIcs.MFCS.2022.22","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2022.22","url":null,"abstract":"We study the problem of online tree exploration by a deterministic mobile agent. Our main objective is to establish what features of the model of the mobile agent and the environment allow linear exploration time. We study agents that, upon entering a node, do not receive as input the edge via which they entered. In such model, deterministic memoryless exploration is infeasible, hence the agent needs to be allowed to use some memory. The memory can be located at the agent or at each node. The existing lower bounds show that if the memory is either only at the agent or only at the nodes, then the exploration needs superlinear time. We show that tree exploration in dual-memory model, with constant memory at the agent and logarithmic in the degree at each node is possible in linear time when one of the two additional features is present: fixed initial state of the memory at each node (so called clean memory) or a single movable token. We present two algorithms working in linear time for arbitrary trees in these two models. On the other hand, in our lower bound we show that if the agent has a single bit of memory and one bit is present at each node, then the exploration may require quadratic time even on paths, if the initial memory at nodes could be set arbitrarily (so called dirty memory). This shows that having clean node memory or a token allows linear time exploration of trees in the dual-memory model, but having neither of those features may lead to quadratic exploration time even on a simple path. of the on feasibility of we show that is possible to complete the tree exploration in the minimum possible linear time using (asymptotically) minimal memory. We show two algorithms in models CleanMem and Token , exploring arbitrary unknown trees in the optimal time O ( n ) if constant memory is located at the agent and logarithmic memory is located at each node. Our results show that in the context of tree exploration in dual-memory model, the assumption about clean (fixed initial state of node can be “traded” for a token.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132963300","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 Algorithms Based on Finitely Many Homomorphism Counts 基于有限多同态计数的算法

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-11-25 DOI: 10.4230/LIPIcs.MFCS.2022.32

Yijia Chen, J. Flum, Mingjun Liu, Zhiyang Xun

{"title":"On Algorithms Based on Finitely Many Homomorphism Counts","authors":"Yijia Chen, J. Flum, Mingjun Liu, Zhiyang Xun","doi":"10.4230/LIPIcs.MFCS.2022.32","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2022.32","url":null,"abstract":"It is well known [Lov'asz, 67] that up to isomorphism a graph~$G$ is determined by the homomorphism counts $hom(F, G)$, i.e., the number of homomorphisms from $F$ to $G$, where $F$ ranges over all graphs. Thus, in principle, we can answer any query concerning $G$ with only accessing the $hom(cdot,G)$'s instead of $G$ itself. In this paper, we deal with queries for which there is a hom algorithm, i.e., there are finitely many graphs $F_1, ldots, F_k$ such that for any graph $G$ whether it is a Yes-instance of the query is already determined by the vector[overrightarrow{hom}_{F_1,ldots,F_k}(G):= big(hom(F_1,G),ldots,hom(F_k,G)big),]where the graphs $F_1, ldots, F_k$ only depend on $varphi$. We observe that planarity of graphs and 3-colorability of graphs, properties expressible in monadic second-order logic, have no hom algorithm. On the other hand, queries expressible as a Boolean combination of universal sentences in first-order logic FO have a hom algorithm. Even though it is not easy to find FO definable queries without a hom algorithm, we succeed to show this for the non-existence of an isolated vertex, a property expressible by the FO sentence $forall xexists y Exy$, somehow the ``simplest'' graph property not definable by a Boolean combination of universal sentences.These results provide a characterization of the prefix classes of first-order logic with the property that each query definable by a sentence of the prefix class has a hom algorithm. For adaptive query algorithms, i.e., algorithms that again access $overrightarrow{hom}_{F_1,ldots,F_k}(G)$ but here $F_{i+1}$ might depend on $hom(F_1,G),ldots,hom(F_i,G)$, we show that three homomorphism counts $hom(cdot,G)$ are both sufficient and in general necessary to determine the isomorphism type of $G$.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128154785","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: 5

A Weyl Criterion for Finite-State Dimension 有限状态维的Weyl准则

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-11-07 DOI: 10.4230/LIPIcs.MFCS.2023.65

J. H. Lutz, S. Nandakumar, Subin Pulari

{"title":"A Weyl Criterion for Finite-State Dimension","authors":"J. H. Lutz, S. Nandakumar, Subin Pulari","doi":"10.4230/LIPIcs.MFCS.2023.65","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2023.65","url":null,"abstract":"Finite-state dimension, introduced early in this century as a finite-state version of classical Hausdorff dimension, is a quantitative measure of the lower asymptotic density of information in an infinite sequence over a finite alphabet, as perceived by finite automata. Finite-state dimension is a robust concept that now has equivalent formulations in terms of finite-state gambling, lossless finite-state data compression, finite-state prediction, entropy rates, and automatic Kolmogorov complexity. The Schnorr-Stimm dichotomy theorem gave the first automata-theoretic characterization of normal sequences, which had been studied in analytic number theory since Borel defined them. This theorem implies that a sequence (or a real number having this sequence as its base-b expansion) is normal if and only if it has finite-state dimension 1. One of the most powerful classical tools for investigating normal numbers is the Weyl criterion, which characterizes normality in terms of exponential sums. Such sums are well studied objects with many connections to other aspects of analytic number theory, and this has made use of Weyl criterion especially fruitful. This raises the question whether Weyl criterion can be generalized from finite-state dimension 1 to arbitrary finite-state dimensions, thereby making it a quantitative tool for studying data compression, prediction, etc. This paper does exactly this. We extend the Weyl criterion from a characterization of sequences with finite-state dimension 1 to a criterion that characterizes every finite-state dimension. This turns out not to be a routine generalization of the original Weyl criterion. Even though exponential sums may diverge for non-normal numbers, finite-state dimension can be characterized in terms of the dimensions of the subsequence limits of the exponential sums. We demonstrate the utility of our criterion though examples.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114204902","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

Fine-Grained Complexity of Rainbow Coloring and its Variants 彩虹着色的细粒度复杂性及其变体

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-10-01 DOI: 10.4230/LIPIcs.MFCS.2017.60

A. Agrawal

引用次数: 2