International Journal of Foundations of Computer Science最新文献_第5页

Vertex and Link Residual Closeness of Graphs of Given Fractional Matching Number 给定分数匹配数的图的顶点和链路残差紧密性

4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-09-09 DOI: 10.1142/s0129054123500193

Hui Dong

引用次数: 1

On the Span of ℓ Distance Coloring of Infinite Hexagonal Grid 无穷六边形网格的距离着色的跨度

4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-09-08 DOI: 10.1142/s012905412350020x

Subhasis Koley, Sasthi C. Ghosh

{"title":"On the Span of ℓ Distance Coloring of Infinite Hexagonal Grid","authors":"Subhasis Koley, Sasthi C. Ghosh","doi":"10.1142/s012905412350020x","DOIUrl":"https://doi.org/10.1142/s012905412350020x","url":null,"abstract":"For a graph [Formula: see text] and [Formula: see text], an [Formula: see text] distance coloring is a coloring [Formula: see text] of [Formula: see text] with [Formula: see text] colors such that [Formula: see text] when [Formula: see text]. Here [Formula: see text] is the distance between [Formula: see text] and [Formula: see text] and is equal to the minimum number of edges that connect [Formula: see text] and [Formula: see text] in [Formula: see text]. The span of [Formula: see text] distance coloring of [Formula: see text], [Formula: see text], is the minimum [Formula: see text] among all [Formula: see text] distance coloring of [Formula: see text]. A class of channel assignment problem in cellular network can be formulated as a distance graph coloring problem in regular grid graphs. The cellular network is often modelled as an infinite hexagonal grid [Formula: see text], and hence determining [Formula: see text] has relevance from practical point of view. Jacko and Jendrol [Discussiones Mathematicae Graph Theory, 2005] determined the exact value of [Formula: see text] for any odd [Formula: see text] and for even [Formula: see text], it is conjectured that [Formula: see text] where [Formula: see text] is an integer, [Formula: see text] and [Formula: see text]. For [Formula: see text], the conjecture has been proved by Ghosh and Koley [[Formula: see text]nd Italian Conference on Theoretical Computer Science, 2021]. In this paper, we prove the conjecture for any even [Formula: see text].","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136362002","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

Approximating All-Points Furthest Pairs and Maximum Spanning Trees in Metric Spaces 度量空间中所有点最远对的逼近与最大生成树

IF 0.8 4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-09-07 DOI: 10.1142/s0129054123500181

Ching-Lueh Chang, Chun-Wei Chang

引用次数: 0

Regularity Conditions for Iterated Shuffle on Commutative Regular Languages 交换正则语言上迭代Shuffle的正则性条件

4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-09-02 DOI: 10.1142/s0129054123430037

Stefan Hoffmann

{"title":"Regularity Conditions for Iterated Shuffle on Commutative Regular Languages","authors":"Stefan Hoffmann","doi":"10.1142/s0129054123430037","DOIUrl":"https://doi.org/10.1142/s0129054123430037","url":null,"abstract":"We introduce the class [Formula: see text] of commutative regular languages that is a positive variety closed under binary shuffle and iterated shuffle (also called shuffle closure). This class arises out of the known positive variety [Formula: see text] by superalphabet closure, an operation on positive varieties we introduce and describe in the present work. We state alternative characterizations for both classes, that the shuffle of any language (resp. any commutative language) with a language from [Formula: see text] gives a regular language [Formula: see text]resp. a language from [Formula: see text] and that [Formula: see text] is also closed for iterated shuffle. Then we introduce the wider class [Formula: see text] that is also closed under iterated shuffle, but fails to be closed for binary shuffle and is not a positive variety. Furthermore, we give an automata-theoretical characterization for the regularity of the iterated shuffle of a regular commutative language. We use this result to show that, for a fixed alphabet, it is decidable in polynomial time whether the iterated shuffle of a commutative regular language given by a deterministic automaton is regular. Lastly, we state some normal form results for the aperiodic, or star-free, commutative languages and the commutative group languages.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134948591","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 Recursive Algorithm for Constructing Dual-CISTs in Hierarchical Folded Cubic Networks 构造分层折叠三次网络中双cist的递归算法

IF 0.8 4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-08-29 DOI: 10.1142/s0129054123500156

Hsin-Jung Lin, Shyue-Ming Tang, Kung-Jui Pai, Jou-Ming Chang

{"title":"A Recursive Algorithm for Constructing Dual-CISTs in Hierarchical Folded Cubic Networks","authors":"Hsin-Jung Lin, Shyue-Ming Tang, Kung-Jui Pai, Jou-Ming Chang","doi":"10.1142/s0129054123500156","DOIUrl":"https://doi.org/10.1142/s0129054123500156","url":null,"abstract":"Let [Formula: see text] be a set of [Formula: see text] spanning trees in a graph [Formula: see text]. The [Formula: see text] spanning trees are called completely independent spanning trees (CISTs for short) if the paths joining every pair of vertices [Formula: see text] and [Formula: see text] in any two trees have neither vertex nor edge in common except for [Formula: see text] and [Formula: see text]. Particularly, [Formula: see text] is called a dual-CIST provided [Formula: see text]. For data transmission applications in reliable networks, the existence of a dual-CIST can provide a configuration of fault-tolerant routing called protection routing. This paper investigates the problem of constructing a dual-CIST in the [Formula: see text]-dimensional hierarchical folded cubic network [Formula: see text]. The network is a two-level network using folded hypercube [Formula: see text] as clusters to reduce the diameter, hardware overhead and improve the fault tolerance ability. We propose a recursive algorithm to construct a dual-CIST of [Formula: see text] in [Formula: see text] time for [Formula: see text], where the time required is the same scale as the number of vertices of [Formula: see text]. Also, the diameter of each constructed CIST is [Formula: see text].","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47507517","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

Algorithms for the Truss Maintenance Problem on Edge-Weighted Graphs 边加权图上桁架维护问题的算法

IF 0.8 4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-08-01 DOI: 10.1142/s0129054123460036

Bin Liu, Zhenming Liu, Feiteng Zhang

引用次数: 0

PSPACE-Completeness of Reversible Deterministic Systems 可逆确定性系统的pspace -完备性

4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-07-29 DOI: 10.1142/s0129054123470032

Erik D. Demaine, Robert A. Hearn, Dylan Hendrickson, Jayson Lynch

{"title":"PSPACE-Completeness of Reversible Deterministic Systems","authors":"Erik D. Demaine, Robert A. Hearn, Dylan Hendrickson, Jayson Lynch","doi":"10.1142/s0129054123470032","DOIUrl":"https://doi.org/10.1142/s0129054123470032","url":null,"abstract":"We prove PSPACE-completeness of several reversible, fully deterministic systems. At the core, we develop a framework for such proofs (building on a result of Tsukiji and Hagiwara and a framework for motion planning through gadgets), showing that any system that can implement three basic gadgets is PSPACE-complete. We then apply this framework to four different systems, showing its versatility. First, we prove that Deterministic Constraint Logic is PSPACE-complete, fixing an error in a previous argument from 2008. Second, we give a new PSPACE-hardness proof for the reversible ‘billiard ball’ model of Fredkin and Toffoli from 40 years ago, newly establishing hardness when only two balls move at once. Third, we prove PSPACE-completeness of zero-player motion planning with any reversible deterministic interacting [Formula: see text]-tunnel gadget and a ‘rotate clockwise’ gadget (a zero-player analog of branching hallways). Fourth, we give simpler proofs that zero-player motion planning is PSPACE-complete with just a single gadget, the 3-spinner. These results should in turn make it even easier to prove PSPACE-hardness of other reversible deterministic systems.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134919522","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

Online Predictions for Online TSP on the Line 在线预测在线TSP在线

IF 0.8 4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-07-25 DOI: 10.1142/s0129054123470020

Jian-Xi Shao, Ya-Chun Liang, Chung-Shou Liao

{"title":"Online Predictions for Online TSP on the Line","authors":"Jian-Xi Shao, Ya-Chun Liang, Chung-Shou Liao","doi":"10.1142/s0129054123470020","DOIUrl":"https://doi.org/10.1142/s0129054123470020","url":null,"abstract":"With a rapidly growing attention on the development of learning-augmented algorithms, we revisit the classical online traveling salesman problem (OLTSP) from the perspective of such learning approaches. A learning-augmented online algorithm, or simply an online algorithm with predictions, considers how to improve its competitive performance with theoretical guarantees by forecasting the information of future requests, e.g., their release time or locations in the OLTSP. In this study, we investigate the OLTSP on the real line, motivated by the parcel picking problem in a smart warehouse, which aims at scheduling a route for a server (saying, a Kiva robot), starting at the origin, serving all online requests and returning to the origin such that the completion time is minimized. Each online request is released over time on the real line and the server moves back and forth along the line with unit speed. We mainly focus on zealous algorithms, a special type of online algorithms for the OLTSP which never allow the sever to wait if there are still unserved requests, and exploit a specific forecasting strategy, called online predictions, which makes a sequence of predictions one by one in an online manner. In order to ensure better competitive performance, we particularly explore the worst-case scenarios that restrict the power of such predictions. Based on the discussion, we make an assumption in which online predictions are guaranteed to be useful, and devise a learning-augmented algorithm with [Formula: see text]-robustness and [Formula: see text]-consistency, [Formula: see text], comparing to the previous lower bound of [Formula: see text], where [Formula: see text] and [Formula: see text] which indicate prediction errors are sufficiently small constants. Moreover, we also conduct numerical experiments to demonstrate the practical effectiveness of the proposed algorithm.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47381529","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

Decidability Boundaries for the Finite-Image Property of Weighted Finite Automata 加权有限自动机有限映象性质的可判定边界

IF 0.8 4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-07-25 DOI: 10.1142/s0129054123450041

M. Droste, Zoltán Fülöp, Dávid Kószó

引用次数: 0

Effective Projections on Group Shifts to Decide Properties of Group Cellular Automata 群移动的有效投影决定群元胞自动机的性质

IF 0.8 4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-07-19 DOI: 10.1142/s0129054123480040

Pierre Béaur, Jarkko Kari

{"title":"Effective Projections on Group Shifts to Decide Properties of Group Cellular Automata","authors":"Pierre Béaur, Jarkko Kari","doi":"10.1142/s0129054123480040","DOIUrl":"https://doi.org/10.1142/s0129054123480040","url":null,"abstract":"Many decision problems concerning cellular automata are known to be decidable in the case of algebraic cellular automata, that is, when the state set has an algebraic structure and the automaton acts as a morphism. The most studied cases include finite fields, finite commutative rings and finite commutative groups. In this paper, we provide methods to generalize these results to the broader case of group cellular automata, that is, the case where the state set is a finite (possibly non-commutative) finite group. The configuration space is not even necessarily the full shift but a subshift — called a group shift — that is a subgroup of the full shift on <math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℤ</mi></mrow><mrow><mi>d</mi></mrow></msup></math>, for any number <math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>d</mi></math> of dimensions. We show, in particular, that injectivity, surjectivity, equicontinuity, sensitivity and nilpotency are decidable for group cellular automata, and non-transitivity is semi-decidable. Injectivity always implies surjectivity, and jointly periodic points are dense in the limit set. The Moore direction of the Garden-of-Eden theorem holds for all group cellular automata, while the Myhill direction fails in some cases. The proofs are based on effective projection operations on group shifts that are, in particular, applied on the set of valid space-time diagrams of group cellular automata. This allows one to effectively construct the traces and the limit sets of group cellular automata. A preliminary version of this work was presented at the conference Mathematical Foundations of Computer Science 2020.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138543449","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