Pub Date : 2023-09-09DOI: 10.1142/s0129054123500193
Hui Dong
Vertex and link residual closeness are two new measures of network vulnerability due to the failure of individual vertices and links, respectively. We identify those graphs with maximum vertex/link residual closeness over all [Formula: see text]-vertex connected graphs with fixed fractional matching number.
{"title":"Vertex and Link Residual Closeness of Graphs of Given Fractional Matching Number","authors":"Hui Dong","doi":"10.1142/s0129054123500193","DOIUrl":"https://doi.org/10.1142/s0129054123500193","url":null,"abstract":"Vertex and link residual closeness are two new measures of network vulnerability due to the failure of individual vertices and links, respectively. We identify those graphs with maximum vertex/link residual closeness over all [Formula: see text]-vertex connected graphs with fixed fractional matching number.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136193151","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}
Pub Date : 2023-09-08DOI: 10.1142/s012905412350020x
Subhasis Koley, Sasthi C. Ghosh
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].
对于一个图形[公式:见文]和[公式:见文]，一个[公式:见文]距离着色是[公式:见文]与[公式:见文]颜色的着色[公式:见文]，使得[公式:见文]在[公式:见文]时[公式:见文]。这里[Formula: see text]是[Formula: see text]和[Formula: see text]之间的距离，等于在[Formula: see text]中连接[Formula: see text]和[Formula: see text]的最小边数。[公式:见文]、[公式:见文]的[公式:见文]距离着色的跨度是所有[公式:见文]的[公式:见文]距离着色的最小[公式:见文]。蜂窝网络中的一类信道分配问题可以表述为正则网格图中的距离图着色问题。蜂窝网络通常被建模为一个无限的六边形网格[公式:见文本]，因此从实际的角度来看，确定[公式:见文本]具有相关性。Jacko和Jendrol [Discussiones Mathematicae Graph Theory, 2005]确定了对于任何奇数[公式:见文本]和偶数[公式:见文本]的确切值，推测[公式:见文本]，其中[公式:见文本]是整数，[公式:见文本]和[公式:见文本]。对于[公式:见文]，这个猜想已经被Ghosh和Koley[[公式:见文]和意大利理论计算机科学会议，2021]证明。在本文中，我们证明了任意偶数的猜想[公式:见文]。
{"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}
Pub Date : 2023-09-07DOI: 10.1142/s0129054123500181
Ching-Lueh Chang, Chun-Wei Chang
Consider the problem of finding a point furthest from [Formula: see text] for each point [Formula: see text] in a metric space [Formula: see text], where [Formula: see text]. We prove this problem to have a deterministic [Formula: see text]-time [Formula: see text]-approximation algorithm. As a corollary, the maximum spanning tree problem in metric spaces has a deterministic [Formula: see text]-time [Formula: see text]-approximation algorithm. We also give a Monte Carlo [Formula: see text]-time algorithm outputting, for each [Formula: see text], a point [Formula: see text] satisfying [Formula: see text], where [Formula: see text]. As a corollary, we have a Monte Carlo [Formula: see text]-time algorithm for finding a spanning tree of weight at least [Formula: see text] in [Formula: see text].
{"title":"Approximating All-Points Furthest Pairs and Maximum Spanning Trees in Metric Spaces","authors":"Ching-Lueh Chang, Chun-Wei Chang","doi":"10.1142/s0129054123500181","DOIUrl":"https://doi.org/10.1142/s0129054123500181","url":null,"abstract":"Consider the problem of finding a point furthest from [Formula: see text] for each point [Formula: see text] in a metric space [Formula: see text], where [Formula: see text]. We prove this problem to have a deterministic [Formula: see text]-time [Formula: see text]-approximation algorithm. As a corollary, the maximum spanning tree problem in metric spaces has a deterministic [Formula: see text]-time [Formula: see text]-approximation algorithm. We also give a Monte Carlo [Formula: see text]-time algorithm outputting, for each [Formula: see text], a point [Formula: see text] satisfying [Formula: see text], where [Formula: see text]. As a corollary, we have a Monte Carlo [Formula: see text]-time algorithm for finding a spanning tree of weight at least [Formula: see text] in [Formula: see text].","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43766941","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}
Pub Date : 2023-09-02DOI: 10.1142/s0129054123430037
Stefan Hoffmann
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.
我们引入了交换正则语言类[公式:见文本]，它是二进制shuffle和迭代shuffle(也称为shuffle闭包)下封闭的正变量。这类是由已知的正变量(公式:见正文)通过超字母闭包产生的，超字母闭包是我们在本工作中介绍和描述的一种对正变量的运算。我们为这两个类说明了可选的特征描述，即任何语言的洗牌(例如:任何可交换的语言)与来自[公式:见文本]的语言相结合，就得到了正则语言[公式:见文本]resp。来自[Formula: see text]的语言，并且[Formula: see text]对于迭代洗牌也是关闭的。然后我们引入更广泛的类[公式:见文本]，它在迭代洗牌下也是封闭的，但在二元洗牌下不能封闭，并且不是一个正变量。此外，我们给出了正则交换语言的迭代洗牌的正则性的自动机理论表征。我们利用这一结果证明，对于一个固定的字母，由确定性自动机给出的可交换正则语言的迭代洗牌是否正则，在多项式时间内是可决定的。最后，我们给出了非周期或无星交换语言和交换群语言的一些正规结果。
{"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}
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].
设[公式:见文]为图[公式:见文]中的一组[公式:见文]生成树。如果在任意两棵树中，除了[公式:见文本]和[公式:见文本]之外，连接每一对顶点[公式:见文本]和[公式:见文本]的路径既没有共同的顶点也没有共同的边，那么[公式:见文本]生成树被称为完全独立生成树(简称cist)。特别是，[公式:见文]被称为双cist提供[公式:见文]。对于可靠网络中的数据传输应用，双cist的存在可以提供一种容错路由的配置，称为保护路由。本文研究了在[公式:见文]-维分层折叠三次网络[公式:见文]中构造双cist的问题。该网络采用折叠超立方体[公式:见文]作为簇，以减少直径、硬件开销和提高容错能力。我们提出了一种递归算法，在[Formula: see text]的[Formula: see text]时间中构造[Formula: see text]的双cist，所需时间与[Formula: see text]的顶点数相同。此外，每个构建的CIST的直径为[公式:见文本]。
{"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}
Pub Date : 2023-08-01DOI: 10.1142/s0129054123460036
Bin Liu, Zhenming Liu, Feiteng Zhang
The [Formula: see text]-truss was proposed by Jonathan Cohen in 2008, and it is a widely used as index in graph analysis for cohesive subgraph mining. There are two basic problems in this area. One is the truss decomposition problem, which is to compute the truss number of every edge; the other is the truss maintenance problem, which is to update the truss numbers of the affected edges in a dynamic graph while avoiding the truss number recomputation of all edges. However, few results are known on edge-weighted graphs. In this paper, we focus on the truss maintenance problem on edge-weighted graphs. Firstly, we propose a basic algorithm for the truss decomposition problem on edge-weighted graphs. Then we propose two indices, weighted growth potential support (WGPS) and weighted remaining potential support (WRPS), to help find the edges with potential changes on their truss numbers. Finally, we propose algorithms for the truss maintenance problem on edge-weighted graphs.
[Formula: see text]-truss是由Jonathan Cohen于2008年提出的，它被广泛用作内聚子图挖掘的图分析索引。这方面有两个基本问题。一是桁架分解问题，即计算每条边的桁架数;另一个是桁架维护问题，即更新动态图中受影响边的桁架数，同时避免所有边的桁架数重新计算。然而，关于边加权图的结果却很少。本文主要研究边加权图上的桁架维护问题。首先，提出了边权图桁架分解问题的基本算法。在此基础上，提出加权生长潜力支持度(WGPS)和加权剩余潜力支持度(WRPS)两个指标，以帮助寻找其桁架数可能发生变化的边缘。最后，我们提出了边加权图上桁架维护问题的算法。
{"title":"Algorithms for the Truss Maintenance Problem on Edge-Weighted Graphs","authors":"Bin Liu, Zhenming Liu, Feiteng Zhang","doi":"10.1142/s0129054123460036","DOIUrl":"https://doi.org/10.1142/s0129054123460036","url":null,"abstract":"The [Formula: see text]-truss was proposed by Jonathan Cohen in 2008, and it is a widely used as index in graph analysis for cohesive subgraph mining. There are two basic problems in this area. One is the truss decomposition problem, which is to compute the truss number of every edge; the other is the truss maintenance problem, which is to update the truss numbers of the affected edges in a dynamic graph while avoiding the truss number recomputation of all edges. However, few results are known on edge-weighted graphs. In this paper, we focus on the truss maintenance problem on edge-weighted graphs. Firstly, we propose a basic algorithm for the truss decomposition problem on edge-weighted graphs. Then we propose two indices, weighted growth potential support (WGPS) and weighted remaining potential support (WRPS), to help find the edges with potential changes on their truss numbers. Finally, we propose algorithms for the truss maintenance problem on edge-weighted graphs.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47780343","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}
Pub Date : 2023-07-29DOI: 10.1142/s0129054123470032
Erik D. Demaine, Robert A. Hearn, Dylan Hendrickson, Jayson Lynch
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.
{"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}
Pub Date : 2023-07-25DOI: 10.1142/s0129054123470020
Jian-Xi Shao, Ya-Chun Liang, Chung-Shou Liao
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.
{"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}
Pub Date : 2023-07-25DOI: 10.1142/s0129054123450041
M. Droste, Zoltán Fülöp, Dávid Kószó
A weighted finite automaton has the finite-image property if the image of the weighted language associated with it is finite. We show two undecidability results concerning the finite-image property of weighted finite automata over semirings, respectively strong bimonoids. Firstly, we give a computable idempotent commutative past-finite ordered semiring such that it is undecidable, for an arbitrary deterministic weighted finite automaton [Formula: see text] over that semiring, whether [Formula: see text] has the finite-image property. Secondly, we give a computable commutative past-finite monotonic ordered strong bimonoid such that it is undecidable, for an arbitrary weighted finite automaton [Formula: see text] over that strong bimonoid, whether [Formula: see text] has the finite-image property. This shows that recent decidability results for suitable weighted finite automata over past-finite monotonic strong bimonoids cannot be extended to natural classes of ordered semirings and ordered strong bimonoids without further assumptions.
{"title":"Decidability Boundaries for the Finite-Image Property of Weighted Finite Automata","authors":"M. Droste, Zoltán Fülöp, Dávid Kószó","doi":"10.1142/s0129054123450041","DOIUrl":"https://doi.org/10.1142/s0129054123450041","url":null,"abstract":"A weighted finite automaton has the finite-image property if the image of the weighted language associated with it is finite. We show two undecidability results concerning the finite-image property of weighted finite automata over semirings, respectively strong bimonoids. Firstly, we give a computable idempotent commutative past-finite ordered semiring such that it is undecidable, for an arbitrary deterministic weighted finite automaton [Formula: see text] over that semiring, whether [Formula: see text] has the finite-image property. Secondly, we give a computable commutative past-finite monotonic ordered strong bimonoid such that it is undecidable, for an arbitrary weighted finite automaton [Formula: see text] over that strong bimonoid, whether [Formula: see text] has the finite-image property. This shows that recent decidability results for suitable weighted finite automata over past-finite monotonic strong bimonoids cannot be extended to natural classes of ordered semirings and ordered strong bimonoids without further assumptions.","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":"49011040","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}
Pub Date : 2023-07-19DOI: 10.1142/s0129054123480040
Pierre Béaur, Jarkko Kari
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 , for any number 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.
{"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":"<p>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 <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℤ</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span><span></span>, for any number <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>d</mi></math></span><span></span> 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.</p>","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：