International Journal of Foundations of Computer Science最新文献_第8页

Vertex-Bipartition: A Unified Approach for Kernelization of Graph Linear Layout Problems Parameterized by Vertex Cover 顶点二分法：用顶点覆盖参数化图线性布局问题核化的统一方法

IF 0.8 4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-05-09 DOI: 10.1142/s0129054123410022

Yunlong Liu, Yixuan Li, Jingui Huang

{"title":"Vertex-Bipartition: A Unified Approach for Kernelization of Graph Linear Layout Problems Parameterized by Vertex Cover","authors":"Yunlong Liu, Yixuan Li, Jingui Huang","doi":"10.1142/s0129054123410022","DOIUrl":"https://doi.org/10.1142/s0129054123410022","url":null,"abstract":"The linear layout of graphs problem asks, given a graph [Formula: see text] and a positive integer [Formula: see text], whether [Formula: see text] admits a layout consisting of a linear ordering of its vertices and a partition of its edges into [Formula: see text] sets such that the edges in each set meet some special requirements. Specific linear layouts include [Formula: see text]-stack layout, [Formula: see text]-queue layout, [Formula: see text]-arch layout, mixed [Formula: see text]-stack [Formula: see text]-queue layout and others. In this paper, we present a unified approach for kernelization of these linear layout problems parameterized by the vertex cover number [Formula: see text] of the input graph. The key point underlying our approach is to partition each set of related vertices into two distinct subsets with respect to the specific layouts, which immediately leads to some efficient reduction rules. We first apply this approach to the mixed [Formula: see text]-stack [Formula: see text]-queue layout problem and show that it admits a kernel of size [Formula: see text], which results in an algorithm running in time [Formula: see text], where [Formula: see text] denotes the size of the input graph. Our work does not only confirm the existence of a fixed-parameter tractable algorithm for this problem mentioned by Bhore et al. (J. Graph Algorithms Appl. 2022), but also derives new results for the [Formula: see text]-stack layout problem and for the [Formula: see text]-queue layout problem respectively. We also employ this approach to the upward [Formula: see text]-stack layout problem and obtain a new result improving that presented by Bhore et al. (GD 2021). Last but not least, we use this approach to the [Formula: see text]-arch layout problem and obtain a similar result.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43743124","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

Drawing Simultaneously Embedded Graphs with Few Bends 绘制同时嵌入图形与少数弯曲

4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-05-09 DOI: 10.1142/s0129054123420017

Luca Grilli, Seok-Hee Hong, Jan Kratochvíl, Ignaz Rutter

引用次数: 0

Closure Properties of Subregular Languages Under Operations 子规则语言在操作下的闭包属性

IF 0.8 4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-05-04 DOI: 10.1142/s0129054123450016

Viktor Olejár, Alexander Szabari

引用次数: 0

Parameterized Complexity Classes Defined by Threshold Circuits and Their Connection with Sorting Networks 阈值电路定义的参数化复杂度类及其与排序网络的联系

IF 0.8 4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-04-27 DOI: 10.1142/s0129054123410046

Raffael M. Paranhos, Janio Carlos Nascimento Silva, U. Souza

{"title":"Parameterized Complexity Classes Defined by Threshold Circuits and Their Connection with Sorting Networks","authors":"Raffael M. Paranhos, Janio Carlos Nascimento Silva, U. Souza","doi":"10.1142/s0129054123410046","DOIUrl":"https://doi.org/10.1142/s0129054123410046","url":null,"abstract":"The main complexity classes of the Parameterized Intractability Theory are based on weighted Boolean circuit satisfiability problems and organized into a hierarchy so-called W-hierarchy. The W-hierarchy enables fine-grained complexity analyses of parameterized problems that are unlikely to belong to the FPT class. In this paper, we introduce the Th-hierarchy, a natural generalization of the W-hierarchy defined by unweighted threshold circuit satisfiability problems. Investigating the relationship between Th-hierarchy and W-hierarchy, we discuss the complexity of transforming Threshold circuits into Boolean circuits, and observe that sorting networks are powerful tools to handle such transformations. First, we show that these hierarchies collapse at the last level (W[P][Formula: see text][Formula: see text][Formula: see text]Th[P]). After that, we present a time complexity analysis of an AKS sorting network construction, which supports some of our results. Finally, we prove that Th[[Formula: see text]] [Formula: see text] W[SAT] for every [Formula: see text]. As a by-product, our studies suggest that it is relevant to consider a new class based on logarithmic depth circuits in the W-hierarchy.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43504068","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

An Improved Approximation Algorithm for the Capacitated Correlation Clustering Problem 一种改进的有能力相关聚类问题逼近算法

4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-04-27 DOI: 10.1142/s0129054123410010

Sai Ji, Yukun Cheng, Jingjing Tan, Zhongrui Zhao

{"title":"An Improved Approximation Algorithm for the Capacitated Correlation Clustering Problem","authors":"Sai Ji, Yukun Cheng, Jingjing Tan, Zhongrui Zhao","doi":"10.1142/s0129054123410010","DOIUrl":"https://doi.org/10.1142/s0129054123410010","url":null,"abstract":"Correlation clustering problem (CorCP) is a classical clustering problem, which clusters data based on the similarity of data set, and has many applications in interaction networks, cross-lingual link detection, and communication networks, etc. In this paper, we study a practical generalization of the CorCP, called the capacitated correlation clustering problem (the capacitated CorCP), by constructing a labeled complete graph. On this labeled complete graph, each vertex represents a piece of data. If two pieces of data are similar, then the edge between the corresponding vertices is marked by a positive label [Formula: see text]. Otherwise, this edge is marked by a negative label −. The objective of the capacitated CorCP is to group some similar data sets into one cluster as far as possible, while satisfying the cluster capacity constraint. To achieve this objective, we shall partition the vertex set of the labeled complete graph into several clusters, each cluster’s size subjecting to an upper bound, so as to minimize the number of disagreements. Here the number of disagreements is defined as the total number of the edges with positive labels between clusters and the edges with negative labels within clusters. Different with the previous algorithm in [18], which subjects to the constraint on the cluster size by a penalty measure, we design an algorithm for the capacitated CorCP to directly output a feasible solution by iteratively constructing clusters based on a preset threshold. Through carefully setting the threshold and sophisticatedly analyzing, our algorithm is proved to have an improved approximation ratio of 5.37. In addition, we also conduct a series of numerical experiments to demonstrate the effectiveness of our algorithm.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136119299","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

Succinct Data Structures for SP, Block-Cactus and 3-Leaf Power Graphs SP, Block-Cactus和3-Leaf Power图的简洁数据结构

IF 0.8 4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-04-21 DOI: 10.1142/s012905412341006x

Sankardeep Chakraborty, Seungbum Jo, K. Sadakane, Srinivasa Rao Satti

引用次数: 1

Routing Among Convex Polygonal Obstacles in the Plane 平面上凸多边形障碍物之间的路由

4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-04-21 DOI: 10.1142/s0129054123410034

R. Inkulu, Pawan Kumar

引用次数: 0

The g-Good-Neighbor Conditional Diagnosabilities of Hypermesh Optical Interconnection Networks Under the PMC and Comparison Models PMC和比较模型下超网状光互连网络的g-Good-Neighbor条件可诊断性

IF 0.8 4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-04-11 DOI: 10.1142/s0129054123500041

引用次数: 0

The Longest Path Problem in Odd-Sized O-Shaped Grid Graphs 奇数尺寸O形网格图的最长路径问题

IF 0.8 4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-03-29 DOI: 10.1142/s0129054123500065

Fatemeh Keshavarz-Kohjerdi, A. Bagheri

引用次数: 0

Embedding Hierarchical Cubic Networks into k-Rooted Complete Binary Trees for Minimum Wirelength 将层次三次网络嵌入k-根完全二叉树中的最小线长

IF 0.8 4区计算机科学

International Journal of Foundations of Computer Science Pub Date : 2023-03-28 DOI: 10.1142/s0129054123500053

Ruyan Guo, Yan Wang, Jianxi Fan, Weibei Fan

{"title":"Embedding Hierarchical Cubic Networks into k-Rooted Complete Binary Trees for Minimum Wirelength","authors":"Ruyan Guo, Yan Wang, Jianxi Fan, Weibei Fan","doi":"10.1142/s0129054123500053","DOIUrl":"https://doi.org/10.1142/s0129054123500053","url":null,"abstract":"In recent years, the growth of data has promoted the development of parallel and distributed systems. Graph embedding is of great importance in improving parallel and distributed system performance. The quality of an embedding can be measured by many important metrics, and wirelength is one of the critical metrics related to communication performance and layout costs of physical systems. The hierarchical cubic network is a well-performing interconnection network and the [Formula: see text]-rooted complete binary tree is a data structure with a hierarchical relationship among its various elements in algorithms and programming. In this paper, we solve the problem of the embedding of hierarchical cubic networks into [Formula: see text]-rooted complete binary trees with minimum wirelength. We first study the optimal set of the hierarchical cubic network, and propose algorithms to give embedding [Formula: see text] which is an embedding scheme of hierarchical cubic networks into [Formula: see text]-rooted complete binary trees with minimum wirelength. Moreover, we give the exact minimum wirelength of this embedding. Finally, we conduct comparative experiments to evaluate the performance of embedding [Formula: see text].","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43895964","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