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A Linear Delay Algorithm for Enumeration of 2-Edge/Vertex-connected Induced Subgraphs 2边/点连通诱导子图枚举的线性延迟算法
International Workshop on Combinatorial Algorithms Pub Date : 2023-02-10 DOI: 10.48550/arXiv.2302.05526
Takumi Tada, Kazuya Haraguchi
{"title":"A Linear Delay Algorithm for Enumeration of 2-Edge/Vertex-connected Induced Subgraphs","authors":"Takumi Tada, Kazuya Haraguchi","doi":"10.48550/arXiv.2302.05526","DOIUrl":"https://doi.org/10.48550/arXiv.2302.05526","url":null,"abstract":"For a set system $(V,{mathcal C}subseteq 2^V)$, we call a subset $Cin{mathcal C}$ a component. A nonempty subset $Ysubseteq C$ is a minimal removable set (MRS) of $C$ if $Csetminus Yin{mathcal C}$ and no proper nonempty subset $Zsubsetneq Y$ satisfies $Csetminus Zin{mathcal C}$. In this paper, we consider the problem of enumerating all components in a set system such that, for every two components $C,C'in{mathcal C}$ with $C'subsetneq C$, every MRS $X$ of $C$ satisfies either $Xsubseteq C'$ or $Xcap C'=emptyset$. We provide a partition-based algorithm for this problem, which yields the first linear delay algorithms to enumerate all 2-edge-connected induced subgraphs, and to enumerate all 2-vertex-connected induced subgraphs.","PeriodicalId":403593,"journal":{"name":"International Workshop on Combinatorial Algorithms","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129697614","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
Multi-Priority Graph Sparsification 多优先级图稀疏化
International Workshop on Combinatorial Algorithms Pub Date : 2023-01-29 DOI: 10.48550/arXiv.2301.12563
Abu Reyan Ahmed, Keaton Hamm, S. Kobourov, Mohammad Javad Latifi Jebelli, F. Sahneh, Richard Spence
{"title":"Multi-Priority Graph Sparsification","authors":"Abu Reyan Ahmed, Keaton Hamm, S. Kobourov, Mohammad Javad Latifi Jebelli, F. Sahneh, Richard Spence","doi":"10.48550/arXiv.2301.12563","DOIUrl":"https://doi.org/10.48550/arXiv.2301.12563","url":null,"abstract":"A emph{sparsification} of a given graph $G$ is a sparser graph (typically a subgraph) which aims to approximate or preserve some property of $G$. Examples of sparsifications include but are not limited to spanning trees, Steiner trees, spanners, emulators, and distance preservers. Each vertex has the same priority in all of these problems. However, real-world graphs typically assign different ``priorities'' or ``levels'' to different vertices, in which higher-priority vertices require higher-quality connectivity between them. Multi-priority variants of the Steiner tree problem have been studied in prior literature but this generalization is much less studied for other sparsification problems. In this paper, we define a generalized multi-priority problem and present a rounding-up approach that can be used for a variety of graph sparsifications. Our analysis provides a systematic way to compute approximate solutions to multi-priority variants of a wide range of graph sparsification problems given access to a single-priority subroutine.","PeriodicalId":403593,"journal":{"name":"International Workshop on Combinatorial Algorithms","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131748483","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
Convex Grid Drawings of Planar Graphswith Constant Edge-Vertex Resolution 具有恒定边顶点分辨率的平面图形的凸网格绘图
International Workshop on Combinatorial Algorithms Pub Date : 2022-04-29 DOI: 10.48550/arXiv.2204.14040
M. Bekos, Martin Gronemann, Fabrizio Montecchiani, A. Symvonis
{"title":"Convex Grid Drawings of Planar Graphswith Constant Edge-Vertex Resolution","authors":"M. Bekos, Martin Gronemann, Fabrizio Montecchiani, A. Symvonis","doi":"10.48550/arXiv.2204.14040","DOIUrl":"https://doi.org/10.48550/arXiv.2204.14040","url":null,"abstract":"We continue the study of the area requirement of convex straight-line grid drawings of 3-connected plane graphs, which has been intensively investigated in the last decades. Motivated by applications, such as graph editors, we additionally require the obtained drawings to have bounded edge-vertex resolution, that is, the closest distance between a vertex and any non-incident edge is lower bounded by a constant that does not depend on the size of the graph. We present a drawing algorithm that takes as input a 3-connected plane graph with n vertices and f internal faces and computes a convex straight-line drawing with edge-vertex resolution at least 1/2 on an integer grid of size (n-2+a)x(n-2+a), where a=min{n-3,f}. Our result improves the previously best-known area bound of (3n-7)x(3n-7)/2 by Chrobak, Goodrich and Tamassia.","PeriodicalId":403593,"journal":{"name":"International Workshop on Combinatorial Algorithms","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131538648","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
An Efficient Algorithm for the Proximity Connected Two Center Problem 邻近连通双中心问题的一种高效算法
International Workshop on Combinatorial Algorithms Pub Date : 2022-04-19 DOI: 10.48550/arXiv.2204.08754
B. Bhattacharya, Amirhossein Mozafari, T. Shermer
{"title":"An Efficient Algorithm for the Proximity Connected Two Center Problem","authors":"B. Bhattacharya, Amirhossein Mozafari, T. Shermer","doi":"10.48550/arXiv.2204.08754","DOIUrl":"https://doi.org/10.48550/arXiv.2204.08754","url":null,"abstract":". Given a set P of n points in the plane, the k -center problem is to find k congruent disks of minimum possible radius such that their union covers all the points in P . The 2-center problem is a special case of the k -center problem that has been extensively studied in the recent past [8,27,29]. In this paper, we consider a generalized version of the 2-center problem called proximity connected 2-center (PCTC) problem. In this problem, we are also given a parameter δ ≥ 0 and we have the additional constraint that the distance between the centers of the disks should be at most δ . Note that when δ = 0, the PCTC problem is reduced to the 1-center(minimum enclosing disk) problem and when δ tends to infinity, it is reduced to the 2-center problem. The PCTC problem first appeared in the context of wireless networks in 1992 [16], but obtaining a nontrivial deterministic algorithm for the problem remained open. In this paper, we resolve this open problem by providing a deterministic O ( n 2 log n ) time algorithm for the problem.","PeriodicalId":403593,"journal":{"name":"International Workshop on Combinatorial Algorithms","volume":"113 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133292911","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
1-Extendability of independent sets 独立集的可拓性
International Workshop on Combinatorial Algorithms Pub Date : 2022-04-12 DOI: 10.48550/arXiv.2204.05809
Pierre Berg'e, A. Busson, Carl Feghali, Rémi Watrigant
{"title":"1-Extendability of independent sets","authors":"Pierre Berg'e, A. Busson, Carl Feghali, Rémi Watrigant","doi":"10.48550/arXiv.2204.05809","DOIUrl":"https://doi.org/10.48550/arXiv.2204.05809","url":null,"abstract":"In the 70s, Berge introduced 1-extendable graphs (also called B-graphs), which are graphs where every vertex belongs to a maximum independent set. Motivated by an application in the design of wireless networks, we study the computational complexity of 1-extendability, the problem of deciding whether a graph is 1-extendable. We show that, in general, 1-extendability cannot be solved in $2^{o(n)}$ time assuming the Exponential Time Hypothesis, where $n$ is the number of vertices of the input graph, and that it remains NP-hard in subcubic planar graphs and in unit disk graphs (which is a natural model for wireless networks). Although 1-extendability seems to be very close to the problem of finding an independent set of maximum size (a.k.a. Maximum Independent Set), we show that, interestingly, there exist 1-extendable graphs for which Maximum Independent Set is NP-hard. Finally, we investigate a parameterized version of 1-extendability.","PeriodicalId":403593,"journal":{"name":"International Workshop on Combinatorial Algorithms","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124325849","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
Lower Bounds for Restricted Schemes in the Two-Adaptive Bitprobe Model 双自适应位探针模型中受限格式的下界
International Workshop on Combinatorial Algorithms Pub Date : 2022-04-07 DOI: 10.48550/arXiv.2204.03266
Sreshth Aggarwal, Deepanjan Kesh, Divyam Singal
{"title":"Lower Bounds for Restricted Schemes in the Two-Adaptive Bitprobe Model","authors":"Sreshth Aggarwal, Deepanjan Kesh, Divyam Singal","doi":"10.48550/arXiv.2204.03266","DOIUrl":"https://doi.org/10.48550/arXiv.2204.03266","url":null,"abstract":". In the adaptive bitprobe model answering membership queries in two bitprobes, we consider the class of restricted schemes as introduced by Kesh and Sharma [1]. In that paper, the authors showed that such restricted schemes storing subsets of size 2 require Ω ( m 23 ) space. In this paper, we generalise the result to arbitrary subsets of size n , and prove that the space required for such restricted schemes will be","PeriodicalId":403593,"journal":{"name":"International Workshop on Combinatorial Algorithms","volume":"200 1‐2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120846146","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
Structure-aware combinatorial group testing: a new method for pandemic screening 结构感知组合组检测:大流行筛查的新方法
International Workshop on Combinatorial Algorithms Pub Date : 2022-02-17 DOI: 10.1007/978-3-031-06678-8_11
Thaís Bardini Idalino, Lucia Moura
{"title":"Structure-aware combinatorial group testing: a new method for pandemic screening","authors":"Thaís Bardini Idalino, Lucia Moura","doi":"10.1007/978-3-031-06678-8_11","DOIUrl":"https://doi.org/10.1007/978-3-031-06678-8_11","url":null,"abstract":"","PeriodicalId":403593,"journal":{"name":"International Workshop on Combinatorial Algorithms","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128405956","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
Using Edge Contractions and Vertex Deletions to Reduce the Independence Number and the Clique Number 使用边收缩和顶点删除来减少独立数和团数
International Workshop on Combinatorial Algorithms Pub Date : 2022-02-17 DOI: 10.1007/978-3-031-06678-8_30
Felicia Lucke, Felix Mann
{"title":"Using Edge Contractions and Vertex Deletions to Reduce the Independence Number and the Clique Number","authors":"Felicia Lucke, Felix Mann","doi":"10.1007/978-3-031-06678-8_30","DOIUrl":"https://doi.org/10.1007/978-3-031-06678-8_30","url":null,"abstract":"","PeriodicalId":403593,"journal":{"name":"International Workshop on Combinatorial Algorithms","volume":"153 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124277573","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
A New Temporal Interpretation of Cluster Editing 聚类编辑的时间新解释
International Workshop on Combinatorial Algorithms Pub Date : 2022-02-02 DOI: 10.1007/978-3-031-06678-8_16
C. Bocci, C. Capresi, Kitty Meeks, John Sylvester
{"title":"A New Temporal Interpretation of Cluster Editing","authors":"C. Bocci, C. Capresi, Kitty Meeks, John Sylvester","doi":"10.1007/978-3-031-06678-8_16","DOIUrl":"https://doi.org/10.1007/978-3-031-06678-8_16","url":null,"abstract":"","PeriodicalId":403593,"journal":{"name":"International Workshop on Combinatorial Algorithms","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116651730","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
Linear Time Construction of Indexable Elastic Founder Graphs 可转位弹性方正图的线性时间构造
International Workshop on Combinatorial Algorithms Pub Date : 2022-01-17 DOI: 10.1007/978-3-031-06678-8_35
Nicola Rizzo, V. Mäkinen
{"title":"Linear Time Construction of Indexable Elastic Founder Graphs","authors":"Nicola Rizzo, V. Mäkinen","doi":"10.1007/978-3-031-06678-8_35","DOIUrl":"https://doi.org/10.1007/978-3-031-06678-8_35","url":null,"abstract":"","PeriodicalId":403593,"journal":{"name":"International Workshop on Combinatorial Algorithms","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125696647","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: 4
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