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Journal of Graph Algorithms and Applications最新文献

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A Range Space with Constant VC Dimension for All-pairs Shortest Paths in Graphs 图中全对最短路径的常VC维范围空间
Journal of Graph Algorithms and Applications Pub Date : 2023-01-01 DOI: 10.7155/jgaa.00636
Alane M. de Lima, Murilo V. G. da Silva, A. L. Vignatti
{"title":"A Range Space with Constant VC Dimension for All-pairs Shortest Paths in Graphs","authors":"Alane M. de Lima, Murilo V. G. da Silva, A. L. Vignatti","doi":"10.7155/jgaa.00636","DOIUrl":"https://doi.org/10.7155/jgaa.00636","url":null,"abstract":". Let G be an undirected graph with non-negative edge weights and let S be a subset of its shortest paths such that, for every pair ( u, v ) of distinct vertices, S contains exactly one shortest path between u and v . In this paper we define a range space associated with S and prove that its VC dimension is 2. As a consequence, we show a bound for the number of shortest paths trees required to be sampled in order to solve a relaxed version of the All-pairs Shortest Paths problem (APSP) in G . In this version of the problem we are interested in computing all shortest paths with a certain “importance” at least ε . Given any 0 < ε , δ < 1, we propose a O ( m + n log n + (diam V ( G ) ) 2 ) sampling algorithm that outputs with probability 1 − δ the (exact) distance and the shortest path between every pair of vertices ( u, v ) that appears as subpath of at least a proportion ε of all shortest paths in the set S , where diam V ( G ) is the vertex-diameter of G . The bound that we obtain for the sample size depends only on ε and δ , and do not depend on the size of the graph.","PeriodicalId":35667,"journal":{"name":"Journal of Graph Algorithms and Applications","volume":"54 1","pages":"603-619"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71225272","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
Planar Confluent Orthogonal Drawings of 4-Modal Digraphs 四模态有向图的平面合流正交图
Journal of Graph Algorithms and Applications Pub Date : 2023-01-01 DOI: 10.7155/jgaa.00632
Sabine Cornelsen, Gregor Diatzko
{"title":"Planar Confluent Orthogonal Drawings of 4-Modal Digraphs","authors":"Sabine Cornelsen, Gregor Diatzko","doi":"10.7155/jgaa.00632","DOIUrl":"https://doi.org/10.7155/jgaa.00632","url":null,"abstract":"","PeriodicalId":35667,"journal":{"name":"Journal of Graph Algorithms and Applications","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136299752","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
Empty Triangles in Generalized Twisted Drawings of $K_n$ K_n广义扭曲图中的空三角形
Journal of Graph Algorithms and Applications Pub Date : 2023-01-01 DOI: 10.7155/jgaa.00637
Alfredo García, Javier Tejel, Birgit Vogtenhuber, Alexandra Weinberger
{"title":"Empty Triangles in Generalized Twisted Drawings of $K_n$","authors":"Alfredo García, Javier Tejel, Birgit Vogtenhuber, Alexandra Weinberger","doi":"10.7155/jgaa.00637","DOIUrl":"https://doi.org/10.7155/jgaa.00637","url":null,"abstract":"","PeriodicalId":35667,"journal":{"name":"Journal of Graph Algorithms and Applications","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135450723","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
Minimum Linear Arrangement of Generalized Sierpinski Graphs 广义Sierpinski图的最小线性排列
Journal of Graph Algorithms and Applications Pub Date : 2023-01-01 DOI: 10.7155/jgaa.00644
Sundara Rajan R, Berin Greeni A, Leo Joshwa P
{"title":"Minimum Linear Arrangement of Generalized Sierpinski Graphs","authors":"Sundara Rajan R, Berin Greeni A, Leo Joshwa P","doi":"10.7155/jgaa.00644","DOIUrl":"https://doi.org/10.7155/jgaa.00644","url":null,"abstract":"","PeriodicalId":35667,"journal":{"name":"Journal of Graph Algorithms and Applications","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135611750","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
The Complexity of Angular Resolution 角分辨率的复杂性
Journal of Graph Algorithms and Applications Pub Date : 2023-01-01 DOI: 10.7155/jgaa.00634
M. Schaefer
{"title":"The Complexity of Angular Resolution","authors":"M. Schaefer","doi":"10.7155/jgaa.00634","DOIUrl":"https://doi.org/10.7155/jgaa.00634","url":null,"abstract":". The angular resolution of a straight-line drawing of a graph is the smallest angle formed by any two edges incident to a vertex. The angular resolution of a graph is the supremum of the angular resolutions of all straight-line drawings of the graph. We show that testing whether a graph has angular resolution at least π/ (2 k ) is complete for ∃ R , the existential theory of the reals, for every fixed k ≥ 2 . This remains true if the graph is planar and a plane embedding of the graph is fixed.","PeriodicalId":35667,"journal":{"name":"Journal of Graph Algorithms and Applications","volume":"1 1","pages":"565-580"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71225261","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-Complex $s,t$ Hamiltonian Paths: Structure and Reconfiguration in Rectangular Grids 复$s， $ t$哈密顿路径:矩形网格的结构与重构
Journal of Graph Algorithms and Applications Pub Date : 2023-01-01 DOI: 10.7155/jgaa.00624
Rahnuma Islam Nishat, Venkatesh Srinivasan, Sue Whitesides
{"title":"1-Complex $s,t$ Hamiltonian Paths: Structure and Reconfiguration in Rectangular Grids","authors":"Rahnuma Islam Nishat, Venkatesh Srinivasan, Sue Whitesides","doi":"10.7155/jgaa.00624","DOIUrl":"https://doi.org/10.7155/jgaa.00624","url":null,"abstract":"","PeriodicalId":35667,"journal":{"name":"Journal of Graph Algorithms and Applications","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135685951","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
The Complexity of Drawing Graphs on Few Lines and Few Planes 在几条线和几面上绘制图形的复杂性
Journal of Graph Algorithms and Applications Pub Date : 2023-01-01 DOI: 10.7155/jgaa.00630
Steven Chaplick, Krzysztof Fleszar, Fabian Lipp, Alexander Ravsky, Oleg Verbitsky, Alexander Wolff
{"title":"The Complexity of Drawing Graphs on Few Lines and Few Planes","authors":"Steven Chaplick, Krzysztof Fleszar, Fabian Lipp, Alexander Ravsky, Oleg Verbitsky, Alexander Wolff","doi":"10.7155/jgaa.00630","DOIUrl":"https://doi.org/10.7155/jgaa.00630","url":null,"abstract":"It is well known that any graph admits a crossing-free straight-line drawing in $mathbb{R}^3$ and that any planar graph admits the same even in $mathbb{R}^2$. For a graph $G$ and $d in {2,3}$, let $rho^1_d(G)$ denote the minimum number of lines in $mathbb{R}^d$ that together can cover all edges of a drawing of $G$. For $d=2$, $G$ must be planar. We investigate the complexity of computing these parameters and obtain the following hardness and algorithmic results. ","PeriodicalId":35667,"journal":{"name":"Journal of Graph Algorithms and Applications","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135783904","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
Improved (In-)Approximability Bounds for d-Scattered Set d-散集的改进(In-)近似界
Journal of Graph Algorithms and Applications Pub Date : 2023-01-01 DOI: 10.7155/jgaa.00621
Ioannis Katsikarelis, Michael Lampis, Vangelis Th. Paschos
{"title":"Improved (In-)Approximability Bounds for d-Scattered Set","authors":"Ioannis Katsikarelis, Michael Lampis, Vangelis Th. Paschos","doi":"10.7155/jgaa.00621","DOIUrl":"https://doi.org/10.7155/jgaa.00621","url":null,"abstract":"In the $d$-Scattered Set problem we are asked to select at least $k$ vertices of a given graph, so that the distance between any pair is at least $d$. We study the problem's (in-)approximability and offer improvements and extensions of known results for Independent Set, of which the problem is a generalization. ","PeriodicalId":35667,"journal":{"name":"Journal of Graph Algorithms and Applications","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135181370","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
Effective Computation of a Feedback Arc Set Using PageRank 基于PageRank的反馈弧集有效计算
Journal of Graph Algorithms and Applications Pub Date : 2023-01-01 DOI: 10.7155/jgaa.00641
Vasileios Geladaris, Panagiotis Lionakis, Ioannis G. Tollis
{"title":"Effective Computation of a Feedback Arc Set Using PageRank","authors":"Vasileios Geladaris, Panagiotis Lionakis, Ioannis G. Tollis","doi":"10.7155/jgaa.00641","DOIUrl":"https://doi.org/10.7155/jgaa.00641","url":null,"abstract":". Computing a minimum Feedback Arc Set (FAS) is important for visualizing directed graphs in hierarchical style. It is the first step of both known frameworks for hierarchical graph drawing of directed graphs and it is NP-hard. We present a new heuristic algorithm for computing a minimum FAS in directed graphs. The new technique produces solutions that, for graph drawing datasets, are better than the ones produced by the best previously known heuristics, often reducing the FAS size by more than 50%. The heuristic is based on computing the PageRank score of the nodes of the directed line graph of the input directed graph. Although the time required by our heuristic is heavily influenced by the size of the produced line graph, our experimental results show that it runs very fast even for very large graphs used in graph drawing. We compare results produced by our heuristic to known exact results for specific graphs used in a previous study and discuss the interesting trade-off. Finally, our experimental results on large web-graphs show that our technique found smaller FAS than it was known before for some web-graphs from a data set used in a recent study.","PeriodicalId":35667,"journal":{"name":"Journal of Graph Algorithms and Applications","volume":"109 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135450045","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
Efficient Point-to-Point Resistance Distance Queries in Large Graphs 大型图中有效的点对点阻力距离查询
Journal of Graph Algorithms and Applications Pub Date : 2023-01-01 DOI: 10.7155/jgaa.00612
C. Gotsman, K. Hormann
{"title":"Efficient Point-to-Point Resistance Distance Queries in Large Graphs","authors":"C. Gotsman, K. Hormann","doi":"10.7155/jgaa.00612","DOIUrl":"https://doi.org/10.7155/jgaa.00612","url":null,"abstract":"","PeriodicalId":35667,"journal":{"name":"Journal of Graph Algorithms and Applications","volume":"1 1","pages":"35-44"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71225317","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
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