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ON NOWHERE DENSE GRAPHS
"... A set A of vertices of a graph G is called dscattered in G if no two dneighborhoods of (distinct) vertices of A intersect. In other words, A is dscattered if no two distinct vertices of A have distance at most 2d. This notion was isolated in the context of finite model theory by Gurevich and rec ..."
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Cited by 7 (0 self)
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of nowhere dense graphs are quasi wide. This not only strictly generalizes the previous results and solves several open problems but it also provides new proofs. It appears that bounded expansion and nowhere dense classes are perhaps a proper setting for investigation of widetype classes as in several
On Nowhere Dense Graphs
"... A set A of vertices of a graph G is called dscattered in G if no two dneighborhoods of (distinct) vertices of A intersect. In other words, A is dscattered if no two distinct vertices of A have distance at most 2d. This notion was isolated in the context of finite model theory by Gurevich and rece ..."
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Cited by 3 (0 self)
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of nowhere dense graphs are quasi wide. This not only strictly generalizes the previous results and solves several open problems but it also provides new proofs. It appears that bounded expansion and nowhere dense classes are perhaps a proper setting for investigation of widetype classes as in several
Characterisations of Nowhere Dense Graphs
, 2013
"... Nowhere dense classes of graphs were introduced by Nešetřil and Ossona de Mendez as a model for “sparsity” in graphs. It turns out that nowhere dense classes of graphs can be characterised in many different ways and have been shown to be equivalent to other concepts studied in areas such as (finite) ..."
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Nowhere dense classes of graphs were introduced by Nešetřil and Ossona de Mendez as a model for “sparsity” in graphs. It turns out that nowhere dense classes of graphs can be characterised in many different ways and have been shown to be equivalent to other concepts studied in areas such as (finite
Deciding firstorder properties of nowhere dense graphs
 In Proceedings of the 46th Annual ACM Symposium on Theory of Computing (STOC
, 2014
"... ar ..."
A new approach to the maximum flow problem
 JOURNAL OF THE ACM
, 1988
"... All previously known efficient maximumflow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortestlength augmenting paths at once (using the layered network approach of Dinic). An alternative method based on the pre ..."
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Cited by 672 (33 self)
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to be shortest paths. The algorithm and its analysis are simple and intuitive, yet the algorithm runs as fast as any other known method on dense. graphs, achieving an O(n³) time bound on an nvertex graph. By incorporating the dynamic tree data structure of Sleator and Tarjan, we obtain a version
Measurement and Analysis of Online Social Networks
 In Proceedings of the 5th ACM/USENIX Internet Measurement Conference (IMC’07
, 2007
"... Online social networking sites like Orkut, YouTube, and Flickr are among the most popular sites on the Internet. Users of these sites form a social network, which provides a powerful means of sharing, organizing, and finding content and contacts. The popularity of these sites provides an opportunity ..."
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Cited by 698 (14 self)
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an opportunity to study the characteristics of online social network graphs at large scale. Understanding these graphs is important, both to improve current systems and to design new applications of online social networks. This paper presents a largescale measurement study and analysis of the structure
Directed Nowhere Dense Classes of Graphs
, 2012
"... Many natural computational problems on graphs such as finding dominating or independent sets of a certain size are well known to be intractable, both in the classical sense as well as in the framework of parameterized complexity. Much work therefore has focussed on exhibiting restricted classes of g ..."
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Cited by 2 (1 self)
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Many natural computational problems on graphs such as finding dominating or independent sets of a certain size are well known to be intractable, both in the classical sense as well as in the framework of parameterized complexity. Much work therefore has focussed on exhibiting restricted classes
ModelChecking in Dense Realtime
 INFORMATION AND COMPUTATION
, 1993
"... Modelchecking is a method of verifying concurrent systems in which a statetransition graph model of the system behavior is compared with a temporal logic formula. This paper extends modelchecking for the branchingtime logic CTL to the analysis of realtime systems, whose correctness depends on t ..."
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Cited by 327 (7 self)
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formula with respect to a timed graph. We argue that choosing a dense domain instead of a discrete domain to mo...
A general approximation technique for constrained forest problems
 SIAM J. COMPUT.
, 1995
"... We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization proble ..."
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Cited by 414 (21 self)
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of these problems. For instance, we obtain a 2approximation algorithm for the minimumweight perfect matching problem under the triangle inequality. Our running time of O(n log n) time compares favorably with the best strongly polynomial exact algorithms running in O(n 3) time for dense graphs. A similar result
Domination Problems in NowhereDense Classes of Graphs
 LEIBNIZ INTERNATIONAL PROCEEDINGS IN INFORMATICS
"... We investigate the parameterized complexity of generalisations and variations of the dominating set problem on classes of graphs that are nowhere dense. In particular, we show that the distanced dominatingset problem, also known as the (k, d)centres problem, is fixedparameter tractable on any cl ..."
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Cited by 5 (4 self)
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We investigate the parameterized complexity of generalisations and variations of the dominating set problem on classes of graphs that are nowhere dense. In particular, we show that the distanced dominatingset problem, also known as the (k, d)centres problem, is fixedparameter tractable on any
Results 1  10
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1,792