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Subexponential parameterized algorithms on graphs of boundedgenus and Hminorfree Graphs
"... ... Building on these results, we develop subexponential fixedparameter algorithms for dominating set, vertex cover, and set cover in any class of graphs excluding a fixed graph H as a minor. Inparticular, this general category of graphs includes planar graphs, boundedgenus graphs, singlecrossing ..."
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Cited by 62 (21 self)
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... Building on these results, we develop subexponential fixedparameter algorithms for dominating set, vertex cover, and set cover in any class of graphs excluding a fixed graph H as a minor. Inparticular, this general category of graphs includes planar graphs, boundedgenus graphs, single
References
"... Polynomialtime approximation schemes for subsetconnectivity problems in boundedgenus graphs. In STACS ’09: Proceedings of the 26th Symposium on Theoretical Aspects of Computer Science, pages 171–182, 2009. ..."
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Polynomialtime approximation schemes for subsetconnectivity problems in boundedgenus graphs. In STACS ’09: Proceedings of the 26th Symposium on Theoretical Aspects of Computer Science, pages 171–182, 2009.
LinearSpace Approximate Distance Oracles for Planar, BoundedGenus, and MinorFree Graphs
"... Abstract. A (1 + ɛ)approximate distance oracle for a graph is a data structure that supports approximate pointtopoint shortestpathdistance queries. The relevant measures for a distanceoracle construction are: space, query time, and preprocessing time. There are strong distanceoracle construct ..."
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Cited by 11 (5 self)
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memory, secondary memory), a high memory requirement in effect may greatly increase the actual running time. Moreover, we would like data structures that can be deployed on small mobile devices, such as handhelds, which have relatively small primary memory. In this paper, for planar graphs, boundedgenus
Abstract In this paper, we reduce PrizeCollecting Steiner TSP (PCTSP), PrizeCollecting Stroll (PCS), PrizeCollecting
"... est (SPCSF), on planar graphs (and also on boundedgenus graphs) to the corresponding problem on graphs of bounded treewidth. More precisely, for each of the mentioned problems, an αapproximation algorithm for the problem on graphs of bounded treewidth implies an (α + )approximation algorithm fo ..."
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est (SPCSF), on planar graphs (and also on boundedgenus graphs) to the corresponding problem on graphs of bounded treewidth. More precisely, for each of the mentioned problems, an αapproximation algorithm for the problem on graphs of bounded treewidth implies an (α + )approximation algorithm
Diameter and Treewidth in MinorClosed Graph Families
, 1999
"... It is known that any planar graph with diameter D has treewidth O(D), and this fact has been used as the basis for several planar graph algorithms. We investigate the extent to which similar relations hold in other graph families. We show that treewidth is bounded by a function of the diameter in a ..."
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Cited by 114 (3 self)
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minorclosed family, if and only if some apex graph does not belong to the family. In particular, the O(D) bound above can be extended to boundedgenus graphs. As a consequence, we extend several approximation algorithms and exact subgraph isomorphism algorithms from planar graphs to other graph
Prizecollecting Steiner Problems on Planar Graphs
"... In this paper, we reduce PrizeCollecting Steiner TSP (PCTSP), PrizeCollecting Stroll (PCS), PrizeCollecting Steiner Tree (PCST), PrizeCollecting Steiner Forest (PCSF), and more generally Submodular PrizeCollecting Steiner Forest (SPCSF), on planar graphs (and also on boundedgenus graphs) to the ..."
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Cited by 9 (2 self)
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) to the corresponding problem on graphs of bounded treewidth. More precisely, for each of the mentioned problems, an αapproximation algorithm for the problem on graphs of bounded treewidth implies an (α + ɛ)approximation algorithm for the problem on planar graphs (and also boundedgenus graphs), for any constant ɛ
Multiple source, single sink maximum flow in a planar graph
 CoRR
"... We give an O(n1.5 logn) time algorithm for finding the maximum flow in a directed planar graph with multiple sources and a single sink. The techniques generalize to a subquadratic time algorithm for bounded genus graphs. 1 ..."
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Cited by 2 (0 self)
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We give an O(n1.5 logn) time algorithm for finding the maximum flow in a directed planar graph with multiple sources and a single sink. The techniques generalize to a subquadratic time algorithm for bounded genus graphs. 1
networks. Networks, 20:109–120, 1990.
"... Polynomialtime approximation schemes for subsetconnectivity problems in boundedgenus graphs. In STACS ’09: Proceedings of the 26th Symposium on Theoretical Aspects of Computer Science, pages 171–182, 2009. Marshall Bern. Faster exact algorithms for Steiner trees in planar ..."
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Polynomialtime approximation schemes for subsetconnectivity problems in boundedgenus graphs. In STACS ’09: Proceedings of the 26th Symposium on Theoretical Aspects of Computer Science, pages 171–182, 2009. Marshall Bern. Faster exact algorithms for Steiner trees in planar
A LinearProcessor PolylogTime Algorithm for Shortest Paths in Planar Graphs
, 1993
"... We give an algorithm requiring polylog time and a linear number of processors to solve singlesource shortest paths in directed planar graphs, boundedgenus graphs, and 2dimensional overlap graphs. More generally, the algorithm works for any graph provided with a decomposition tree constructed using ..."
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Cited by 16 (5 self)
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We give an algorithm requiring polylog time and a linear number of processors to solve singlesource shortest paths in directed planar graphs, boundedgenus graphs, and 2dimensional overlap graphs. More generally, the algorithm works for any graph provided with a decomposition tree constructed
Results 11  20
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22,725