Two fixed-parameter algorithms for Vertex Covering by Paths on Trees

Guo, Jiong; Niedermeier, Rolf; Uhlmann, Johannes

doi:10.1016/j.ipl.2007.10.007

Cited by 1 publication

(3 citation statements)

References 9 publications

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“…From a graph point of view, this algorithm is related to the tree covering [14] problem. More precisely, we would like to have the minimal sub-set of heaviest paths from a given set of paths which covers the set of edges of the graph.…”

Section: Covering the Graphmentioning

confidence: 99%

“…It is equivalent to the edge covering problem using a given set of paths with the constraints of minimal cardinality and maximum weight. Such a problem is NP-hard even for trees [14]. The exact algorithm proposed by Guo [14] is based on dynamic programming and computes the whole set of covering solution from a given set of paths.…”

Section: Covering the Graphmentioning

confidence: 99%

“…Such a problem is NP-hard even for trees [14]. The exact algorithm proposed by Guo [14] is based on dynamic programming and computes the whole set of covering solution from a given set of paths. This algorithm computes a vertex covering, but can be easily converted into an edge covering algorithm.…”

Section: Covering the Graphmentioning

confidence: 99%

See 2 more Smart Citations

Tree Covering within a Graph Kernel Framework for Shape Classification

Dupé¹,

Brun²

2009

Image Analysis and Processing – ICIAP 2009

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Abstract. Shape classification using graphs and skeletons usually involves edition processes in order to reduce the influence of structural noise. However, edition distances can not be readily used within the kernel machine framework as they generally lead to indefinite kernels. In this paper, we propose a graph kernel based on bags of paths and edit operations which remains positive-definite according to the bags. The robustness of this kernel is based on a selection of the paths according to their relevance in the graph. Several experiments prove the efficiency of this approach compared to alternative kernel.

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Section: Covering the Graphmentioning

confidence: 99%

Section: Covering the Graphmentioning

confidence: 99%