Approximating The Tree And Tour Covers Of A Graph

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APPROXIMATING THE TREE AND TOUR COVERS OF A GRAPH

http://math.tau.ac.il/%7Ehassin/tree_cover.pdf

the tree (resp. tour) cover problem, and we conclude with open problems and discussion. 2 Approximating the tree cover 2.1 Weighted Tree Cover We begin with a formal definition of the problem: Problem 2.1 (Tree Cover Problem) Given a graph G = (V,E) and weight on the edges w e ≥ 0 for all e ∈ E, find a minimum weight tree, T

Approximating the tree and tour covers of a graph ...

https://www.sciencedirect.com/science/article/pii/002001909390072H

Oct 18, 1993 · The tree and tour cover problems on an edge-weighted graph are to compute a minimum weight tree and closed walk, respectively, whose vertices from a vertex cover. Both problems are NP-hard. In this note we give strongly polynomial time, constant factor approximation algorithms for both problems. An interesting feature of our algorithms is how they combine approximations of other …Cited by: 96

CiteSeerX — Approximating The Tree And Tour Covers Of A Graph

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.7949

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): The tree and tour cover problems on an edge-weighted graph are to compute a minimum weight tree and closed walk, respectively, whose vertices form a vertex cover. Both problems are NP-hard. In this note we give strongly polynomial time, constant factor approximation algorithms for both problems.

Approximating The Tree And Tour Covers Of A Graph - CORE

https://core.ac.uk/display/24326039

Approximating The Tree And Tour Covers Of A Graph . By Esther M. Arkin, Magnús M. Halldórsson and Refael Hassin. Abstract. The tree and tour cover problems on an edge-weighted graph are to compute a minimum weight tree and closed walk, respectively, whose vertices form a vertex cover. Both problems are NP-hard.

Approximating The Tree And Tour Covers Of A Graph - CORE

http://core.ac.uk/display/22616465

Approximating The Tree And Tour Covers Of A Graph . By Esther M. Arkin, Magnus M. Halldorsson and Refael Hassin. Abstract. The tree and tour cover problems on an edge-weighted graph are to compute a minimum weight tree and closed walk, respectively, whose vertices form a vertex cover. Both problems are NP-hard.

(PDF) Approximating the tree and tour covers of a graph ...

https://www.academia.edu/1456377/Approximating_the_tree_and_tour_covers_of_a_graph

Approximating the tree and tour covers of a graph

(PDF) Approximating the Minimum Tour Cover of a Digraph

https://www.researchgate.net/publication/220654878_Approximating_the_Minimum_Tour_Cover_of_a_Digraph

Approximating the Minimum Tour Cover of a Digraph.pdf. Available via license: CC BY 4.0. ... Hassin R. Approximating the tree and tour covers of a graph. Inf. Pro. Lett. 1993, 47, ...

Approximating the Minimum Tour Cover of a Digraph - MDPI

https://www.mdpi.com/1999-4893/4/2/75/htm

1. Introduction. Let G = (V, A) be a directed graph with a (non-negative) cost function c: A ⇒ ℚ + defined on the arcs. A directed tour cover T is a subgraph T = (U, F) such that. For every e ∈ A, F contains an arc f intersecting e, i.e., f and e have at least one end-node in common.. T is a closed directed walk (or branching in the case of tree cover).. We consider in this paper the ...

Approximating the Minimum Tour Cover with a Compact Linear ...

https://link.springer.com/chapter/10.1007/978-3-319-06569-4_7

A tour cover of an edge-weighted graph is a set of edges which forms a closed walk and covers every other edge in the graph. The minimum tour cover problem is to find a minimum weight tour cover. This problem is introduced by Arkin, Halldórsson and Hassin (Information Processing Letters 47:275-282, 1993) where the author prove the NP -hardness ...

Approximating the Minimum Tour Cover with a Compact Linear ...

https://www.researchgate.net/publication/282652506_Approximating_the_Minimum_Tour_Cover_with_a_Compact_Linear_Program

A tree (tour) cover of an edge-weighted graph is a set of edges which forms a tree (closed walk) and covers every other edge in the graph. Arkin et al. give approximation algorithms with ratios 3 ...

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