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Approximating minimum bounded degree spanning trees to within one of optimal

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Approximating minimum bounded degree spanning trees to within one of optimal
In the MINIMUM BOUNDED DEGREE SPANNING TREE problem, we are given an undirected graph with a degree upper bound Bv on each vertex v, and the task is to find a spanning tree of minimum cost which satisfies all the degree bounds. Let OPT be the cost of an optimal solution to this problem. In this paper, we present a polynomial time algorithm which returns a spanning tree T of cost at most OPT and dT (v) Bv + 1 for all v, where dT (v) denotes the degree of v in T. This generalizes a result of Furer and Raghavachari [8] to weighted graphs, and settles a 15-year-old conjecture of Goemans [10] affirmatively. The algorithm generalizes when each vertex v has a degree lower bound Av and a degree upper bound Bv, and returns a spanning tree with cost at most OPT and Av - 1 dT (v) Bv + 1 for all v. This is essentially the best possible. The main technique used is an extension of the iterative rounding method introduced by Jain [12] for the design of approximation algorithms. Categories and Sub...
Mohit Singh, Lap Chi Lau
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2007
Where STOC
Authors Mohit Singh, Lap Chi Lau
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