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) \u2264 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 \u2212 1 \u2264 dT (v) \u2264 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.<\/p>\n","protected":false},"excerpt":{"rendered":"
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 […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"ACM","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"Journal of ACM (JACM), 2015. 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