{"id":157284,"date":"2006-07-01T00:00:00","date_gmt":"2006-07-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/delegate-and-conquer-an-lp-based-approximation-algorithm-for-minimum-degree-msts\/"},"modified":"2018-10-16T21:52:13","modified_gmt":"2018-10-17T04:52:13","slug":"delegate-and-conquer-an-lp-based-approximation-algorithm-for-minimum-degree-msts","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/delegate-and-conquer-an-lp-based-approximation-algorithm-for-minimum-degree-msts\/","title":{"rendered":"Delegate and Conquer: An LP-Based Approximation Algorithm for Minimum Degree MSTs"},"content":{"rendered":"<p class=\"Para\">In this paper, we study the minimum degree minimum spanning tree problem: Given a graph <em class=\"EmphasisTypeItalic \">G<\/em> = (<em class=\"EmphasisTypeItalic \">V<\/em>,<em class=\"EmphasisTypeItalic \">E<\/em>) and a non-negative cost function <em class=\"EmphasisTypeItalic \">c<\/em> on the edges, the objective is to find a minimum cost spanning tree <em class=\"EmphasisTypeItalic \">T<\/em> under the cost function <em class=\"EmphasisTypeItalic \">c<\/em> such that the maximum degree of any node in <em class=\"EmphasisTypeItalic \">T<\/em> is minimized.<\/p>\n<p class=\"Para\">We obtain an algorithm which returns an MST of maximum degree at most \u0394<sup>*<\/sup>+<em class=\"EmphasisTypeItalic \">k<\/em> where \u0394<sup>*<\/sup> is the minimum maximum degree of any MST and <em class=\"EmphasisTypeItalic \">k<\/em> is the distinct number of costs in any MST of <em class=\"EmphasisTypeItalic \">G<\/em>. We use a lower bound given by a linear programming relaxation to the problem and strengthen known graph-theoretic results on minimum degree subgraphs [3,5] to prove our result. Previous results for the problem [1,4] used a combinatorial lower bound which is weaker than the LP bound we use.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this paper, we study the minimum degree minimum spanning tree problem: Given a graph G = (V,E) and a non-negative cost function c on the edges, the objective is to find a minimum cost spanning tree T under the cost function c such that the maximum degree of any node in T is minimized. 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