Probabilistic Analysis of the Degree Bounded Minimum Spanning Tree Problem
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چکیده
In the b-degree constrained Euclidean minimum spanning tree problem (bMST) we are given n points in [0; 1] and a degree constraint b 2. The aim is to nd a minimum weight spanning tree in which each vertex has degree at most b. In this paper we analyze the probabilistic version of the problem and prove in a rmative the conjecture of Yukich stated in 1998 on the asymptotics of the problem for uniformly (and also some non-uniformly) distributed points in [0; 1]: the optimal length LbMST (X1; : : : ; Xn) of a b-degree constrained minimal spanning tree on X1; : : : ; Xn given by iid random variables with values in [0; 1] d
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تاریخ انتشار 2007