Divide et Impera is almost optimal for the bounded-hop MST problem on random Euclidean instances
نویسندگان
چکیده
The d-Dim h-hops MST problem is defined as follows: Given a set S of points in the ddimensional Euclidean space and s ∈ S, find a minimum-cost spanning tree for S rooted at s with height at most h. We investigate the problem for any constants h and d > 0. We prove the first non trivial lower bound on the solution cost for almost all Euclidean instances (i.e. the lower-bound holds with hight probability). Then we introduce an easy-to-implement, very fast divide et impera heuristic and we prove that its solution cost matches the lower bound.
منابع مشابه
On the bounded-hop MST problem on random Euclidean instances
The d-Dim h-hops MST problem is defined as follows: Given a set S of points in the d-dimensional Euclidean space and s ∈ S, find a minimum-cost spanning tree for S rooted at s with height at most h. We investigate the problem for any constant h and d > 0. We prove the first non trivial lower bound on the solution cost for almost all Euclidean instances (i.e. the lower-bound holds with high prob...
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