Abstract
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 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 high probability). Then we introduce an easy-to-implement, very fast divide and conquer heuristic and we prove that its solution cost matches the lower bound.
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Clementi, A.E.F., Di Ianni, M., Monti, A., Lauria, M., Rossi, G., Silvestri, R. (2005). Divide and Conquer Is Almost Optimal for the Bounded-Hop MST Problem on Random Euclidean Instances. In: Pelc, A., Raynal, M. (eds) Structural Information and Communication Complexity. SIROCCO 2005. Lecture Notes in Computer Science, vol 3499. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11429647_9
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DOI: https://doi.org/10.1007/11429647_9
Publisher Name: Springer, Berlin, Heidelberg
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