Abstract
In this work we consider some NP-hard cases of the metric p-source communication spanning tree problem (metric p-OCT). Given an undirected complete graph G = (V,E) with non-negative length ω(e) associated to each edge e ∈ E satisfying the triangular inequality, a set S ⊆ V of p vertices and non-negative routing requirements ψ(u,v) between all pairs of nodes u ∈ S and v ∈ V, the metric p-OCT’s objective is to find a spanning tree T of G, that minimizes: ∑ u ∈ S ∑ v ∈ Vψ(u,v)d(T,u,v), where d(H,x,y) is the minimum distance between nodes x and y in a graph H ⊆ G. This problem is a particular case of the optimum communication spanning tree problem (OCT). We prove a general result which allows us to derive polynomial approximation schemes for some NP-hard cases of the metric p-OCT improving the existing ratios for these problems.
This research is supported by the following projects: FAPESP 2013/03447 − 6, CNPq 477203/2012 − 4 and CNPq 302736/2010 − 7.
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Ravelo, S.V., Ferreira, C.E. (2015). PTAS’s for Some Metric p-source Communication Spanning Tree Problems. In: Rahman, M.S., Tomita, E. (eds) WALCOM: Algorithms and Computation. WALCOM 2015. Lecture Notes in Computer Science, vol 8973. Springer, Cham. https://doi.org/10.1007/978-3-319-15612-5_13
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DOI: https://doi.org/10.1007/978-3-319-15612-5_13
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