A distributed approximation algorithm for the minimum degree minimum weight spanning trees

Abstract

Fischer has shown how to compute a minimum weight spanning tree of degree at most $b{\Delta }^{\ast }+\lceil \log \_bn\rceil$ in time $O(n^{4+1/\ln b})$ for any constant $b>1$, where ${\Delta }^{\ast }$ is the value of an optimal solution and $n$ is the number of nodes in the network. In this paper, we propose a distributed version of Fischer's algorithm that requires messages and time complexity $O(n^{2+1/\ln b})$, and O(n) space per node.