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

TL;DR

This paper introduces a distributed algorithm for finding minimum degree, minimum weight spanning trees that improves message and time complexity over previous methods, making it more efficient for large networks.

Contribution

It presents a distributed version of Fischer's algorithm with reduced message and time complexity, enhancing scalability for network applications.

Findings

Message complexity is reduced to O(n^{2 + 1/ln b})

Time complexity is improved to O(n^{2 + 1/ln b})

Space per node remains O(n)

Abstract

Fischer has shown how to compute a minimum weight spanning tree of degree at most $b \Delta^* + \lceil \log\_b n\rceil$ in time $O(n^{4 + 1/\ln b})$ for any constant $b > 1$, where $\Delta^*$ 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.