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- W2805536941 abstract "The minimum degree spanning tree (MDST) problem requires the construction of a spanning tree $T$ for graph $G=(V,E)$ with $n$ vertices, such that the maximum degree $d$ of $T$ is the smallest among all spanning trees of $G$. In this paper, we present two new distributed approximation algorithms for the MDST problem. Our first result is a randomized distributed algorithm that constructs a spanning tree of maximum degree $hat d = O(dlog{n})$. It requires $O((D + sqrt{n}) log^2 n)$ rounds (w.h.p.), where $D$ is the graph diameter, which matches (within log factors) the optimal round complexity for the related minimum spanning tree problem. Our second result refines this approximation factor by constructing a tree with maximum degree $hat d = O(d + log{n})$, though at the cost of additional polylogarithmic factors in the round complexity. Although efficient approximation algorithms for the MDST problem have been known in the sequential setting since the 1990's, our results are first efficient distributed solutions for this problem." @default.
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- W2805536941 date "2018-06-08" @default.
- W2805536941 modified "2023-10-18" @default.
- W2805536941 title "Distributed Algorithms for Minimum Degree Spanning Trees." @default.
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