Improving MST Weight Approximation in Sublinear Time
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Patlin, Gryphon
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Minimum spanning trees have a variety of applications in computer science as they often form useful sub-structures which aid in computation. Unfortunately, in the modern world, many graph datasets are so intractably large (some even infinite in size) that running a standard MST construction algorithm is impossible. We present an algorithm which, for average degree d, edge weight ratio ω, and error constant ϵ can compute an approximation for the weight of the minimum spanning tree in an general graph in time O(dwϵ−2 log(ωϵ−1)). Additionally as a sub result, we present a deterministic algorithm which maps MST edges to unique graph vertices in expected time O(d log(n)). This result pushes the known upper bound time complexity of the MST weight approximation problem closer to Chazelle, Rubinfeld, and Trevisan’s lower bound of Ω(dωϵ−2).
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Undergraduate Research Option Thesis