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Graph Sparsification, Spectral Sketches, and Faster Resistance Computation, via Short Cycle Decompositions
[article]

2018
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arXiv
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pre-print

We develop a framework for graph sparsification and sketching, based on a new tool, short cycle decomposition -- a decomposition of an unweighted graph into an edge-disjoint collection of short cycles, plus few extra edges. A simple observation gives that every graph G on n vertices with m edges can be decomposed in O(mn) time into cycles of length at most 2 n, and at most 2n extra edges. We give an m^1+o(1) time algorithm for constructing a short cycle decomposition, with cycles of length

arXiv:1805.12051v1
fatcat:6jz5yc74srfydjhrcept4ohwnm