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- W4226076914 abstract "We introduce the notion of {em fair cuts} as an approach to leverage approximate $(s,t)$-mincut (equivalently $(s,t)$-maxflow) algorithms in undirected graphs to obtain near-linear time approximation algorithms for several cut problems. Informally, for any $alphageq 1$, an $alpha$-fair $(s,t)$-cut is an $(s,t)$-cut such that there exists an $(s,t)$-flow that uses $1/alpha$ fraction of the capacity of emph{every} edge in the cut. (So, any $alpha$-fair cut is also an $alpha$-approximate mincut, but not vice-versa.) We give an algorithm for $(1+epsilon)$-fair $(s,t)$-cut in $tilde{O}(m)$-time, thereby matching the best runtime for $(1+epsilon)$-approximate $(s,t)$-mincut [Peng, SODA '16]. We then demonstrate the power of this approach by showing that this result almost immediately leads to several applications: - the first nearly-linear time $(1+epsilon)$-approximation algorithm that computes all-pairs maxflow values (by constructing an approximate Gomory-Hu tree). Prior to our work, such a result was not known even for the special case of Steiner mincut [Dinitz and Vainstein, STOC '94; Cole and Hariharan, STOC '03]; - the first almost-linear-work subpolynomial-depth parallel algorithms for computing $(1+epsilon)$-approximations for all-pairs maxflow values (again via an approximate Gomory-Hu tree) in unweighted graphs; - the first near-linear time expander decomposition algorithm that works even when the expansion parameter is polynomially small; this subsumes previous incomparable algorithms [Nanongkai and Saranurak, FOCS '17; Wulff-Nilsen, FOCS '17; Saranurak and Wang, SODA '19]." @default.
- W4226076914 created "2022-05-05" @default.
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- W4226076914 date "2022-03-01" @default.
- W4226076914 modified "2023-10-07" @default.
- W4226076914 title "Near-Linear Time Approximations for Cut Problems via Fair Cuts" @default.
- W4226076914 doi "https://doi.org/10.48550/arxiv.2203.00751" @default.
- W4226076914 hasPublicationYear "2022" @default.
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