Sparsification of Directed Graphs via Cut Balance
In this paper, we consider the problem of designing cut sparsifiers and sketches for directed graphs. To bypass known lower bounds, we allow the sparsifier/sketch to depend on the balance of the input graph, which smoothly interpolates between undirected and directed graphs. We give nearly matching upper and lower bounds for both for-all (cf. Benczúr and Karger, STOC 1996) and for-each (Andoni et al., ITCS 2016) cut sparsifiers/sketches as a function of cut balance, defined the maximum ratio of the cut value in the two directions of a directed graph (Ene et al., STOC 2016). We also show an interesting application of digraph sparsification via cut balance by using it to give a very short proof of a celebrated maximum flow result of Karger and Levine (STOC 2002).
Graph sparsification
directed graphs
cut sketches
space complexity
Theory of computation~Sparsification and spanners
45:1-45:21
Track A: Algorithms, Complexity and Games
Debmalya Panigrahi and Kevin Sun: This work was supported in part by NSF grants CCF-1535972, CCF-1955703, and an NSF CAREER Award CCF-1750140.
https://arxiv.org/abs/2006.01975
Part of the work was done while Yu Cheng was visiting the Institute for Advanced Study.
Ruoxu
Cen
Ruoxu Cen
Duke University, Durham, NC, USA
Yu
Cheng
Yu Cheng
University of Illinois at Chicago, IL, USA
Debmalya
Panigrahi
Debmalya Panigrahi
Duke University, Durham, NC, USA
Kevin
Sun
Kevin Sun
Duke University, Durham, NC, USA
10.4230/LIPIcs.ICALP.2021.45
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Ruoxu Cen, Yu Cheng, Debmalya Panigrahi, and Kevin Sun
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