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Sparsification of Directed Graphs via Cut Balance

Authors Ruoxu Cen, Yu Cheng, Debmalya Panigrahi, Kevin Sun

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Author Details

Ruoxu Cen
  • Duke University, Durham, NC, USA
Yu Cheng
  • University of Illinois at Chicago, IL, USA
Debmalya Panigrahi
  • Duke University, Durham, NC, USA
Kevin Sun
  • Duke University, Durham, NC, USA

Funding

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.

Acknowledgements

Part of the work was done while Yu Cheng was visiting the Institute for Advanced Study.

Cite As Get BibTex

Ruoxu Cen, Yu Cheng, Debmalya Panigrahi, and Kevin Sun. Sparsification of Directed Graphs via Cut Balance. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 45:1-45:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ICALP.2021.45

Abstract

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).

Subject Classification

ACM Subject Classification
  • Theory of computation → Sparsification and spanners
Keywords
  • Graph sparsification
  • directed graphs
  • cut sketches
  • space complexity

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