Towards (1 + ε)-Approximate flow sparsifiers

Alexandr Andoni, Anupam Gupta, Robert Krauthgamer

Research output: Chapter in Book/Report/Conference proceedingConference contribution


A useful approach to "compress" a large network G is to represent it with a flow-sparsifier, i.e., a small network H that supports the same flows as G, up to a factor q ≥ 1 called the quality of sparsifier. Specifically, we assume the network G contains a set of k terminals T, shared with the network H, i.e., T ⊆V(G) ∩V(H), and we want H to preserve all multicommodity flows that can be routed between the terminals T. The challenge is to construct H that is small. These questions have received a lot of attention in recent years, leading to some known tradeoffs between the sparsifier's quality q and its size \V(H)\. Nevertheless, it remains an outstanding question whether every G admits a flow-sparsifier H with quality q = 1 + ε, or even q = O(1), and size |V(H)| < f(k, ε) (in particular, independent of |V(G)| and the edge capacities). Making a first step in this direction, we present new constructions for several scenarios: Our main result is that for quasi-bipartite networks G, one can construct a (1 + ε)-flow-sparsifier of size poly(k/ ε). In contrast, exact (q = 1) sparsifiers for this family of networks are known to require size 2Ω(k) For networks G of bounded treewidth w, we construct a flow-sparsifier with quality q = O(logw/loglogw) and size O(w .poly(k)). For general networks G, we construct a sketch sk(G), that stores all the feasible multicommodity flows up to factor q = 1 + ε, and its size (storage requirement) is f(k, ε).

Original languageEnglish (US)
Title of host publicationProceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014
PublisherAssociation for Computing Machinery
Number of pages15
ISBN (Print)9781611973389
StatePublished - 2014
Event25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014 - Portland, OR, United States
Duration: Jan 5 2014Jan 7 2014

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms


Other25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014
Country/TerritoryUnited States
CityPortland, OR

ASJC Scopus subject areas

  • Software
  • General Mathematics


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