2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) (2016)

New Brunswick, New Jersey, USA

Oct. 9, 2016 to Oct. 11, 2016

ISSN: 0272-5428

ISBN: 978-1-5090-3933-3

pp: 335-344

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/FOCS.2016.44

ABSTRACT

We initiate the study of fast dynamic algorithms for graph sparsification problems and obtain fully dynamic algorithms, allowing both edge insertions and edge deletions, that take polylogarithmic time after each update in the graph. Our three main results are as follows. First, we give a fully dynamic algorithm for maintaining a (1 ± ε)-spectral sparsifier with amortized update time poly(log n, ε–1). Second, we give a fully dynamic algorithm for maintaining a (1 ± ε)-cut sparsifier with worst-case update time poly(log n, ε–1). Both sparsifiers have size n · poly(log n, ε–1). Third, we apply our dynamic sparsifier algorithm to obtain a fully dynamic algorithm for maintaining a (1 — ε)-approximation to the value of the maximum flow in an unweighted, undirected, bipartite graph with amortized update time poly(log n, ε–1).

INDEX TERMS

Heuristic algorithms, Approximation algorithms, Data structures, Laplace equations, Bipartite graph, Clustering algorithms, Algorithm design and analysis

CITATION

I. Abraham, D. Durfee, I. Koutis, S. Krinninger and R. Peng, "On Fully Dynamic Graph Sparsifiers,"

*2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)*, New Brunswick, New Jersey, USA, 2016, pp. 335-344.

doi:10.1109/FOCS.2016.44

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