Title:
A Cache-Aware Parallel Implementation of the Push-Relabel Network Flow Algorithm and Experimental Evaluation of the Gap Relabeling Heuristic
A Cache-Aware Parallel Implementation of the Push-Relabel Network Flow Algorithm and Experimental Evaluation of the Gap Relabeling Heuristic
Author(s)
Bader, David A.
Sachdeva, Vipin
Sachdeva, Vipin
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Abstract
The maximum flow problem is a combinatorial problem of significant importance in a wide variety
of research and commercial applications. It has been extensively studied and implemented
over the past 40 years. The push-relabel method has been shown to be superior to other methods,
both in theoretical bounds and in experimental implementations. Our study discusses the implementation
of the push-relabel network flow algorithm on present-day symmetric multiprocessors
(SMP's) with large shared memories. The maximum flow problem is an irregular graph problem
and requires frequent fine-grained locking of edges and vertices. Over a decade ago, Anderson and
Setubal implemented Goldberg's push-relabel algorithm for shared memory parallel computers;
however, modern systems differ significantly from those targeted by their implementation in that
SMP's today have deep memory hierarchies and different performance costs for synchronization
and fine-grained locking. Besides our new cache-aware implementation of Goldberg's parallel
algorithm for modern shared-memory parallel computers, our main new contribution is the first
parallel implementation and analysis of the gap relabeling heuristic that runs from 2.1 to 4.3 times
faster for sparse graphs.
Sponsor
This work was supported in part by NSF Grants CAREER ACI-00-93039, NSF DBI-0420513, ITR ACI-00-
81404, DEB-99-10123, ITR EIA-01-21377, Biocomplexity DEB-01-20709, and ITR EF/BIO 03-31654; and DARPA
Contract NBCH30390004.
Date Issued
2006-02-25
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Technical Report