We describe a 3/2approximation algorithm, \lse, for computing a bedgecover of minimum weight in a graph with weights on the edges. The bedgecover problem is a generalization of the betterknown Edge Cover problem in graphs, where the objective is to choose a subset C of edges in the graph such that at least a specified number b(v) of edges in C are incident on each vertex v. In the weighted bedgecover problem, we minimize the sum of the weights of the edges in C. We prove that the Locally Subdominant edge (LSE) algorithm computes the same bedge cover as the one obtained by the Greedy algorithm for the problem. However, the Greedy algorithm requires edges to be sorted by their effective weights, and these weights need to be updated after each iteration. These requirements make the Greedy algorithm sequential and impractical for massive graphs. The LSE algorithm avoids the sorting step, and is amenable for parallelization. We implement the algorithm on a serial machine and compare its performance against a collection of approximation algorithms for the bedge cover problem. Our results show that the algorithm is 3 to 5 times faster than the Greedy algorithm on a serial processor. Themore »
A Parallel Approximation Algorithm for Maximizing Submodular bMatching
We design new serial and parallel approximation algorithms for computing a maximum weight bmatching in an edgeweighted graph with a submodular objective function. This problem is NPhard; the new algorithms have approximation ratio 1/3, and are relaxations of the Greedy algorithm that rely only on local information in the graph, making them parallelizable. We have designed and implemented Local Lazy Greedy algorithms for both serial and parallel computers. We have applied the approximate submodular bmatching algorithm to assign tasks to processors in the computation of Fock matrices in quantum chemistry on parallel computers. The assignment seeks to reduce the run time by balancing the computational load on the processors and bounding the number of messages that each processor sends. We show that the new assignment of tasks to processors provides a four fold speedup over the currently used assignment in the NWChemEx software on 8000 processors on the Summit supercomputer at Oak Ridge National Lab.
 Editors:
 Bender, M.; Gilbert, J.; Hendrickson, B.; Sullivan, B.
 Award ID(s):
 1637534
 Publication Date:
 NSFPAR ID:
 10300888
 Journal Name:
 Proceedings of the 2021 SIAM Conference on Applied and Computational Discrete Algorithms (ACDA21)
 Volume:
 1
 Issue:
 1
 Page Range or eLocationID:
 4556
 Sponsoring Org:
 National Science Foundation
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