A Parallel Approximation Algorithm for Maximizing Submodular $b$-Matching

TL;DR

This paper introduces parallel approximation algorithms with a 1/3 ratio for maximizing submodular b-matchings, enabling faster task assignments in quantum chemistry computations on supercomputers.

Contribution

It presents novel parallel and serial algorithms for submodular b-matching with provable approximation guarantees, and demonstrates their effectiveness in quantum chemistry applications.

Findings

Achieved a fourfold speedup in task assignment on 8000 processors.

Designed local greedy algorithms suitable for parallel implementation.

Validated algorithms on high-performance computing platforms.

Abstract

We design new serial and parallel approximation algorithms for computing a maximum weight $b$-matching in an edge-weighted graph with a submodular objective function. This problem is NP-hard; 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 $b$-matching 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.