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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. 

Preventing and slowing the spread of epidemics is achieved through techniques such as vaccination and social distancing. Given practical limitations on the number of vaccines and cost of administration, optimization becomes a necessity. Previous approaches using mathematical programming methods have shown to be effective but are limited by computational costs. In this work, we present PREEMPT, a new approach for intervention via maximizing the influence of vaccinated nodes on the network.We prove submodular properties associated with the objective function of our method so that it aids in construction of an efficient greedy approximation strategy. Consequently, we present a new parallel algorithm based on greedy hill climbing for PREEMPT, and present an efficient parallel implementation for distributed CPU-GPU heterogeneous platforms. Our results demonstrate that PREEMPT is able to achieve a significant reduction (up to 6:75) in the percentage of people infected and up to 98% reduction in the peak of the infection on a cityscale network. We also show strong scaling results of PREEMPT on up to 128 nodes of the Summit supercomputer. Our parallel implementation is able to significantly reduce time to solution, from hours to minutes on large networks. This work represents a first-of-its-kind effort in parallelizing greedy hill climbing and applying it toward devising effective interventions for epidemics.