Performance Bounds with Curvature for Batched Greedy Optimization

Yajing Liu (), Zhenliang Zhang (), Edwin K. P. Chong () and Ali Pezeshki ()
Additional contact information
Yajing Liu: Colorado State University
Zhenliang Zhang: Intel Labs
Edwin K. P. Chong: Colorado State University
Ali Pezeshki: Colorado State University

Journal of Optimization Theory and Applications, 2018, vol. 177, issue 2, No 12, 535-562

Abstract: Abstract The batched greedy strategy is an approximation algorithm to maximize a set function subject to a matroid constraint. Starting with the empty set, the batched greedy strategy iteratively adds to the current solution set a batch of elements that results in the largest gain in the objective function while satisfying the matroid constraints. In this paper, we develop bounds on the performance of the batched greedy strategy relative to the optimal strategy in terms of a parameter called the total batched curvature. We show that when the objective function is a polymatroid set function, the batched greedy strategy satisfies a harmonic bound for a general matroid constraint and an exponential bound for a uniform matroid constraint, both in terms of the total batched curvature. We also study the behavior of the bounds as functions of the batch size. Specifically, we prove that the harmonic bound for a general matroid is nondecreasing in the batch size and the exponential bound for a uniform matroid is nondecreasing in the batch size under the condition that the batch size divides the rank of the uniform matroid. Finally, we illustrate our results by considering a task scheduling problem and an adaptive sensing problem.

Keywords: Curvature; Greedy; Matroid; Polymatroid; Submodular; 90C27; 90C59 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-017-1177-1

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