Guess Free Maximization of Submodular and Linear Sums

Moran Feldman

Research output: Contribution to journalArticlepeer-review


We consider the problem of maximizing the sum of a monotone submodular function and a linear function subject to a general solvable polytope constraint. Recently, Sviridenko et al. (Math Oper Res 42(4):1197–1218, 2017) described an algorithm for this problem whose approximation guarantee is optimal in some intuitive and formal senses. Unfortunately, this algorithm involves a guessing step which makes it less clean and significantly affects its time complexity. In this work we describe a clean alternative algorithm that uses a novel weighting technique in order to avoid the problematic guessing step while keeping the same approximation guarantee as the algorithm of Sviridenko et al. (2017). We also show that the guarantee of our algorithm becomes slightly better when the polytope is down-monotone, and that this better guarantee is tight for such polytopes.

Original languageEnglish
Pages (from-to)853-878
Number of pages26
Issue number3
StatePublished - Mar 2021

Bibliographical note

Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.


  • Continuous greedy
  • Curvature
  • Submodular maximization


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