Guess Free Maximization of Submodular and Linear Sums

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. [16] described an algorithm for this problem whose approximation guarantee is optimal in some intuitive and formal sens...

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Bibliographic Details
Published inAlgorithms and Data Structures Vol. 11646; pp. 380 - 394
Main Author Feldman, Moran
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 2019
Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
Continuous greedy
Curvature
Submodular maximization
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ISBN3030247651
9783030247652
ISSN0302-9743
1611-3349
DOI10.1007/978-3-030-24766-9_28

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Summary: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. [16] 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 [16].
Bibliography:This research was partially supported by Israel Science Foundation grant number 1357/16.
ISBN:3030247651
9783030247652
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-030-24766-9_28