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. (Math Oper Res 42(4):1197–1218, 2017) described an algorithm for this problem whose approximation guarantee is optimal...

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Vydáno v:Algorithmica Ročník 83; číslo 3; s. 853 - 878
Hlavní autor: Feldman, Moran
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.03.2021
Springer Nature B.V
Témata:
Algorithm Analysis and Problem Complexity
Algorithms
Algorithms and Data Structures (WADS 2019)
Approximation
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Linear functions
Mathematical analysis
Mathematics of Computing
Maximization
Optimization
Polytopes
Theory of Computation
68Q25
Continuous greedy
68W25
90C27
Submodular maximization
Curvature
ISSN:0178-4617, 1432-0541
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-020-00757-9