Non-oblivious local search for MAX 2-CCSP with application to MAX DICUT

Alimonti, Paola

doi:10.1007/bfb0024483

Cited by 15 publications

(19 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is perhaps the most noteworthy of our algorithms; it proceeds by locally optimizing a smoothed variant of f (S), obtained by biased sampling depending on S. The approach of locally optimizing a modified function has been referred to as "non-oblivious local search" in the literature; e.g., see [2] for a non-oblivious local search 2 5 -approximation for the Max Di-Cut problem. Another (simpler) 2 5 -approximation algorithm for Max DiCut appears in [21]. However, these algorithms do not generalize naturally to ours and the re-appearance of the same approximation factor seems coincidental.…”

Section: Modelmentioning

confidence: 99%

Maximizing Non-Monotone Submodular Functions

Feigc

Mirrokni

Vondrak

2007

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)

109

125

View full text Add to dashboard Cite

Submodular maximization generalizes many important problems including Max Cut in directed/undirected graphs and hypergraphs, certain constraint satisfaction problems and maximum facility location problems. Unlike the problem of minimizing submodular functions, the problem of maximizing submodular functions is NP-hard.In this paper, we design the first constant-factor approximation algorithms for maximizing nonnegative submodular functions. In particular, we give a deterministic local search 1 3 -approximation and a randomized 2 5 -approximation algorithm for maximizing nonnegative submodular functions. We also show that a uniformly random set gives a 1 4 -approximation. For symmetric submodular functions, we show that a random set gives a 1 2 -approximation, which can be also achieved by deterministic local search.These algorithms work in the value oracle model where the submodular function is accessible through a black box returning f (S) for a given set S. We show that in this model, 1 2 -approximation for symmetric submodular functions is the best one can achieve with a subexponential number of queries. For the case where the function is given explicitly (as a sum of nonnegative submodular functions, each depending only on a constant number of elements), we prove that it is NP-hard to achieve a ( 3 4 + )-approximation in the general case (or a ( 5 6 + )-approximation in the symmetric case).

show abstract

Section: Modelmentioning

confidence: 99%

Maximizing Non-Monotone Submodular Functions

Feigc

Mirrokni

Vondrak

2007

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)

109

125

View full text Add to dashboard Cite

show abstract

“…Unlike submodular minimization [44,26], submodular function maximization is NP-hard as it generalizes many NP-hard problems, like Max-Cut [19,14] and maximum facility location [9,10,2]. Other than generalizing combinatorial optimization problems like Max Cut [19], Max Directed Cut [4,22], hypergraph cut problems, maximum facility location [2,9,10], and certain restricted satisfiability problems [25,14], maximizing non-monotone submodular functions have applications in a variety of problems, e.g, computing the core value of supermodular games [46], and optimal marketing for revenue maximization over social networks [23]. As an example, we describe one important application in the statistical design of experiments.…”

Section: Introductionmentioning

confidence: 99%

“…Our main technique for the above results is local search. Our local search algorithms are different from the previously used variant of local search for unconstrained maximization of a non-negative submodular function [15], or the local search algorithms used for Max Directed Cut [4,22]. In the design of our algorithms, we also use structural properties of matroids, a fractional relaxation of submodular functions, and a randomized rounding technique.…”

Section: Introductionmentioning

confidence: 99%

Non-monotone submodular maximization under matroid and knapsack constraints

Lee¹,

Mirrokni

Nagarajan

et al. 2009

Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing

184

186

View full text Add to dashboard Cite

Submodular function maximization is a central problem in combinatorial optimization, generalizing many important problems including Max Cut in directed/undirected graphs and in hypergraphs, certain constraint satisfaction problems, maximum entropy sampling, and maximum facility location problems. Unlike submodular minimization, submodular maximization is NP-hard.In this paper, we give the first constant-factor approximation algorithm for maximizing any non-negative submodular function subject to multiple matroid or knapsack constraints. We emphasize that our results are for non-monotone submodular functions. In particular, for any constant k, we present a " 1 k+2+ 1 k + " -approximation for the submodular maximization problem under k matroid constraints, and a`1 5 − ´-approximation algorithm for this problem subject to k knapsack constraints ( > 0 is any constant). We improve the approximation guarantee of our algorithm to 1 k+1+ 1 k−1 + for k ≥ 2 partition matroid constraints. This idea also gives a " 1 k+ "-approximation for maximizing a monotone submodular function subject to k ≥ 2 partition matroids, which improves over the previously best known guarantee of 1 k+1 .

show abstract

“…Unlike submodular minimization [46,26], submodular function maximization is NP-hard as it generalizes many NP-hard problems, like Max-Cut [19,14] and maximum facility location [9,10,2]. Other than generalizing combinatorial optimization problems like Max Cut [19], Max Directed Cut [4,22], hypergraph cut problems, maximum facility location [2,9,10], and certain restricted satisfiability problems [25,14], maximizing non-monotone submodular functions has applications in a variety of problems, e.g, computing the core value of supermodular games [48], and optimal marketing for revenue maximization over social networks [23]. As an example, we describe one important application in the statistical design of experiments.…”

mentioning

confidence: 99%