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Maximizing non-monotone submodular functions

WebSubmodular set function maximization. Unlike the case of minimization, maximizing a generic submodular function is NP-hard even in the unconstrained setting. Thus, most of … WebS A;S2Ig, is monotone submodular. More generally, given w: N!R +, the weighted rank function de ned by r M;w(A) = maxfw(S) : S A;S2Igis a monotone submodular function. Cut functions in graphs and hypergraphs: Given an undirected graph G= (V;E) and a non-negative capacity function c: E!R +, the cut capacity function f: 2V!R + de ned by f(S) = …

Fast Adaptive Non-Monotone Submodular Maximization Subject …

Web28 okt. 2024 · Submodular functions arise naturally from combinatorial optimization as several combinatorial functions turn out to be submodular. A few examples of such … WebSubmodular maximization also appears in maximizing the difference of a monotone submodular function and a modular function. An illustrative example of this type is the … photo flyer noel https://amgoman.com

On maximizing a monotone k-submodular function under a …

Webmonotone submodular maximization problem, which we will describe below. Definition 1. The cardinality constrained monotone submodular maximization problem takes as … Webgeneral non-monotone submodular objectives. In this work we present a new unified continuous greedy algorithm which finds approximate fractional solutions for both the non-monotone and monotone cases, and improves on the approximation ratio for many applications. For general non-monotone submodular objective functions, Web1 jan. 2024 · 1. Introduction. A k -submodular function is a generalization of submodular function, where the input consists of k disjoint subsets of the domain, instead of a single … photo floue photoshop

Non-monotone k-Submodular Function Maximization with …

Category:[1711.02515v1] Non-monotone Continuous DR-submodular …

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Maximizing non-monotone submodular functions

On maximizing a monotone k-submodular function under a …

Web1 jan. 2024 · In this note, we study the maximization problem of a non-negative monotone k -submodular function under a knapsack constraint, and give a deterministic -approximation algorithm (see Theorem 1 ). It is an adaption to Sviridenko's -approximation algorithm for submodular knapsack maximization [14]. Related works. Web23 okt. 2007 · Maximizing Non-Monotone Submodular Functions. Abstract: Submodular maximization generalizes many important problems including Max Cut in …

Maximizing non-monotone submodular functions

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WebOn non-monotone submodular functions Lee et al. [37] provided a 5-approximation algorithm for kknapsack constraints, which was the first constant factor algorithm for the problem. Fadaei et al. [19] building on the approach of Lee et al. [37], reduced this factor to 4. One of the most interesting Web26 mei 2024 · We first consider the problem of maximizing a non-negative symmetric submodular function f :2 N → R + subject to a down-monotone solvable polytope P ⊆ [0, 1] N. For this problem, we describe an algorithm producing a fractional solution of value at least 0.432 ċ f ( OPT ), where OPT is the optimal integral solution.

http://proceedings.mlr.press/v80/bai18a/bai18a.pdf WebWe emphasize that our results are for non-monotone submodular functions. In particular, for any constant k, we present a (1/k+2+1/k+ε)-approximation for the submodular maximization problem under k matroid constraints, and a (1/5-ε)-approximation algorithm for this problem subject to k knapsack constraints (ε>0 is any constant).

Web20 nov. 2024 · As many combinatorial optimization problems also involve non-monotone or non-submodular objective functions, we consider these two general problem classes, … Webof maximizing submodular and non-submodular functions on the integer lattice has received a lot of recent attention. In this paper, we study streaming algorithms for the problem of maximizing a monotone non-submodular functions with cardinality constraint on the integer lattice. For a monotone non-submodular function f: Zn + →

Webmaximizing submodular functions is NP-hard. Inthispaper, wedesignthefirstconstant-factorapproxi-mation algorithms for maximizing nonnegative submodular functions. …

WebWeak submodularity is a natural relaxation of the diminishing return property, which is equivalent to submodularity. Weak submodularity has been used to show that many (monotone) functions that arise in practice can be… how does fish breathe in waterWeb13 apr. 2024 · In the set function optimization, the analysis on submodular functions, especially on monotone nondecreasing submodular functions, has been very well studied , so that although maximization and constrained minimization of submodular functions are often NP-hard, there exist many theoretical guaranteed approximation solutions for … how does fish make babiesWeb17 jul. 2024 · 3 The greedy algorithm for maximizing a monotone non-submodular function under a knapsack constraint We present the greedy algorithm for ( 1) as … photo focus colombo