Maximizing non-monotone submodular 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 … Webit holds for maximizing a submodular function gover any down monotone constraint [2]. Hence it is conceivable that an algorithm that uses both fand gto choose the next …
Maximizing non-monotone submodular functions
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Web4 mrt. 2015 · The problem of maximizing non-negative monotone submodular functions under a certain constraint has been intensively studied in the last decade. In this paper, … WebThe combination for all buyers is a non-monotone submodular function. It also is non-negative at~0 and~1, by extending the model and accounting for extra revenue gains from buyers with free trials. Our Results. Maximizing a submodular function over the hypercube is at least as difficult as over
Web28 okt. 2024 · Submodular functions arise naturally from combinatorial optimization as several combinatorial functions turn out to be submodular. A few examples of such … Web1 jul. 2024 · Maximizing a monotone non-submodular function under a knapsack constraint July 2024 Authors: Zhenning Zhang Bin Liu Yishui Wang Dachuan Xu Abstract and Figures Submodular optimization has been...
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) = … Web17 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 …
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).
Web11 feb. 2024 · In the problem of maximizing non-monotone k -submodular function f under individual size constraints, the goal is to maximize the value of k disjoint subsets with … hate to say i told you so bass tabWeb4 nov. 2024 · DR-submodular continuous functions are important objectives with wide real-world applications spanning MAP inference in determinantal point processes … boots chelsea femme zalandoWeb23 okt. 2007 · Maximizing Non-Monotone Submodular Functions. Abstract: Submodular maximization generalizes many important problems including Max Cut in … hate to say i told you so bass tab youtubeWeb12 apr. 2024 · A k-submodular function is a generalization of a submodular function. The definition domain of a k-submodular function is a collection of k-disjoint subsets instead of simple subsets of ground set. In this paper, we consider the maximization of a k-submodular function with the intersection of a knapsack and m matroid constraints. … boots cheltenham high streetWeb27 mrt. 2024 · 2024. TLDR. This work introduces a decreasing threshold greedy algorithm with a binary search as its subroutine to solve the problem of maximizing the sum of a monotone non-negative diminishing return submodular (DR-submodular) function and a supermodular function on the integer lattice subject to a cardinality constraint. 5. hate to say i told you so / the hivesWeb1 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. boots chemist 2 day testWeb20 sep. 2014 · This work considers the problem of maximizing a non-negative symmetric submodular function f:2N → R+ subject to a down-monotone solvable polytope P ⊆ [0, 1]N and describes a deterministic linear-time 1/2-approximation algorithm solution. Symmetric submodular functions are an important family of submodular functions … boots cheltenham high street phone number