Webmetric2 submodular function [15]. However, the algorithms developed in [15] for non-monotone submodular maximiza-tion do not handle any extra constraints. For the problem of maximizing a monotone submodular function subject to a matroid or multiple knapsack con-straints, tight ` 1− 1 e ´-approximations are known [39, 7, 51, 49, 28]. Web20 nov. 2024 · As many combinatorial optimization problems also involve non-monotone or non-submodular objective functions, we consider these two general problem classes, maximizing non-monotone submodular functions without constraints and maximizing monotone non-submodular functions with a size constraint.
Maximizing non-monotone submodular functions
Weba monotone submodular function g and a linear function ℓ. Motivated by the above applications, Sviridenko et al. [17] also initialized the study of the optimization of g + ℓ sums. In particular, they described algorithms with optimal approximation guarantees for this problem when g is a non-negative monotone submodular function, ℓ is a linear Webfor maximizing non-monotone k-submodular functions with individual size constraints [SGW20]. Tang, Wang, and Chan propose an (1 2− 1 2e)-approximation algorithm for … commercials with little girls
Submodular set function - Wikipedia
WebIn 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 size upper bounds B 1, B 2, …, B k, respectively. This problem generalized both submodular maximization and k -submodular maximization problem with total size constraint. WebSubmodular maximization generalizes many important problems including Max Cut in directed and undirected graphs and hypergraphs, certain constraint satisfaction problems, and maximum facility location problems. Unlike the problem of minimizing submodular … 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) = … dss research reviews