2019/07/09 by Takanori Maehara, Maehara, Takanori, So Nakashima +3
Computer Science · #Complexity and Algorithms in Graphs #Cryptography and Data Security #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Optimization and Search Problems
paper · pdf · doi:10.48550/arxiv.1907.04279
openalex publication_date 2019/07/09 · openalex created_date 2019/07/23 · openalex updated_date 2026/07/28
We consider a problem of maximizing a monotone DR-submodular function under multiple order-consistent knapsack constraints on a distributive lattice. Since a distributive lattice is used to represent a dependency constraint, the problem can represent a dependency constrained version of a submodular maximization problem on a set. We propose a 1 - 1/e approximation algorithm for this problem. To achieve this result, we generalize the continuous greedy algorithm to distributive lattices: We choose a median complex as a continuous relaxation of a distributive lattice and define the multilinear extension on it. We show that the median complex admits special curves, named uniform linear motions, such that the multilinear extension of a DR-submodular function is concave along a positive uniform linear motion, which is a key property of the continuous greedy algorithm.