Maximizing k-submodular functions under budget constraint: applications and streaming algorithms

• Published in: Journal of combinatorial optimization Vol. 44; no. 1; pp. 723 - 751
• Main Authors: Pham, Canh V., Vu, Quang C., Ha, Dung K. T., Nguyen, Tai T., Le, Nguyen D.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2022; Springer Nature B.V
• Subjects: Algorithms; Budgets; Combinatorial analysis; Combinatorics; Convex and Discrete Geometry; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Maximization; Operations Research/Decision Theory; Optimization; Theory of Computation; Streaming algorithm; submodular; Approximation algorithm; Budget constraint
• ISSN: 1382-6905; 1573-2886
• DOI: 10.1007/s10878-022-00858-x

Motivated by the practical applications in solving plenty of important combinatorial optimization problems, this paper investigates the Budgeted k -Submodular Maximization problem defined as follows: Given a finite set V , a budget B and a k -submodular function f : ( k + 1 ) V ↦ R + , the problem asks to find a solution s = ( S 1 , S 2 , … , S k ) ∈ ( k + 1 ) V , in which an element e ∈ V has a cost c i ( e ) when added into the i -th set S i , with the total cost of s that does not exceed B so that f ( s ) is maximized. To address this problem, we propose two single pass streaming algorithms with approximation guarantees: one for the case that an element e has only one cost value when added to all i -th sets and one for the general case with different values of c i ( e ) . We further investigate the performance of our algorithms in two applications of the problem, Influence Maximization with k topics and sensor placement of k types of measures. The experiment results indicate that our algorithms can return competitive results but require fewer the number of queries and running time than the state-of-the-art methods.