We investigate the problem of maximizing the sum of submodular and supermodular functions under a fairness *** sum function is non-submodular in *** an offline model,we introduce two approximation algorithms:A greedy ...
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We investigate the problem of maximizing the sum of submodular and supermodular functions under a fairness *** sum function is non-submodular in *** an offline model,we introduce two approximation algorithms:A greedyalgorithm and a thresholdgreedy *** a streaming model,we propose a one-pass streaming *** also analyze the approximation ratios of these algorithms,which all depend on the total curvature of the supermodular *** total curvature is computable in polynomial time and widely utilized in the literature.
Arising from practical problems such as in sensor placement and influence maximization in social network, submodular and non-submodular maximization on the integer lattice has attracted much attention recently. In thi...
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Arising from practical problems such as in sensor placement and influence maximization in social network, submodular and non-submodular maximization on the integer lattice has attracted much attention recently. In this work, we consider 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. By exploiting the special combinatorial structures in the problem, we introduce a decreasing threshold greedy algorithm with a binary search as its subroutine to solve the problem. To avoid introducing the diminishing return ratio and submodularity ratio of the objective function, we generalize the total curvatures of submodular functions and supermodular functions to the integer lattice version. We show that our algorithm has a constant approximation ratio parameterized by the new introduced total curvatures on integer lattice with a polynomial query complexity.
In this paper, we provide a streaming algorithm for the problem of maximizing the sum of a supermodular function and a nonnegative monotone diminishing return submodular (MDR-submodular) function with a knapsack const...
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In this paper, we provide a streaming algorithm for the problem of maximizing the sum of a supermodular function and a nonnegative monotone diminishing return submodular (MDR-submodular) function with a knapsack constraint on the integer lattice. Inspired by the SIEVE-STREAMING algorithm, we present a two-pass streaming algorithm by using the threshold technique. Then, we improve the two-pass streaming algorithm to one-pass and further reduce its space complexity. The proposed algorithms are proved to have polynomial time and space complexity, and a performance guarantee dependent on the curvature of the supermodular function. Finally, we carry out numerical experiments to verify the performance of the algorithm.
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