Fast algorithms for k-submodular maximization subject to a matroid constraint
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In this paper, we apply a Threshold-Decreasing Algorithm to maximize k-submodular functions under a matroid constraint, which reduces the query complexity of the algorithm compared to the greedy algorithm with little loss in approximation ratio. We give a (1/2 - ϵ)-approximation algorithm for monotone k-submodular function maximization, and a (1/3 - ϵ)-approximation algorithm for non-monotone case, with complexity O(n(k· EO + IO)/ϵlogr/ϵ), where r denotes the rank of the matroid, and IO, EO denote the number of oracles to evaluate whether a subset is an independent set and to compute the function value of f, respectively. Since the constraint of total size can be looked as a special matroid, called uniform matroid, then we present the fast algorithm for maximizing k-submodular functions subject to a total size constraint as corollaries. corollaries.
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