Abstract
The two-stage stochastic maximum-weight independent set problem extends the classical independent set problem. Given an independent system associated with one deterministic weight function and a random weight function both defined over the same ground set, the problem is to select two nonoverlapping independent subsets, one in the first stage and the other in the second stage, whose union has the maximum total expected weight. In this paper, we show that this problem can be formulated as a submodular function maximization subject to a matroid constraint if the independent system is a matroid. Furthermore, we also show that the two-stage stochastic maximum-weight knapsack independent set problem is neither submodular nor supermodular maximization problem by designing a counterexample.
This paper is supported by National Science Foundation of China (No. 12001335) and Natural Science Foundation of Shandong Province (Nos. ZR2019PA004, ZR2020MA029) of China.
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Li, M., Liu, Q., Zhou, Y. (2021). Two-Stage Stochastic Max-Weight Independent Set Problems. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Combinatorial Optimization and Applications. COCOA 2021. Lecture Notes in Computer Science(), vol 13135. Springer, Cham. https://doi.org/10.1007/978-3-030-92681-6_17
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DOI: https://doi.org/10.1007/978-3-030-92681-6_17
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