Abstract
In this paper, we study the maximum bounded connected bipartition problem (2-BCBP): given a vertex-weighted connected graph \(G=(V,E;w)\) and an upper bound B, the vertex set V is partitioned into two subsets denoted as \((V_1,V_2)\) such that both subgraphs induced by \(V_1\) and \(V_2\) are connected and the total weight of these two subgraphs is maximized, where the weight of the subgraph is the minimum of the sum of the weight of all vertices and B. The 2-BCBP is a hybrid variant of the maximum balanced connected partition problem on connected graphs and the maximum total early work problem in scheduling theory. In this paper, we consider the 2-BCBP and present an \(\frac{8}{7}\)-approximation algorithm. In particular, we consider the 2-BCBP on interval graphs and present a fully polynomial-time approximation scheme.
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Acknowledgements
The work is supported in part by the National Natural Science Foundation of China [No. 12071417], and Project for Innovation Team (Cultivation) of Yunnan Province [No. 202005AE160006].
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Li, Y., Li, W., Liu, X., Yang, J. (2021). Approximation Algorithms for the Maximum Bounded Connected Bipartition Problem. In: Wu, W., Du, H. (eds) Algorithmic Aspects in Information and Management. AAIM 2021. Lecture Notes in Computer Science(), vol 13153. Springer, Cham. https://doi.org/10.1007/978-3-030-93176-6_3
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