Combinatorial approximation algorithms for the maximum bounded connected bipartition problem

Xiaofei Liu (), Yajie Li, Weidong Li and Jinhua Yang
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Xiaofei Liu: Yunnan University
Yajie Li: Yunnan University
Weidong Li: Yunnan University
Jinhua Yang: Dianchi College

Journal of Combinatorial Optimization, 2023, vol. 45, issue 1, No 51, 21 pages

Abstract: Abstract In this paper, we study the maximum bounded connected bipartition problem: given a vertex-weighted connected graph $$G=(V,E;w)$$ G = ( V , E ; w ) and an upper bound B, the vertex set V is partitioned into two subsets $$(V_1,V_2)$$ ( V 1 , V 2 ) such that the total weight of the two subgraphs induced by $$V_1$$ V 1 and $$V_2$$ V 2 is maximized, and these subgraphs are connected, where the weight of a subgraph is the minimum of B and the total weight of all vertices in the subgraph. In this paper, we prove that this problem is NP-hard even when G is a completed graph, a grid graph with only 3 rows or an interval graph, and we present an $$\frac{8}{7}$$ 8 7 -approximation algorithm. In particular, we present a $$\frac{14}{13}$$ 14 13 -approximation algorithm for the case of grid graphs, and we present a fully polynomial-time approximation scheme for the case of interval graphs.

Keywords: Connected bipartition problem; Grid graph; Interval graph; Approximation algorithm (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10878-022-00981-9

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