Abstract.
Given a grid graph with two rows, an arbitrary number N of columns (briefly, a ladder ) and a weight function defined on its vertex set V , one wants to partition V into a given number p of connected components, so as to maximize the smallest weight of a component. We present an O(N 4 pmax {p,log N}) -time algorithm, which combines dynamic programming with pre-processing and search techniques. An O(N) -time algorithm for the case p=2 is also given.
In a companion paper [2] we show that the problem for a grid graph with three rows is NP-hard, and we give approximate algorithms for grid graphs with an arbitrary number of rows.
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Received September 21, 1999. Online publication April 9, 2001.
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Becker, R., Lari, I., Lucertini, M. et al. A Polynomial-Time Algorithm for Max-Min Partitioning of Ladders. Theory Comput. Systems 34, 353–374 (2001). https://doi.org/10.1007/s00224-001-0008-8
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DOI: https://doi.org/10.1007/s00224-001-0008-8