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A Polynomial-Time Algorithm for Max-Min Partitioning of Ladders

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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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Authors and Affiliations

  1. Department of Mathematics, University of Cape Town,Rondebosch 7700, South Africa, ZA

    R. Becker

  2. Department of Statistics,Italy, University of Rome ``La Sapienza'',Piazzale Aldo Moro 5, 00185 Rome,, IT

    I. Lari & B. Simeone

  3. Department of Electrical Engineering, Italy, Centro Matematico Vito Volterra, University of Rome ``Tor Vergata'', Via O. Raimondo, 00173 Rome, IT

    M. Lucertini

Authors
  1. R. Becker
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  2. I. Lari
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  3. M. Lucertini
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  4. B. Simeone
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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

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