Approximation algorithms for MAX-MIN tiling

Piotr Berman, Bhaskar DasGupta, S. Muthukrishnan

    Research output: Contribution to journalArticlepeer-review


    The MAX-MIN tiling problem is as follows. We are given A[1,..., n][1,..., n], a two-dimensional array where each entry A[i][j] stores a non-negative number. Define a tile of A to be a subarray A[l,..., r][t,..., b] of A, the weight of a tile to be the sum of all array entries in it, and a tiling of A to be a collection of tiles of A such that each entry A[i][j] is contained in exactly one tile. Given a weight bound W the goal of our MAX-MIN tiling problem is to find a tiling of A such that: (1) each tile is of weight at leant W (the MIN condition), and (2) the number of tiles is maximized (the MAX condition). The MAX-MIN tiling problem is known to be NP-hard; here, we present first non-trivial approximations algorithms for solving it.

    Original languageEnglish (US)
    Pages (from-to)122-134
    Number of pages13
    JournalJournal of Algorithms
    Issue number2
    StatePublished - Jul 2003

    ASJC Scopus subject areas

    • Control and Optimization
    • Computational Mathematics
    • Computational Theory and Mathematics


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