Approximation algorithms for array partitioning problems

• Published in: Journal of algorithms Vol. 54; no. 1; pp. 85 - 104
• Main Authors: Muthukrishnan, S., Suel, Torsten
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 2005; Elsevier
• Subjects: Algebra; Algorithmics. Computability. Computer arithmetics; Applied sciences; Computer science; control theory; systems; Exact sciences and technology; Mathematics; Number theory; Sciences and techniques of general use; Theoretical computing; Array; Cutting; Partitioning; Image processing; Database; NP complete problem; Optimal approximation; Two-dimensional calculations; Parallel computation; Approximation algorithm; Fast algorithm
• ISSN: 0196-6774; 1090-2678
• DOI: 10.1016/j.jalgor.2003.11.006

We study the problem of optimally partitioning a two-dimensional array of elements by cutting each coordinate axis into p (respectively, q) intervals, resulting in p× q rectangular regions. This problem arises in several applications in databases, parallel computation, and image processing. Our main contribution are new approximation algorithms for these NP-complete problems that improve significantly over previously known bounds. The algorithms are fast and simple, work for a variety of measures of partitioning quality, generalize to dimensions d>2, and achieve almost optimal approximation ratios. We also extend previous NP-completeness results for this class of problems.