Tight Bounds for Minimax Grid Matching, with Applications to the Average Case Analysis of Algorithms
Name
MIT-LCS-TM-298.pdf
Size
7.61 MB
Format
Adobe PDF
Checksum (MD5)
0f5450f075a44ab7831611ce4543024e
Author(s)
Leighton, Tom
Shor, Peter
Date Issued
May 1986
Series/Report no.
MIT-LCS-TM-298
Abstract
The minimax grid matching problem is a fundamental combinatorial problem associated with the average case analysis of algorithms. The problem has arisen in a number of interesting and seemingly unrelated areas, including wafer-scale integration of systolic arrays, two-dimentsional discrepancy problems, and testing pseudorandom number generators. However, the minimax grid matching problem is best known for its application to the maximum up-right matching problem. The maximum up-right matching problem was originally defined by Karp, Luby and Marchetti-Spaccamela in association with algorithms for 2-dimensional bin packing. More recently, the up-right matching problem has arisen in the average case analysis of on-line algorithms for 1-dimensional bin packing and dynamic allocation. In this paper, we solve both the minimax grid matching problem and the maximum up-right matching problem. As a direct result, we obtain tight upper bounds on the average case behavior of the best algorithms known for 2-dimensional bin packing, 1-dimensional on-line packing and on-line dynamic allocation. The results also solve a long-open question in mathematical statistics.
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