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Tight Bounds for Minimax Grid Matching, with Applications to the Average Case Analysis of Algorithms.
Interim research rept.,
MASSACHUSETTS INST OF TECH CAMBRIDGE LAB FOR COMPUTER SCIENCE
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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-dimensional 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. This paper solves 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.
APPROVED FOR PUBLIC RELEASE