Tight Bounds for Minimax Grid Matching, with Applications to the Average Case Analysis of Algorithms,
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-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. In this paper, the authors solve both the minimax grid matching problem and the maximum up-right matching problem. As a direct result, they 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1986
- Accession Number
- ADA169627
Entities
People
- Peter Shor
- Tom Leighton
Organizations
- Massachusetts Institute of Technology