Estimating the efficiency of backtrack programs

Author:
Donald E. Knuth

Journal:
Math. Comp. **29** (1975), 122-136

MSC:
Primary 68A20

DOI:
https://doi.org/10.1090/S0025-5718-1975-0373371-6

MathSciNet review:
0373371

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Abstract | References | Similar Articles | Additional Information

Abstract: One of the chief difficulties associated with the so-called backtracking technique for combinatorial problems has been our inability to predict the efficiency of a given algorithm, or to compare the efficiencies of different approaches, without actually writing and running the programs. This paper presents a simple method which produces reasonable estimates for most applications, requiring only a modest amount of hand calculation. The method should prove to be of considerable utility in connection with D. H. Lehmer's branch-and-bound approach to combinatorial optimization.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1975-0373371-6

Keywords:
Backtrack,
analysis of algorithms,
Monte Carlo method,
Instant Insanity,
color cubes,
knight's tours,
tree functions,
branch and bound

Article copyright:
© Copyright 1975
American Mathematical Society