Estimating the efficiency of backtrack programs

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.