Showing papers on "Backtracking published in 1974"
TL;DR: This paper presents a simple method which produces reasonable estimates for most applications, requiring only a modest amount of hand calculation, and should prove to be of considerable utility in connection with D. H. Lehmer''s branch-and-bound approach to combinatorial optimization.
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.
317 citations
TL;DR: The basic backtracking algorithm is described in terms of chains of partitions on the set S in order to solve the isomorph rejection problem of a group G acting on a finite set.
Abstract: A basic algorithm for solving many discrete problems is the so-called “backtracking” algorithm. The basic problem is that of generating the elements of a subset $S_0 $ of a finite set in an efficient manner. If a group G acts on $S_0 $, then one might wish to obtain only nonisomorphic elements of $S_0 $. In this paper the basic backtracking algorithm is described in terms of chains of partitions on the set S. The corresponding isomorph rejection problem is described in terms of G-invariant chains of partitions on S. Examples and flow charts are given.
23 citations
TL;DR: The computational efficiency of the algorithm results primarily from the concise tableau format and the fact that in the backtracking and dual variable change, the inverse of the basis need not be generated explicitly.
15 citations
TL;DR: A numerical investigation of various techniques reported in the branch-and-bound literature applied to the specific problem of optimal redundancy allocation compares two common backtracking strategies, deep and broad search, along with a zero-one versus direct problem formulation.
Abstract: This note presents a numerical investigation of various techniques reported in the branch-and-bound literature applied to the specific problem of optimal redundancy allocation. It compares two common backtracking strategies, deep and broad search, along with a zero-one versus direct problem formulation. Also reported are some highly successful modifications exploiting the specific problem structure.
11 citations
TL;DR: An implicit-enumeration scheme that, while maintaining a low storage requirement, allows the same flexibility in backward branching backtracking is no longer mandatory as the authors commonly have in forward branching.
Abstract: Each of the main enumerative methods for zero-one programming has a drawback: the branch-and-bound multi-branch approach may require an inordinate amount of storage capacity and the backtrack implicit-enumeration single-branch approach circumvents this storage problem only by restricting the flexibility of the search. This paper outlines an implicit-enumeration scheme that, while maintaining a low storage requirement, allows the same flexibility in backward branching backtracking is no longer mandatory as we commonly have in forward branching. Preliminary computational results are presented.
6 citations