A Sufficient Condition for Backtrack-Free Search

@article{Freuder1982ASC,
  title={A Sufficient Condition for Backtrack-Free Search},
  author={Eugene C. Freuder},
  journal={J. ACM},
  year={1982},
  volume={29},
  pages={24-32}
}
A constraint satisfaction problem revolves finding values for a set of variables subject to a set of constraints (relations) on those variables Backtrack search is often used to solve such problems. A relationship involving the structure of the constraints is described which characterizes to some degree the extreme case of mimmum backtracking (none) The relationship involves a concept called "width," which may provide some guidance in the representation of constraint satisfaction problems and… 

Figures from this paper

A sufficient condition for backtrack-bounded search
TLDR
A relationship involving the structure of the constraints is described that provides a bound on the backtracking required to advance deeper into the backtrack tree, which leads to upper bounds on the effort required for solution of a class of constraint satisfaction problems.
Backtrack-free and backtrack-bounded search
TLDR
Conditions are identified under which bounds can be placed on the amount of backtracking required to solve constraint satisfaction search problems, and problem complexity is shown to have a bound exponential in the size of the largest biconnected component of the problem’s constraint graph.
Dynamization of Backtrack-Free Search for the Constraint Satisfaction Problem
Many AI tasks can be formulated as a Constraint Satisfaction Problem (CSP), i.e. the problem of finding an assignment of values for a set of variables subject to a given collection of constraints. In
Multi-Level Variable Ordering Heuristics for theConstraint Satisfaction
The usual way for solving constraint satisfaction problems is to use a backtracking algorithm. One of the key factors in its eeciency is the rule it will use to decide on which variable to branch
Backtracking Algorithms for Constraint Satisfaction Problems -- a Survey
TLDR
This survey describes the basic backtrack search within the search space framework and then presents a number of improvements including look-back methods such as backjumping, constraint recording, backmarking, and look-ahead methodssuch as, forward checking, and dynamic variable ordering.
Satisfaction Guaranteed ∗
A constraint satisfaction problem (CSP) model can be preprocessed to ensure that any choices made will lead to solutions, without the need to backtrack. This can be especially useful in an
A dynamic constraint-directed ordered search algorithm for solving constraint satisfaction problems
TLDR
This work has applied the Dynamic Constraint-directed Ordered Search to the Graph Coloring Problem and the Zebra Problem with a second order network consistency algorithm and obtained almost-backtrack-free searches for both cases.
A Space-Efficient Backtrack-Free Representation for Constraint Satisfaction Problems
TLDR
A radical approach to obtaining a backtrack-free representation for a constraint satisfaction problem: remove values that lead to dead-ends that elucidates, for the first time, a three-way trade-off between space complexity, potential backtracks, and solution loss.
A Case Based Method for Solving Relatively Stable Dynamic Constraint Satisfaction Problems
This paper discusses some key issues in using case based methods to solve large constraint satisfaction problems. The problem addressed here is characterised by the large cardinality of the
...
...

References

SHOWING 1-10 OF 34 REFERENCES
Synthesizing constraint expressions
TLDR
An algorithm is developed that can achieve any level of consistency desired, in order to preprocess the problem for subsequent back track search, or to function as an alternative to backtrack search by explicitly determining all solutions.
Estimating the efficiency of backtrack programs.
TLDR
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.
Tree Size by Partial Backtracking
TLDR
The efficiency of Knuth's method can be greatly improved by occasionally following more than one path from a node, which results in an improvement which increases exponentially with the height of the tree.
Backtrack programming techniques
TLDR
It is shown how the use of macros can considerably shorten the computation time in many cases and the general backtrack technique has allowed the solution of two previously open combinatorial problems, the computation of new terms in a well-known series, and the substantial reduction in computation time for the solution to another combinatorsial problem.
Review of "Problem-Solving Methods in Artificial Intelligence by Nils J. Nilsson", McGraw-Hill Pub.
TLDR
This book is not a survey on theorem proving programs, but the description of a program developed from 1960 to 1965, and includes three chapters that deal with resolution-based theorem-proving in the predicate calculus and its applications to problem solving.
New Programming Languages for Artificial Intelligence Research
TLDR
An overview of the nature of these features, and their implementation in fourprincipal families of AI language*: SAILPLANNER/COXXIVER; QLISP/INTERLISp; and POPLER,POP-2.
Understanding Line drawings of Scenes with Shadows
TLDR
A detailed discussion of the standard approach to computer interpretation of line drawings as three-dimensional scenes as well as some alternative approaches to this approach are discussed.
...
...