On the Conversion between Non-Binary and Binary Constraint Satisfaction Problems

Fahiem Bacchus, Peter van Beek

It is well known that any non-binary discrete constraint satisfaction problem (CSP) can be translated into an equivalent binary CSP. Two translations are known: the dual graph translation and the hidden variable translation. However, there has been little theoretical or experimental work on how well backtracking algorithms perform on these binary representations in comparison to their performance on the corresponding non-binary CSP. We present both theoretical and empirical results to help understand the tradeoffs involved. In particular, we show that translating a non-binary CSP into a binary representation can be a viable solution technique in certain circumstances. The ultimate aim of this research is to give guidance for when one should consider translating between non-binary and binary representations. Our results supply some initial answers to this question.

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