Abstract
We present a quantum algorithm for finite domain constraint solving, where the constraints have arity 2. It is complete and runs in \( O\left( {\left( {\left[ {d/2} \right]} \right)^{n/2} } \right) \) time, where d is size of the domain of the variables and n the number of variables. For the case of d = 3 we provide a method to obtain an upper time bound of O(8n/8) ≈ O(1.2968n). Also for d = 5 the upper bound has been improved. Using this method in a slightly different way we can decide 3-colourability in O(1.2185n) time.
The research is supported in part by CUGS — National Graduate School in Computer Science, Sweden.
The research is supported by CUGS — National Graduate School in Computer Science, Sweden.
Partially supported by the Swedish Research Council (VR) under grant 221-2000-361.
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Angelsmark, O., Dahllöf, V., Jonsson, P. (2002). Finite Domain Constraint Satisfaction Using Quantum Computation. In: Diks, K., Rytter, W. (eds) Mathematical Foundations of Computer Science 2002. MFCS 2002. Lecture Notes in Computer Science, vol 2420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45687-2_7
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DOI: https://doi.org/10.1007/3-540-45687-2_7
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