From backdoor key to backdoor completability: improving a known measure of hardness for the satisfiable CSP

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Escamocher, Guillaume
Siala, Mohamed
O'Sullivan, Barry
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Springer Verlag
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Many studies have been conducted on the complexity of Constraint Satisfaction Problem (CSP) classes. However, there exists little theoretical work on the hardness of individual CSP instances. In this context, the backdoor key fraction (BKF) [17] was introduced as a quantifier of problem hardness for individual satisfiable instances with regard to backtracking search. In our paper, after highlighting the weaknesses of the BKF, we propose a better characterization of the hardness of an individual satisfiable CSP instance based on the ratio between the size of the solution space and that of the search space. We formally show that our measure is negatively correlated with instance hardness. We also show through experiments that this measure evaluates more accurately the hardness of individual instances than the BKF.
Constraint Satisfaction Problem (CSP) , Artificial intelligence , Computer programming , Constraint theory , Hardness , Operations research , Backtracking search , Problem hardness , Search spaces , Show through , Solution space
Escamocher G., Siala M., O’Sullivan B. (2018) From Backdoor Key to Backdoor Completability: Improving a Known Measure of Hardness for the Satisfiable CSP. In: van Hoeve WJ. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2018, Delft, Netherlands, 26-28 June, Lecture Notes in Computer Science, vol 10848. Springer, Cham, pp. 198-214. doi:10.1007/978-3-319-93031-2_14
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