From Backdoor Key to Backdoor Completability: Improving a Known Measure of Hardness for the Satisfiable CSP

  • Guillaume Escamocher
  • Mohamed SialaEmail author
  • Barry O’Sullivan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10848)


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.



This research has been funded by Science Foundation Ireland (SFI) under Grant Number SFI/12/RC/2289.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Guillaume Escamocher
    • 1
  • Mohamed Siala
    • 1
    Email author
  • Barry O’Sullivan
    • 1
  1. 1.Insight Centre for Data Analytics, Department of Computer ScienceUniversity College CorkCorkIreland

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