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dc.contributor.authorGent, Ian Philip
dc.contributor.authorJefferson, Christopher Anthony
dc.contributor.authorNightingale, Peter William
dc.identifier.citationGent , I P , Jefferson , C A & Nightingale , P W 2017 , ' Complexity of n -Queens Completion ' , Journal of Artificial Intelligence Research , vol. 59 , pp. 815-848 .
dc.identifier.otherPURE: 250936552
dc.identifier.otherPURE UUID: 937f8137-b104-447e-9d10-17a9eb8ca99a
dc.identifier.otherORCID: /0000-0002-5052-8634/work/36661744
dc.identifier.otherScopus: 85043331921
dc.identifier.otherWOS: 000411179900019
dc.identifier.otherORCID: /0000-0003-2979-5989/work/60887557
dc.description.abstractThe n-Queens problem is to place n chess queens on an n by n chessboard so that no two queens are on the same row, column or diagonal. The n-Queens Completion problem is a variant, dating to 1850, in which some queens are already placed and the solver is asked to place the rest, if possible. We show that n-Queens Completion is both NP-Complete and #P-Complete. A corollary is that any non-attacking arrangement of queens can be included as a part of a solution to a larger n-Queens problem. We introduce generators of random instances for n-Queens Completion and the closely related Blocked n-Queens and Excluded Diagonals Problem. We describe three solvers for these problems, and empirically analyse the hardness of randomly generated instances. For Blocked n-Queens and the Excluded Diagonals Problem, we show the existence of a phase transition associated with hard instances as has been seen in other NP-Complete problems, but a natural generator for n-Queens Completion did not generate consistently hard instances. The significance of this work is that the n-Queens problem has been very widely used as a benchmark in Artificial Intelligence, but conclusions on it are often disputable because of the simple complexity of the decision problem. Our results give alternative benchmarks which are hard theoretically and empirically, but for which solving techniques designed for n-Queens need minimal or no change.
dc.relation.ispartofJournal of Artificial Intelligence Researchen
dc.rights© 2017 AI Access Foundation. This work has been made available online in accordance with the publisher’s policies. This is the final published version of the work, which was originally published at:
dc.subjectConstraint satisfaction problemen
dc.subjectConstraint programmingen
dc.subjectFormal methodsen
dc.subjectQA75 Electronic computers. Computer scienceen
dc.titleComplexity of n-Queens Completionen
dc.typeJournal articleen
dc.contributor.sponsorThe Royal Societyen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. School of Computer Scienceen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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