Knuth's Algorithm X: Difference between revisions

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'''Algorithm X''' is an [[algorithm]] for solving the [[exact cover]] problem. It is a straightforward [[Recursion (computer science)|recursive]], [[Nondeterministic algorithm|nondeterministic]], [[depth-first]], [[backtracking]] algorithm used by [[Donald Knuth]] to demonstrate an efficient implementation called DLX, which uses the [[dancing links]] technique.<ref name="knuth">{{cite arXiv | author = Knuth, Donald | author-link = Donald Knuth | title = Dancing links | year = 2000 | eprint = cs/0011047 }}</ref><ref>{{Cite journal |last=Banerjee |first=Bikramjit |last2=Kraemer |first2=Landon |last3=Lyle |first3=Jeremy |date=2010-07-04 |title=Multi-Agent Plan Recognition: Formalization and Algorithms |url=https://ojs.aaai.org/index.php/AAAI/article/view/7746 |journal=Proceedings of the AAAI Conference on Artificial Intelligence |volume=24 |issue=1 |pages=1059–1064 |doi=10.1609/aaai.v24i1.7746 |issn=2374-3468|doi-access=free }}</ref>

==Algorithm==

The exact cover problem is represented in Algorithm X by aan [[incidence matrix]] ''A'' consisting of 0s and 1s. The goal is to select a subset of the rows such that the digit 1 appears in each column exactly once.

Algorithm X works as follows: