Elsevier

Journal of Algorithms

Volume 12, Issue 3, September 1991, Pages 393-408
Journal of Algorithms

The set of minimal braids is co-NP-complete

https://doi.org/10.1016/0196-6774(91)90011-MGet rights and content

Abstract

Braids can be represented as two-dimensional diagrams showing the crossings of strings or as words over the generators of a braid group. A minimal braid is one with the fewest crossings (or the shortest words) among all possible representations topologically equivalent to that braid. The main result of this paper is that the set of minimal braids is co-NP-complete.

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This work was carried out during a visit to Warwick University by the second author, supported by a Visiting Fellowship from the SERC of the UK. The first author was partially supported by a Senior Fellowship from the SERC and by the ESPRIT II BRA Programme of the EC under Contract 3075 (ALCOM).

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