Groupoid Action and Rearrangement Problem of Bicolor Arrays by Prefix Reversals
- 150 Downloads
We consider a rearrangement problem of two-dimensional bicolor arrays by prefix reversals as a generalization of the burnt pancake problem. An equivalence relation on the set of bicolor arrays is induced by prefix reversals, and the rearrangement problem is to characterize the equivalence classes. While previously studied the rearrangement problem for unicolor arrays made use of the classical group theoretic tools, the present problem is quite different. For bicolor arrays a rearrangement can be described by partial injections, and thus we characterize the equivalence classes in terms of a groupoid action. We also outline an algorithm for rearrangement by prefix reversals and estimate a minimum number of rearrangements needed to rearrange bicolor arrays by prefix reversals.
KeywordsGroupoids Groupoid actions Rearrangement problem Burnt pancake problem Prefix reversals
- 8.Kaplan, H., Shamir, R., Tarjan, R.E.: Faster and simpler algorithm for sorting signed permutations by reversals. In: ACM-SIAM SODA 1997, pp. 178–187 (1997)Google Scholar