Loopless Generation of Multiset Permutations using a Constant Number of Variables by Prefix Shifts [chapter]

Aaron Williams
2009 Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms  
This paper answers the following mathematical question: Can multiset permutations be ordered so that each permutation is a prefix shift of the previous permutation? Previously, the answer was known for the permutations of any set, and the permutations of any multiset whose corresponding set contains only two elements. This paper also answers the following algorithmic question: Can multiset permutations be generated by a loopless algorithm that uses sublinear additional storage? Previously, the
more » ... e? Previously, the best loopless algorithm used a linear amount of additional storage. The answers to these questions are both yes.
doi:10.1137/1.9781611973068.107 fatcat:v4ojap64kndldciakokkrkad34