Counting linear extensions is #P-complete
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Sorting by reversals is difficult
RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
The Book of Traces
An algorithm to enumerate all sorting reversals
Proceedings of the sixth annual international conference on Computational biology
WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
Advances on sorting by reversals
Discrete Applied Mathematics
Hurdles Hardly Have to Be Heeded
RECOMB-CG '08 Proceedings of the international workshop on Comparative Genomics
Sorting Signed Permutations by Inversions in O(nlogn) Time
RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
Bioinformatics
The solution space of sorting by reversals
ISBRA'07 Proceedings of the 3rd international conference on Bioinformatics research and applications
An improved algorithm to enumerate all traces that sort a signed permutation by reversals
Proceedings of the 2010 ACM Symposium on Applied Computing
Listing all sorting reversals in quadratic time
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
Partial enumeration of solutions traces for the problem of sorting by signed reversals
Proceedings of the 2nd ACM Conference on Bioinformatics, Computational Biology and Biomedicine
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In comparative genomics studies, finding a minimum length sequences of reversals, so called sorting by reversals, has been the topic of a huge literature. Since there are many minimum length sequences, another important topic has been the problem of listing all parsimonious sequences between two genomes, called the All Sorting Sequences by Reversals (ASSR) problem. In this paper, we revisit the ASSR problem for uni-chromosomal genomes when no duplications are allowed and when the relative order of the genes is known. We put the current body of work in perspective by illustrating the fundamental framework that is common for all of them, a perspective that allows us for the first time to theoretically compare their running times. The paper also proposes an improved framework that empirically speeds up all known algorithms.