RLE Edit Distance in Near Optimal Time

Raphaël Clifford, Pawel Gawrychowski, Tomasz Kociumaka, Daniel P. Martin, Przemyslaw Uznanski, Michael Wagner
2019 International Symposium on Mathematical Foundations of Computer Science  
We show that the edit distance between two run-length encoded strings of compressed lengths m and n respectively, can be computed in O(mn log(mn)) time. This improves the previous record by a factor of O(n/ log(mn)). The running time of our algorithm is within subpolynomial factors of being optimal, subject to the standard SETH-hardness assumption. This effectively closes a line of algorithmic research first started in 1993. ACM Subject Classification Theory of computation → Design and analysis
more » ... of algorithms; Theory of computation → Data structures design and analysis
doi:10.4230/lipics.mfcs.2019.66 dblp:conf/mfcs/CliffordGKMU19 fatcat:pu6uwgwtkzfntlfm6jiq3lm3r4