Improved bounds on sorting with length-weighted reversals

Authors:
Michael A. Bender;Dongdong Ge;Simai He;Haodong Hu;Ron Y. Pinter;Steven Skiena;Firas Swidan
Affiliations:
SUNY Stony Brook, Stony Brook, NY;SUNY Stony Brook, Stony Brook, NY;SUNY Stony Brook, Stony Brook, NY;SUNY Stony Brook, Stony Brook, NY;Technion - Israel Institute of Technology, Haifa, Israel;SUNY Stony Brook, Stony Brook, NY;Technion - Israel Institute of Technology, Haifa, Israel
Venue:
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2004

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Abstract

We study the problem of sorting integer sequences and permutations by length-weighted reversals. We consider a wide class of cost functions, namely f(l) = lα for all α ≥ 0, where l is the length of the reversed subsequence. We present tight or nearly tight upper and lower bounds on the worst-case cost of sorting by reversals. Then we develop algorithms to approximate the optimal cost to sort a given input. Furthermore, we give polynomial-time algorithms to determine the optimal reversal sequence for a restricted but interesting class of sequences and cost functions. Our results have direct application in computational biology to the field of comparative genomics.