Improved bounds on sorting by length-weighted reversals

We study the problem of sorting binary sequences and permutations by length-weighted reversals. We consider a wide class of cost functions, namely f( ) = for all 0, where 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.

• Type: Journal
• Year: 2008
• Where: JCSS
• Authors: Michael A. Bender, Dongdong Ge, Simai He, Haodong Hu, Ron Y. Pinter, Steven Skiena, Firas Swidan
• Keywords: Binary Sequences, Cost Functions, JCSS 2008, Optimal Reversal Sequence