TY - CHAP
T1 - Efficient data structures and a new randomized approach for sorting signed permutations by reversals
AU - Kaplan, Haim
AU - Verbin, Elad
PY - 2003
Y1 - 2003
N2 - The problem of sorting signed permutations by reversals (SBR) is a fundamental problem in computational molecular biology. The goal is, given a signed permutation, to find a shortest sequence of reversals that transforms it into the positive identity permutation, where a reversal is the operation of taking a segment of the permutation, reversing it, and flipping the signs of its elements. In this paper we describe a randomized algorithm for SBR. The algorithm tries to sort the permutation by performing a random walk on the oriented Caylay-like graph of signed permutations under its oriented reversals, until it gets "stuck". We show that if we get stuck at the identity permutation, then we have found a shortest sequence. Empirical testing shows that this process indeed succeeds with high probability on a random permutation. To implement our algorithm we describe an efficient data structure to maintain a permutation under reversals and draw random oriented reversals in sub-linear time per operation. With this data structure we can implement the random walk in time O(n3/2 √log n), thus obtaining an algorithm for SBR that almost always runs in subquadratic time. The data structures we present may also be of independent interest for developing other algorithms for SBR, and for other problems.
AB - The problem of sorting signed permutations by reversals (SBR) is a fundamental problem in computational molecular biology. The goal is, given a signed permutation, to find a shortest sequence of reversals that transforms it into the positive identity permutation, where a reversal is the operation of taking a segment of the permutation, reversing it, and flipping the signs of its elements. In this paper we describe a randomized algorithm for SBR. The algorithm tries to sort the permutation by performing a random walk on the oriented Caylay-like graph of signed permutations under its oriented reversals, until it gets "stuck". We show that if we get stuck at the identity permutation, then we have found a shortest sequence. Empirical testing shows that this process indeed succeeds with high probability on a random permutation. To implement our algorithm we describe an efficient data structure to maintain a permutation under reversals and draw random oriented reversals in sub-linear time per operation. With this data structure we can implement the random walk in time O(n3/2 √log n), thus obtaining an algorithm for SBR that almost always runs in subquadratic time. The data structures we present may also be of independent interest for developing other algorithms for SBR, and for other problems.
UR - http://www.scopus.com/inward/record.url?scp=35248859756&partnerID=8YFLogxK
U2 - 10.1007/3-540-44888-8_13
DO - 10.1007/3-540-44888-8_13
M3 - פרק
AN - SCOPUS:35248859756
SN - 3540403116
SN - 9783540403111
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 170
EP - 185
BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
A2 - Baeza-Yates, Ricardo
A2 - Chavez, Edgar
A2 - Crochemore, Maxime
PB - Springer Verlag
ER -