TY - JOUR

T1 - The smoothed complexity of edit distance

AU - Andoni, Alexandr

AU - Krauthgamer, Robert

N1 - NSF [CCR-0133849]; David and Lucille Packard Fellowship; Alfred P. Sloan Fellowship; Fusfeld Research Fund; Israel Science Foundation [452/08]Part of this work of was done while A. Andoni was a student at MIT, supported in part by NSF CAREER award CCR-0133849, David and Lucille Packard Fellowship and Alfred P. Sloan Fellowship, and while an intern at IBM Almaden Research Center.Part of the work of R. Krauthgamer was done while he was at the IBM Almaden Research Center. This research was supported in part by a grant from the Fusfeld Research Fund, and by the Israel Science Foundation grant #452/08.

PY - 2012/9

Y1 - 2012/9

N2 - We initiate the study of the smoothed complexity of sequence alignment, by proposing a semi-random model of edit distance between two input strings, generated as follows: First, an adversary chooses two binary strings of length d and a longest common subsequence Aof them. Then, every character is perturbed independently with probability p, except that A is perturbed in exactly the same way inside the two strings. We design two efficient algorithms that compute the edit distance on smoothed instances up to a constant factor approximation. The first algorithm runs in near-linear time, namely d{1+ε} for any fixed ε > 0. The second one runs in time sublinear in d, assuming the edit distance is not too small. These approximation and runtime guarantees are significantly better than the bounds that were known for worst-case inputs. Our technical contribution is twofold. First, we rely on finding matches between substrings in the two strings, where two substrings are considered a match if their edit distance is relatively small, a prevailing technique in commonly used heuristics, such as PatternHunter of Ma et al. [2002]. Second, we effectively reduce the smoothed edit distance to a simpler variant of (worst-case) edit distance, namely, edit distance on permutations (a.k.a. Ulam's metric). We are thus able to build on algorithms developed for the Ulam metric, whose much better algorithmic guarantees usually do not carry over to general edit distance.

AB - We initiate the study of the smoothed complexity of sequence alignment, by proposing a semi-random model of edit distance between two input strings, generated as follows: First, an adversary chooses two binary strings of length d and a longest common subsequence Aof them. Then, every character is perturbed independently with probability p, except that A is perturbed in exactly the same way inside the two strings. We design two efficient algorithms that compute the edit distance on smoothed instances up to a constant factor approximation. The first algorithm runs in near-linear time, namely d{1+ε} for any fixed ε > 0. The second one runs in time sublinear in d, assuming the edit distance is not too small. These approximation and runtime guarantees are significantly better than the bounds that were known for worst-case inputs. Our technical contribution is twofold. First, we rely on finding matches between substrings in the two strings, where two substrings are considered a match if their edit distance is relatively small, a prevailing technique in commonly used heuristics, such as PatternHunter of Ma et al. [2002]. Second, we effectively reduce the smoothed edit distance to a simpler variant of (worst-case) edit distance, namely, edit distance on permutations (a.k.a. Ulam's metric). We are thus able to build on algorithms developed for the Ulam metric, whose much better algorithmic guarantees usually do not carry over to general edit distance.

UR - http://www.scopus.com/inward/record.url?scp=84870204326&partnerID=8YFLogxK

U2 - https://doi.org/10.1145/2344422.2344434

DO - https://doi.org/10.1145/2344422.2344434

M3 - مقالة

SN - 1549-6325

VL - 8

JO - ACM Transactions on Algorithms

JF - ACM Transactions on Algorithms

IS - 4

M1 - 2344434

ER -