TY - CHAP
T1 - Large edit distance with multiple block operations
AU - Shapira, Dana
AU - Storer, James A.
PY - 2003
Y1 - 2003
N2 - We consider the addition of some or all of the operations block move, block delete, block copy, block reversals, and block copy reversals, to the traditional edit distance problem (finding the minimum number of insert-character and delete-character operations to convert one string to another). When all of the above operations are allowed, the problem, called the nearest neighbors problem, is NP hard, and the best known approximation is O(log n log* n), which was achieved by Muthukrishnan and Sahinalp [2000,2002a]. In this paper we show that this problem can be approximated by a constant factor of 3.5 using a simple sliding window method. When eliminating reversals, the same method reduces the best known approximation of 12, achieved by Ergun, Muthukrishnan and Sahinalp [2003], down to a factor of 4. Both constant factors are proved to be tight. Allowing only subsets of these operations does not necessarily make the problem easier. Shapira and Storer [2002] present a log n factor approximation algorithm for edit distance with block moves (which is also an NP-complete problem). Here, we show that edit distance with block deletions can be solved optimally, but edit distance with block moves and block deletions remains NP-complete and can be reduced to the problem of block moves only, keeping the same log n factor approximation.
AB - We consider the addition of some or all of the operations block move, block delete, block copy, block reversals, and block copy reversals, to the traditional edit distance problem (finding the minimum number of insert-character and delete-character operations to convert one string to another). When all of the above operations are allowed, the problem, called the nearest neighbors problem, is NP hard, and the best known approximation is O(log n log* n), which was achieved by Muthukrishnan and Sahinalp [2000,2002a]. In this paper we show that this problem can be approximated by a constant factor of 3.5 using a simple sliding window method. When eliminating reversals, the same method reduces the best known approximation of 12, achieved by Ergun, Muthukrishnan and Sahinalp [2003], down to a factor of 4. Both constant factors are proved to be tight. Allowing only subsets of these operations does not necessarily make the problem easier. Shapira and Storer [2002] present a log n factor approximation algorithm for edit distance with block moves (which is also an NP-complete problem). Here, we show that edit distance with block deletions can be solved optimally, but edit distance with block moves and block deletions remains NP-complete and can be reduced to the problem of block moves only, keeping the same log n factor approximation.
UR - http://www.scopus.com/inward/record.url?scp=0142249968&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-39984-1_29
DO - 10.1007/978-3-540-39984-1_29
M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.chapter???
AN - SCOPUS:0142249968
SN - 3540201777
SN - 9783540201779
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 369
EP - 377
BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
A2 - Nascimento, Mario A.
A2 - de Moura, Edleno S.
A2 - Oliveira, Arlindo L.
PB - Springer Verlag
ER -