TY - GEN

T1 - Constant factor approximations to edit distance on far input pairs in nearly linear time

AU - Koucký, Michal

AU - Saks, Michael

N1 - Funding Information:
∗The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement no. 616787. Partially supported by the Grant Agency of the Czech Republic under the grant agreement no. 19-27871X. †Supported in part by Simons Foundation under award 332622.
Publisher Copyright:
© 2020 ACM.

PY - 2020/6/8

Y1 - 2020/6/8

N2 - For any T ≥ 1, there are constants R=R(T) ≥ 1 and ζ=ζ(T)>0 and a randomized algorithm that takes as input an integer n and two strings x,y of length at most n, and runs in time O(n1+1/T) and outputs an upper bound U on the edit distance of edit(x,y) that with high probability, satisfies U ≤ R(edit(x,y)+n1-ζ). In particular, on any input with edit(x,y) ≥ n1-ζ the algorithm outputs a constant factor approximation with high probability. A similar result has been proven independently by Brakensiek and Rubinstein (this proceedings).

AB - For any T ≥ 1, there are constants R=R(T) ≥ 1 and ζ=ζ(T)>0 and a randomized algorithm that takes as input an integer n and two strings x,y of length at most n, and runs in time O(n1+1/T) and outputs an upper bound U on the edit distance of edit(x,y) that with high probability, satisfies U ≤ R(edit(x,y)+n1-ζ). In particular, on any input with edit(x,y) ≥ n1-ζ the algorithm outputs a constant factor approximation with high probability. A similar result has been proven independently by Brakensiek and Rubinstein (this proceedings).

KW - Almost linear-time algorithm

KW - Approximation algorithm

KW - Edit distance

KW - Randomized algorithm

UR - http://www.scopus.com/inward/record.url?scp=85086765514&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85086765514&partnerID=8YFLogxK

U2 - 10.1145/3357713.3384307

DO - 10.1145/3357713.3384307

M3 - Conference contribution

AN - SCOPUS:85086765514

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 699

EP - 712

BT - STOC 2020 - Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing

A2 - Makarychev, Konstantin

A2 - Makarychev, Yury

A2 - Tulsiani, Madhur

A2 - Kamath, Gautam

A2 - Chuzhoy, Julia

PB - Association for Computing Machinery

T2 - 52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020

Y2 - 22 June 2020 through 26 June 2020

ER -