TY - GEN

T1 - An optimal decomposition algorithm for tree edit distance

AU - Demaine, Erik D.

AU - Mozes, Shay

AU - Rossman, Benjamin

AU - Weimann, Oren

PY - 2007

Y1 - 2007

N2 - The edit distance between two ordered rooted trees with vertex labels is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as inserting new nodes. In this paper, we present a worst-case O(n 3)-time algorithm for this problem, improving the previous best O(n3 log n)-time algorithm [7]. Our result requires a novel adaptive strategy for deciding how a dynamic program divides into subproblems, together with a deeper understanding of the previous algorithms for the problem. We prove the optimality of our algorithm among the family of decomposition strategy algorithms-which also includes the previous fastest algorithms-by tightening the known lower bound of Q(n2 log2 n) [4] to Ωn 3), matching our algorithm's running time. Furthermore, we obtain matching upper and lower bounds of ⊖(nm2(1 + log m/n)) when the two trees have sizes m and n where m < n.

AB - The edit distance between two ordered rooted trees with vertex labels is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as inserting new nodes. In this paper, we present a worst-case O(n 3)-time algorithm for this problem, improving the previous best O(n3 log n)-time algorithm [7]. Our result requires a novel adaptive strategy for deciding how a dynamic program divides into subproblems, together with a deeper understanding of the previous algorithms for the problem. We prove the optimality of our algorithm among the family of decomposition strategy algorithms-which also includes the previous fastest algorithms-by tightening the known lower bound of Q(n2 log2 n) [4] to Ωn 3), matching our algorithm's running time. Furthermore, we obtain matching upper and lower bounds of ⊖(nm2(1 + log m/n)) when the two trees have sizes m and n where m < n.

UR - http://www.scopus.com/inward/record.url?scp=38149078101&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-73420-8_15

DO - 10.1007/978-3-540-73420-8_15

M3 - Conference contribution

AN - SCOPUS:38149078101

SN - 3540734198

SN - 9783540734192

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 146

EP - 157

BT - Automata, Languages and Programming - 34th International Colloquium, ICALP 2007, Proceedings

PB - Springer Verlag

T2 - 34th International Colloquium on Automata, Languages and Programming, ICALP 2007

Y2 - 9 July 2007 through 13 July 2007

ER -