Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, December 17, 2024, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Jakob Nogler

Faster Tree Edit Distance via APSP Equivalence

The tree edit distance (TED) between two rooted ordered trees with n nodes labeled from an alphabet Σ is the minimum cost of transforming one tree into the other by a sequence of valid operations consisting of insertions, deletions and relabeling of nodes. First introduced by Selkow in the late 1970s, its running time has seen many improvements which culminated in a O(n³)-time algorithm [DMRW 2010].
In this work, we show that TED is fine-grained equivalent to the All-Pair-Shortest-Path Problem (APSP). Our reduction of TED to APSP is tight enough, so that combined with the fastest APSP algorithm to-date [Williams 2018] it gives the first ever subcubic time algorithm for TED running in n³ / 2^{Ω(sqrt(log(n)))} time.
We also consider the unweighted tree edit distance problem in which the cost of each edit is one. For unweighted TED, a truly subcubic algorithm is known due to Mao [Mao 2022], later improved slightly by Dürr [Dürr 2023] to run in O(n^2.9148). Their algorithm uses bounded monotone min-plus product as a crucial subroutine, and the best running time for this product is O(n^(3+ω)/2) < O(n^2.6857) (where ω is the exponent of fast matrix multiplication). We close this gap and give an algorithm for unweighted TED that runs in O(n^(3+ω)/2) time.

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