Subtree Isomorphism Revisited
Name
1510.04622.pdf
Description
Submitted version
Size
447.78 KB
Format
Adobe PDF
Checksum (MD5)
3477052d71198bf49c080d08a5d32f88
Author(s)
Abboud, Amir
Backurs, Arturs
Hansen, Thomas Dueholm
Vassilevska Williams, Virginia
Zamir, Or
Date Issued
July 16, 2018
Publisher
Association for Computing Machinery (ACM)
Citation
Abboud, Amir, Backurs, Arturs, Hansen, Thomas Dueholm, Vassilevska Williams, Virginia and Zamir, Or. 2018. "Subtree Isomorphism Revisited." 14 (3).
Version
Original manuscript
Abstract
© 2018 ACM. The Subtree Isomorphism problem asks whether a given tree is contained in another given tree. The problem is of fundamental importance and has been studied since the 1960s. For some variants, e.g., orderedtrees, near-linear time algorithms are known, but for the general case truly subquadratic algorithms remain elusive. Our first result is a reduction from the Orthogonal Vectors problem to Subtree Isomorphism, showing that a truly subquadratic algorithm for the latter refutes the Strong Exponential Time Hypothesis (SETH). In light of this conditional lower bound, we focus on natural special cases for which no truly subquadratic algorithms are known. We classify these cases against the quadratic barrier, showing in particular that: • Even for binary, rooted trees, a truly subquadratic algorithm refutes SETH. • Even for rooted trees of depthO(log logn), wheren is the total number of vertices, a truly subquadratic algorithm refutes SETH. • For every constant d, there is a constant εd > 0 and a randomized, truly subquadratic algorithm for degree-d rooted trees of depth at most (1 + εd) logd n. In particular, there is an O(min{2.85h,n2}) algorithm for binary trees of depth h. Our reductions utilize new “tree gadgets” that are likely useful for future SETH-based lower bounds for problems on trees. Our upper bounds apply a folklore result from randomized decision tree complexity.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1145/3093239
