Tree Edit Distance Cannot be Computed in Strongly Subcubic Time (Unless APSP Can)
Autor: | Paweł Gawrychowski, Karl Bringmann, Shay Mozes, Oren Weimann |
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Rok vydání: | 2020 |
Předmět: |
FOS: Computer and information sciences
Sequence Exponential time hypothesis Matching (graph theory) String (computer science) 0102 computer and information sciences 02 engineering and technology 01 natural sciences Upper and lower bounds Dynamic programming Combinatorics Tree (data structure) Mathematics (miscellaneous) 010201 computation theory & mathematics 020204 information systems Computer Science - Data Structures and Algorithms 0202 electrical engineering electronic engineering information engineering Data Structures and Algorithms (cs.DS) Edit distance Mathematics |
Zdroj: | ACM Transactions on Algorithms. 16:1-22 |
ISSN: | 1549-6333 1549-6325 |
DOI: | 10.1145/3381878 |
Popis: | The edit distance between two rooted ordered trees with n nodes labeled from an alphabet Ʃ 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. Tree edit distance is a well-known generalization of string edit distance. The fastest known algorithm for tree edit distance runs in cubic O ( n 3 ) time and is based on a similar dynamic programming solution as string edit distance. In this article, we show that a truly subcubic O ( n 3-ε ) time algorithm for tree edit distance is unlikely: For |Ʃ| = Ω ( n ), a truly subcubic algorithm for tree edit distance implies a truly subcubic algorithm for the all pairs shortest paths problem. For |Ʃ| = O (1), a truly subcubic algorithm for tree edit distance implies an O ( n k-ε ) algorithm for finding a maximum weight k -clique. Thus, while in terms of upper bounds string edit distance and tree edit distance are highly related, in terms of lower bounds string edit distance exhibits the hardness of the strong exponential time hypothesis (Backurs, Indyk STOC’15) whereas tree edit distance exhibits the hardness of all pairs shortest paths. Our result provides a matching conditional lower bound for one of the last remaining classic dynamic programming problems. |
Databáze: | OpenAIRE |
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