Earth mover distance over high-dimensional spaces
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Overcoming the l1 non-embeddability barrier: algorithms for product metrics
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
LCS Approximation via Embedding into Local Non-repetitive Strings
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Information complexity: a tutorial
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Near-optimal sublinear time algorithms for Ulam distance
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Lower bounds for edit distance and product metrics via Poincaré-type inequalities
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
LCS approximation via embedding into locally non-repetitive strings
Information and Computation
The streaming complexity of cycle counting, sorting by reversals, and other problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Efficient communication protocols for deciding edit distance
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We prove the first non-trivial communication complexity lower bound for the problem of estimating the edit distance (aka Levenshtein distance) between two strings. A major feature of our result is that it provides the first setting in which the complexity of computing the edit distance is provably larger than that of Hamming distance. Our lower bound exhibits a trade-off between approximation and communication, asserting, for example, that protocols with {\rm O}(1) bits of communication can only obtain approximation \alpha\geqslant \Omega (\log d/\log \log d), where d is the length of the input strings. This case of {\rm O}(1) communication is of particular importance, since it captures constant-size sketches as well as embeddings into spaces like L_1 and squared-L_2, two prevailing algorithmic approaches for dealing with edit distance. Furthermore, the bound holds not only for strings over alphabet \sum { = \{ 0,1\} }, but also for strings that are permutations (called the Ulam metric). Besides being applicable to a much richer class of algorithms than all previous results, our bounds are neartight in at least one case, namely of embedding permutations into L_1. The proof uses a new technique, that relies on Fourier analysis in a rather elementary way.