Interactive communication: balanced distributions, correlated files, and average-case complexity
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Communication complexity
SIAM Journal on Computing
Communication complexity of document exchange
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A sublinear algorithm for weakly approximating edit distance
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Efficient randomized pattern-matching algorithms
IBM Journal of Research and Development - Mathematics and computing
Approximating Edit Distance Efficiently
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
The string edit distance matching problem with moves
ACM Transactions on Algorithms (TALG)
Estimating the sortedness of a data stream
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Low distortion embeddings for edit distance
Journal of the ACM (JACM)
The Computational Hardness of Estimating Edit Distance [Extended Abstract]
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Polylogarithmic Approximation for Edit Distance and the Asymmetric Query Complexity
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Improved sketching of hamming distance with error correcting
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
Homomorphic fingerprints under misalignments: sketching edit and shift distances
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Hi-index | 0.00 |
In this paper we present two communication protocols on computing edit distance. In our first result, we give a one-way protocol for the following Document Exchange problem. Namely given x∈Σn to Alice and y∈Σn to Bob and integer k to both, Alice sends a message to Bob so that he learns x or truthfully reports that the edit distance between x and y is greater than k. For this problem, we give a randomized protocol in which Alice transmits at most $\tilde{O}(k\log^2 n)$ bits and each party's time complexity is $\tilde{O}(n\log n +k^2\log^2n)$. Our second result is a simultaneous protocol for edit distance over permutations. Here Alice and Bob both send a message to a third party (the referee) who does not have access to the input strings. Given the messages, the referee decides if the edit distance between x and y is at most k or not. For this problem we give a protocol in which Alice and Bob run a O(nlogn)-time algorithm and they transmit at most $\tilde{O}(k\log^2 n)$ bits. The running time of the referee is bounded by $\tilde{O}(k^2\log^2n)$. To our knowledge, this result is the first upper bound for this problem. Our results are obtained through mapping strings to the Hamming cube. For this, we use the Locally Consistent Parsing method of [5,6] in combination with the Karp-Rabin fingerprints. In addition to yielding non-trivial bounds for the edit distance problem, this paper suggest a new conceptual framework and raises new questions regarding the embeddability of edit distance into the Hamming cube which might be of independent interest.