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Electronic Colloquium on Computational Complexity

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Reports tagged with Edit Distance:
TR04-096 | 4th November 2004
Eldar Fischer, Frederic Magniez, Michel de Rougemont

Property and Equivalence Testing on Strings

Revisions: 1

Using a new statistical embedding of words which has similarities with the Parikh mapping, we first construct a tolerant tester for the equality of two words, whose complexity is independent of the string size, where the distance between inputs is measured by the normalized edit distance with moves. As a ... more >>>

TR15-111 | 8th July 2015
Diptarka Chakraborty, Elazar Goldenberg, Michal Koucky

Low Distortion Embedding from Edit to Hamming Distance using Coupling

Revisions: 1

The Hamming and the edit metrics are two common notions of measuring distances between pairs of strings $x,y$ lying in the Boolean hypercube. The edit distance between $x$ and $y$ is defined as the minimum number of character insertion, deletion, and bit flips needed for converting $x$ into $y$. ... more >>>

TR15-116 | 21st July 2015
Joshua Brakensiek, Venkatesan Guruswami, Samuel Zbarsky

Efficient Low-Redundancy Codes for Correcting Multiple Deletions

Revisions: 1

We consider the problem of constructing binary codes to recover from $k$-bit deletions with efficient encoding/decoding, for a fixed $k$. The single deletion case is well understood, with the Varshamov-Tenengolts-Levenshtein code from 1965 giving an asymptotically optimal construction with $\approx 2^n/n$ codewords of length $n$, i.e., at most $\log n$ ... more >>>

TR15-117 | 21st July 2015
Boris Bukh, Venkatesan Guruswami

An improved bound on the fraction of correctable deletions

Revisions: 1

We consider codes over fixed alphabets against worst-case symbol deletions. For any fixed $k \ge 2$, we construct a family of codes over alphabet of size $k$ with positive rate, which allow efficient recovery from a worst-case deletion fraction approaching $1-\frac{2}{k+1}$. In particular, for binary codes, we are able to ... more >>>

TR16-056 | 8th April 2016
Shafi Goldwasser, Dhiraj Holden

On the Fine Grained Complexity of Polynomial Time Problems Given Correlated Instances

We set out to study the impact of having access to correlated instances on the fine grained complexity of polynomial time problems, which have notoriously resisted improvement.
In particular, we show how to use a logarithmic number of auxiliary correlated instances to obtain $o(n^2)$ time algorithms for the longest common ... more >>>

TR17-079 | 1st May 2017
Alexander A. Sherstov, Pei Wu

Optimal Interactive Coding for Insertions, Deletions, and Substitutions

Interactive coding, pioneered by Schulman (FOCS 1992, STOC 1993), is concerned with making communication protocols resilient to adversarial noise. The canonical model allows the adversary to alter a small constant fraction of symbols, chosen at the adversary's discretion, as they pass through the communication channel. Braverman, Gelles, Mao, and Ostrovsky ... more >>>

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