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Computing the edit distance of two strings is one of the most basic problems in computer science and combinatorial optimization. Tree edit distance is a natural generalization of edit distance in which the task is to compute a measure of…
A binary 1-error-correcting code can always be embedded in a 1-perfect code of some larger length
This paper considers insertion and deletion channels with the additional assumption that the channel input sequence is implicitly divided into segments such that at most one edit can occur within a segment. No segment markers are available…
We study the following substring suffix selection problem: given a substring of a string T of length n, compute its k-th lexicographically smallest suffix. This a natural generalization of the well-known question of computing the maximal…
We introduce synchronization strings as a novel way of efficiently dealing with synchronization errors, i.e., insertions and deletions. Synchronization errors are strictly more general and much harder to deal with than commonly considered…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
In many applications, it is necessary to determine the string similarity. Edit distance[WF74] approach is a classic method to determine Field Similarity. A well known dynamic programming algorithm [GUS97] is used to calculate edit distance…
Classically, the edit distance of two length-$n$ strings can be computed in $O(n^2)$ time, whereas an $O(n^{2-\epsilon})$-time procedure would falsify the Orthogonal Vectors Hypothesis. If the edit distance does not exceed $k$, the running…
Maximum run-length limited codes are constraint codes used in communication and data storage systems. Insertion/deletion correcting codes correct insertion or deletion errors caused in transmitted sequences and are used for combating…
The problem called "String reconstruction from substrings" is a mathematical model of sequencing by hybridization that plays an important role in DNA sequencing. In this problem, we are given a blackbox oracle holding an unknown string…
Two strings are considered to have parameterized matching when there exists a bijection of the parameterized alphabet onto itself such that it transforms one string to another. Parameterized matching has application in software duplication…
A sequence $e_0,e_1,\ldots$ of edit operations in a string $T$ is called ephemeral if operation $e_i$ constructing string $T^i$, for all $i=2k$ with $k\in\mathbb{N}$, is reverted by operation $e_{i+1}$ that reconstructs $T$. Such a sequence…
We present a full quantum error correcting procedure with the semion code: an off-shell extension of the double semion model. We construct open strings operators that recover the quantum memory from arbitrary errors and closed string…
Permutation codes and multi-permutation codes have been widely considered due to their various applications, especially in flash memory. In this paper, we consider permutation codes and multi-permutation codes against a burst of stable…
By taking into account the physical nature of quantum errors it is possible to improve the efficiency of quantum error correction. Here we consider an optimisation to conventional quantum error correction which involves exploiting…
For variable-length coding with an almost-sure distortion constraint, Zhang et al. show that for discrete sources the redundancy is upper bounded by $\log n/n$ and lower bounded (in most cases) by $\log n/(2n)$, ignoring lower order terms.…
Suppose we have two players $A$ and $C$, where player $A$ has a string $s[0..u-1]$ and player $C$ has a string $t[0..u-1]$ and none of the two players knows the other's string. Assume that $s$ and $t$ are both over an integer alphabet…
In order to achieve fault tolerance, highly reliable system often require the ability to detect errors as soon as they occur and prevent the speared of erroneous information throughout the system. Thus, the need for codes capable of…
Nanopore sequencing, superior to other sequencing technologies for DNA storage in multiple aspects, has recently attracted considerable attention. Its high error rates, however, demand thorough research on practical and efficient coding…
We study edit distance computation with preprocessing: the preprocessing algorithm acts on each string separately, and then the query algorithm takes as input the two preprocessed strings. This model is inspired by scenarios where we would…