cyclic cover

Practical lower and upper bounds for the Shortest Linear Superstring

Given a set P of words, the Shortest Linear Superstring (SLS) problem is an optimisation problem that asks for a superstring of P of minimal length. SLS has applications in data compression, where a superstring is a compact representation of P, and …

Superstrings with multiplicities

A superstring of a set of words $P = s_1, ..., s_p $ is a string that contains each word of P as substring. Given P, the well known Shortest Linear Superstring problem (SLS), asks for a shortest superstring of P. In a variant of SLS, called …

Superstring Graph: A New Approach for Genome Assembly

With the increasing impact of genomics in life sciences, the inference of high quality, reliable, and complete genome sequences is becoming critical. Genome assembly remains a major bottleneck in bioinformatics: indeed, high throughput sequencing …

Approximation of Greedy Algorithms for Max-ATSP, Maximal Compression, Maximal Cycle Cover, and Shortest Cyclic Cover of Strings

Covering a directed graph by a Hamiltonian path or a set of words by a superstring belong to well studied optimisation problems that prove difficult to approximate. Indeed, the Maximum Asymmetric Travelling Salesman Problem (Max-ATSP), which asks for …