Paper Info
Title
Relationship between superstring and compression measures: New insights on the greedy conjecture.
Abstract
A superstring of a set of words is a string that contains each input word as a substring. Given such a set, the Shortest Superstring Problem (SSP) asks for a superstring of minimum length. SSP is an important theoretical problem related to the Asymmetric Travelling Salesman Problem, and also has practical applications in data compression and in bioinformatics. Indeed, it models the question of assembling a genome from a set of sequencing reads. Unfortunately, SSP is known to be NP-hard even on a binary alphabet and also hard to approximate with respect to the superstring length or to the compression achieved by the superstring. Even the variant in which all words share the same length r, called r-SSP, is NP-hard whenever r>2. Numerous involved approximation algorithms achieve approximation ratio above 2 for the superstring, but remain difficult to implement in practice. In contrast the greedy conjecture asked in 1988 whether a simple greedy algorithm achieves ratio of 2 for SSP. Here, we present a novel approach to bound the superstring approximation ratio with the compression ratio, which, when applied to the greedy algorithm, shows a 2 approximation ratio for 3-SSP, and also that greedy achieves ratios smaller than 2. This leads to a new version of the greedy conjecture.
Year
DOI
Venue
2018
10.1016/j.dam.2017.04.017
Discrete Applied Mathematics
Keywords
Field
DocType
Approximation algorithm,Shortest Common Superstring Problem,Stringology,Data compression,Assembly,Greedy conjecture
Superstring theory,Approximation algorithm,Discrete mathematics,Combinatorics,Substring,Greedy algorithm,Travelling salesman problem,Data compression,Greedy randomized adaptive search procedure,Conjecture,Mathematics
Journal
Volume
ISSN
Citations 
245
0166-218X
0
PageRank 
References 
Authors
0.34
11
2
Name
Order
Citations
PageRank
Bastien Cazaux1106.65
E Rivals2136.29