Approximating the Shortest Superstring Problem Using de Bruijn Graphs

The best known approximation ratio for the shortest superstring problem is 2 11 23 (Mucha, 2012). In this note, we improve this bound for the case when the length of all input strings is equal to r, for r ≤ 7. For example, for strings of length 3 we get a 1 1 3 -approximation. An advantage of the algorithm is that it is extremely simple both to implement and to analyze. Another advantage is that it is based on de Bruijn graphs. Such graphs are widely used in genome assembly (one of the most important practical applications of the shortest common superstring problem). At the same time these graphs have only few applications in theoretical investigations of the shortest superstring problem.