What is an approximation factor for the Greedy Motif Search algorithm?
Quoting Master’s Thesis in Computer Science by Finn Rosenbech Jensen0, Dec. 2010, Greedy Motif algorithm approximation factor, using common superstring1 and its linear approximation2, was proved it cannot be better then 2.
Using proof by Kaplan and Shafir3 author shows that $\mid t_{greedy}\mid = 3.5 * OPT(S)$.

[0]: Master thesis by Rosenbech Jensen
[1]: Tarhio, J. and E. Ukkonen (1988).  A greedy approximation algorithm for constructing shortest common superstrings.Theor. Comput. Sci. 57(1),131–145.
[2]: Blum,  A.,  T.  Jiang,  M.  Li,  J.  Tromp,  and  M.  Yannakakis  (1994,  May).Linear approximation of shortest superstrings.   InProceedings of the23rd Annual ACM Symposium on Theory of Computing, pp. 328–336. 
[3]: Kaplan, H. and N. Shafrir (2005).  The greedy algorithm for shortest su-perstrings.Inf. Process. Lett. 93(1), 13–17.