Stony Brook Algorithm Repository

Shortest Common Superstring


Input Description: A set of strings \(s_1, ..., s_m\).
Problem: Find the shortest string \(S\) which contains each \(s_i\) as a substring of \(S\).

Excerpt from The Algorithm Design Manual: Shortest common superstring arises in a variety of applications, including sparse matrix compression. Suppose we have an \(n X m\) matrix with most of the elements being zero. We can partition each row into \(m/k\) runs of \(k\) elements each and construct the shortest common superstring \(S'\) of these runs. We now have reduced the problem to storing the superstring, plus an \(n X m/k\) array of pointers into the superstring denoting where each of the runs starts. Accessing a particular element \(M[i,j]\) still takes constant time, but there is a space savings when \(|S| << mn\).


CAP (rating 9)
Celera Assembler (rating 8)
superstring (rating 5)

Recommended Books

Algorithms on Strings, Trees, and Sequences by Dan Gusfield Introduction to Computational Biology by M. Waterman

Related Problems

Longest Common Substring/Subsequence

Suffix Trees and Arrays

Text Compression

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