12 Overlap Graphs

Posted 2020-10-01 thinkanddo

Problem

A graph whose nodes have all been labeled can be represented by an adjacency list, in which each row of the list contains the two node labels corresponding to a unique edge.

A directed graph (or digraph) is a graph containing directed edges, each of which has an orientation. That is, a directed edge is represented by an arrow instead of a line segment; the starting and ending nodes of an edge form its tail and head, respectively. The directed edge with tail vv and head ww is represented by (v,w)(v,w) (but not by (w,v)(w,v)). A directed loop is a directed edge of the form (v,v)(v,v).

For a collection of strings and a positive integer kk, the overlap graph for the strings is a directed graph OkOk in which each string is represented by a node, and string ss is connected to string ttwith a directed edge when there is a length kk suffix of ss that matches a length kk prefix of tt, as long as s≠ts≠t; we demand s≠ts≠t to prevent directed loops in the overlap graph (although directed cycles may be present).

Given: A collection of DNA strings in FASTA format having total length at most 10 kbp.

Return: The adjacency list corresponding to O3O3. You may return edges in any order.

Sample Dataset

>Rosalind_0498
AAATAAA
>Rosalind_2391
AAATTTT
>Rosalind_2323
TTTTCCC
>Rosalind_0442
AAATCCC
>Rosalind_5013
GGGTGGG

Sample Output

Rosalind_0498 Rosalind_2391
Rosalind_0498 Rosalind_0442
Rosalind_2391 Rosalind_2323