GRPH: Overlap Graphs | Ben Cunningham

# GRPH: Overlap Graphs

Problem by Rosalind · on July 1, 2012

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 $v$ and head $w$ is represented by $(v, w)$ (but not by $(w, v)$). A directed loop is a directed edge of the form $(v, v)$.

For a collection of strings and a positive integer $k$, the overlap graph for the strings is a directed graph $\mathrm{O}_k$ in which each string is represented by a node, and string $s$ is connected to string $t$ with a directed edge when there is a length $k$ suffix of $s$ that matches a length $k$ prefix of $t$, as long as $s \neq t$; we demand $s \neq t$ 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 $\mathrm{O}_3$. 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


# R

library(dplyr)
library(seqinr)
library(stringr)
library(tidyr)

f <- "grph.txt"
raw <- unlist(read.fasta(f, as.string = TRUE))

dna <- data_frame(
id = names(raw),
x = toupper(raw),
beg = str_extract(x, "^.{3}"),
end = str_extract(x, ".{3}$") ) adj <- dna %>% inner_join(dna, by = c("end" = "beg")) %>% filter(id.x != id.y) %>% mutate(out = paste(id.x, id.y)) cat(adj$out, sep = "\n")

Rosalind_0498 Rosalind_2391
Rosalind_0498 Rosalind_0442
Rosalind_2391 Rosalind_2323