An Efficient Algorithm For Chinese Postman Walk on Bi-directed de Bruijn Graphs

TL;DR

This paper introduces a faster algorithm for solving the cyclic Chinese Postman problem on bi-directed de Bruijn graphs, which improves efficiency in genome sequence assembly by avoiding flow reduction techniques.

Contribution

It presents a novel algorithm that solves the cyclic CPP on weighted bi-directed de Bruijn graphs more efficiently than previous flow-based methods, especially when imbalance is low.

Findings

The new algorithm has a time complexity of ?(p(|V| + |E|) log(|V|) + (dmaxp)^3).

Experimental results show p/|V| between 0.08% and 0.13% in datasets.

The algorithm outperforms bidirected flow algorithms when p is much less than |V|.

Abstract

Sequence assembly from short reads is an important problem in biology. It is known that solving the sequence assembly problem exactly on a bi-directed de Bruijn graph or a string graph is intractable. However finding a Shortest Double stranded DNA string (SDDNA) containing all the k-long words in the reads seems to be a good heuristic to get close to the original genome. This problem is equivalent to finding a cyclic Chinese Postman (CP) walk on the underlying un-weighted bi-directed de Bruijn graph built from the reads. The Chinese Postman walk Problem (CPP) is solved by reducing it to a general bi-directed flow on this graph which runs in O(|E|2 log2(|V |)) time. In this paper we show that the cyclic CPP on bi-directed graphs can be solved without reducing it to bi-directed flow. We present a ?(p(|V | + |E|) log(|V |) + (dmaxp)3) time algorithm to solve the cyclic CPP on a weighted bi-directed de Bruijn graph, where p = max{|{v|din(v) - dout(v) > 0}|, |{v|din(v) - dout(v) < 0}|} and dmax = max{|din(v) - dout(v)}. Our algorithm performs asymptotically better than the bidirected flow algorithm when the number of imbalanced nodes p is much less than the nodes in the bi-directed graph. From our experimental results on various datasets, we have noticed that the value of p/|V | lies between 0.08% and 0.13% with 95% probability.