双向de Bruijn图上中国邮递员行走的一个有效算法
An Efficient Algorithm For Chinese Postman Walk on Bi-directed de Bruijn Graphs
摘要：
短读段的序列组装是生物学中的一个重要问题。已知在双向de Bruijn图或串图上精确求解序列组装问题是困难的。然而，找到一个最短的双链DNA串（SDDNA）包含所有的k长的字在读段似乎是一个很好的启发式接近原始基因组。这个问题等价于在从读段构建的底层未加权双向de Bruijn图上找到循环中国邮递员（CP）行走。中国邮递员步行问题（CPP）通过将其简化为图上的一般双向流来解决，该图的运行时间为O（|E| 2 log 2（|V|））时间。在本文中，我们证明了循环CPP双向图可以解决，而不减少它的双向流。我们提出一个？(p(|+ |E|）log（|V|）+（dmaxp）3）时间算法来求解加权双向de Bruijn图上的循环CPP，其中p = max{|{v|（v）- dout（v）> 0}|, |{v|（v）- dout（v）|dmax = max{|din（v）- dout（v）}。|din(v) - dout(v)}.当不平衡节点数p远小于双向图中的节点数时，我们的算法的性能渐近优于双向流算法。从我们在各种数据集上的实验结果中，我们注意到p/|V|在0.08%和0.13%之间，概率为95%。
英文摘要：
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.
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