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AN EFFICIENT ALGORITHM FOR CHINESE POSTMAN WALK ON BI-DIRECTED DE BRUIJN GRAPHS.

Vamsi Kundeti1, Sanguthevar Rajasekaran1, Heiu Dinh1

  • 1Department of Computer Science and Engineering, University of Connecticut Storrs, CT 06269, USA.

Discrete Mathematics, Algorithms, and Applications
|November 4, 2014
PubMed
Summary
This summary is machine-generated.

This study presents a faster algorithm for genome assembly by solving the cyclic Chinese Postman walk problem on bi-directed graphs. The new method improves efficiency, especially for large genomes with sparse imbalanced nodes.

Keywords:
Chinese Postman problemSequence assembly algorithmsbi-directed graphsbioinformatics

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Area of Science:

  • Bioinformatics
  • Computational Biology
  • Genomics

Background:

  • Sequence assembly from short reads is a critical challenge in genomics.
  • Exact solutions for sequence assembly on de Bruijn or string graphs are computationally intractable.
  • The shortest double-stranded DNA (SDDNA) problem is a heuristic for genome assembly, equivalent to finding a cyclic Chinese Postman (CP) walk.

Purpose of the Study:

  • To develop a more efficient algorithm for solving the cyclic Chinese Postman (CP) walk problem on bi-directed graphs.
  • To improve upon existing methods that rely on bi-directed flow, which can be computationally expensive.
  • To provide a practical solution for the SDDNA problem and identify maximal sub-graphs with CP walks in complex biological data.

Main Methods:

  • Developed a novel algorithm for the cyclic CP problem on weighted bi-directed de Bruijn graphs, avoiding reduction to bi-directed flow.
  • The algorithm's time complexity is Θ(p(|V| + |E|) log(|V|) + (d_max*p)^3), offering asymptotic improvements when imbalanced nodes (p) are sparse.
  • Implemented a heuristic algorithm with Θ(p(|V| + |E|)) time complexity for the SDDNA problem and tested it on plant genome data.

Main Results:

  • The new cyclic CP algorithm is asymptotically faster than bi-directed flow methods for graphs with a low proportion of imbalanced nodes (p/|V| typically 0.08%-0.13%).
  • The implemented heuristic for SDDNA achieved an approximation ratio of at most 1.0134 on plant genome short reads.
  • The algorithm effectively handles graphs lacking cyclic CP walks, identifying maximal bi-directed sub-graphs amenable to CP walks.

Conclusions:

  • The proposed algorithm offers a significant advancement in solving the cyclic Chinese Postman problem on bi-directed graphs, with direct applications in genome assembly.
  • This approach provides a more efficient and robust method for constructing shortest double-stranded DNA strings from sequencing reads.
  • The study also presents an efficient algorithm for the single-source shortest path problem on bi-directed de Bruijn graphs.