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Optimal Omnitig Listing for Safe and Complete Contig Assembly

Authors Massimo Cairo, Paul Medvedev, Nidia Obscura Acosta, Romeo Rizzi, Alexandru I. Tomescu

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Massimo Cairo
Paul Medvedev
Nidia Obscura Acosta
Romeo Rizzi
Alexandru I. Tomescu

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Massimo Cairo, Paul Medvedev, Nidia Obscura Acosta, Romeo Rizzi, and Alexandru I. Tomescu. Optimal Omnitig Listing for Safe and Complete Contig Assembly. In 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 29:1-29:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)


Genome assembly is the problem of reconstructing a genome sequence from a set of reads from a sequencing experiment. Typical formulations of the assembly problem admit in practice many genomic reconstructions, and actual genome assemblers usually output contigs, namely substrings that are promised to occur in the genome. To bridge the theory and practice, Tomescu and Medvedev [RECOMB 2016] reformulated contig assembly as finding all substrings common to all genomic reconstructions. They also gave a characterization of those walks (omnitigs) that are common to all closed edge-covering walks of a (directed) graph, a typical notion of genomic reconstruction. An algorithm for listing all maximal omnitigs was also proposed, by launching an exhaustive visit from every edge. In this paper, we prove new insights about the structure of omnitigs and solve several open questions about them. We combine these to achieve an O(nm)-time algorithm for outputting all the maximal omnitigs of a graph (with n nodes and m edges). This is also optimal, as we show families of graphs whose total omnitig length is Omega(nm). We implement this algorithm and show that it is 9-12 times faster in practice than the one of Tomescu and Medvedev [RECOMB 2016].
  • genome assembly
  • graph algorithm
  • edge-covering walk
  • strong bridge


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