From de Bruijn Graphs to Rectangle Graphs for Genome Assembly
Jigsaw puzzles were originally constructed by painting a picture on a rectangular piece of wood and further cutting it into smaller pieces with a jigsaw. The Jigsaw Puzzle Problem is to find an arrangement of these pieces that fills up the rectangle in such a way that neighboring pieces have “matching” boundaries with respect to color and texture. While the general Jigsaw Puzzle Problem is NP-complete , we discuss its simpler version (called Rectangle Puzzle Problem) and study the rectangle graphs, recently introduced by Bankevich et al., 2012 , for assembling such puzzles. We establish the connection between Rectangle Puzzle Problem and the problem of assembling genomes from read-pairs, and further extend the analysis in  to real challenges encountered in applications of rectangle graphs in genome assembly. We demonstrate that addressing these challenges results in an assembler SPAdes+ that improves on existing assembly algorithms in the case of bacterial genomes (including particularly difficult case of genome assemblies from single cells).
SPAdes+ is freely available from http://bioinf.spbau.ru/spades.
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