A Flow Procedure for the Linearization of Genome Sequence Graphs

Efforts to incorporate human genetic variation into the reference human genome have converged on the idea of a graph representation of genetic variation within a species, a genome sequence graph. A sequence graph represents a set of individual haploid reference genomes as paths in a single graph. When that set of reference genomes is sufficiently diverse, the sequence graph implicitly contains all frequent human genetic variations, including translocations, inversions, deletions, and insertions. In representing a set of genomes as a sequence graph one encounters certain challenges. One of the most important is the problem of graph linearization, essential both for efficiency of storage and access, as well as for natural graph visualization and compatibility with other tools. The goal of graph linearization is to order nodes of the graph in such a way that operations such as access, traversal and visualization are as efficient and effective as possible. A new algorithm for the linearization of sequence graphs, called the flow procedure, is proposed in this paper. Comparative experimental evaluation of the flow procedure against other algorithms shows that it outperforms its rivals in the metrics most relevant to sequence graphs.

[1]  A. B. Kahn,et al.  Topological sorting of large networks , 1962, CACM.

[2]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[3]  Xuemin Lin,et al.  A Fast and Effective Heuristic for the Feedback Arc Set Problem , 1993, Inf. Process. Lett..

[4]  Paul Medvedev,et al.  Maximum Likelihood Genome Assembly , 2009, J. Comput. Biol..

[5]  F. Brandenburg,et al.  Sorting Heuristics for the Feedback Arc Set Problem ? , 2011 .

[6]  Eric V. Denardo,et al.  Flows in Networks , 2011 .

[7]  Fanica Gavril,et al.  Some NP-complete problems on graphs , 2011, CISS 2011.

[8]  Juan José Pantrigo,et al.  Branch and bound for the cutwidth minimization problem , 2013, Comput. Oper. Res..

[9]  Xin-She Yang,et al.  Introduction to Algorithms , 2021, Nature-Inspired Optimization Algorithms.

[10]  David Haussler,et al.  Building a Pan-Genome Reference for a Population , 2015, J. Comput. Biol..

[11]  Glenn Hickey,et al.  Superbubbles, Ultrabubbles and Cacti , 2017, bioRxiv.