Flow Decomposition With Subpath Constraints

Abstract

Flow network decomposition is a natural model for problems where we are given a flow network arising from superimposing a set of weighted paths and would like to recover the underlying data, i.e., decompose the flow into the original paths and their weights. Thus, variations on flow decomposition are often used as subroutines in multiassembly problems such as RNA transcript assembly. In practice, we frequently have access to information beyond flow values in the form of subpaths, and many tools incorporate these heuristically. But despite acknowledging their utility in practice, previous work has not formally addressed the effect of subpath constraints on the accuracy of flow network decomposition approaches. We formalize the flow decomposition with subpath constraints problem, give the first algorithms for it, and study its usefulness for recovering ground truth decompositions. For finding a minimum decomposition, we propose both a heuristic and an FPT algorithm. Experiments on RNA transcript datasets show that for instances with larger solution path sets, the addition of subpath constraints finds 13% more ground truth solutions when minimal decompositions are found exactly, and 30% more ground truth solutions when minimal decompositions are found heuristically.

Fast, Flexible, and Exact Minimum Flow Decompositions via ILP

“…If errors are minimal, the weights on the edges should form a flow on the network, and the underlying sequences and their abundances must be some decomposition of the flow into weighted paths. For RNA assembly, recent work [22,59] has confirmed the common assertion (e.g., by [49,43,23,31,63,28,30]) that the true transcripts and abundances should be minimum flow decomposition. No such study has been done for viral quasispecies assembly, but existing tools seek minimum-sized decompositions [4,57].…”

“…For example, many tools account for paired-end reads by requiring that they be included in the same path. Another common strategy is to incorporate longer reads as subpath constraints or phasing paths [38,43,59] which again must be covered by some predicted transcript (i.e. flow path).…”

“…We compare InexactFlowILP with IFDSolver, which is an implementation of a heuristic algorithm for MIFD by [58]. Given the size of the datasets, we set a time limit for each graph, as also done by [22,59] (we use 1 minute in all cases, except that we also include a run of Toboggan with a 5 minute time limit). The runtimes of our ILP implementations include the linear scan in increasing order to find the smallest k for which there is a k-flow decomposition.…”

Safety and Completeness in Flow Decompositions for RNA Assembly

“…In both cases, the weighted transcripts are superimposed to build splice graphs as described above. This dataset has also been used in other flow decomposition benchmarking studies [26,57]. There are 17,335,407 graphs in total in this dataset, of which 8,301,682 are non-trivial (47.89%).…”

“…If there are multiple optimal flow decomposition solutions, then the reconstructed sequences may not match the original ones, and thus be incorrect. While many popular multiassembly tools look for minimum flow decompositions, Williams et al [57] analyzed an error-free transcript dataset to find that 20% of human genes admit multiple minimum flow decomposition solutions.…”