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Cufflinks (Trapnell et al., 2010) attaches weights to edges and models the isoform reconstruction problem as a minimum path cover problem, while Scripture (Guttman et al., 2010) creates a statistical model to identify significant segments as isoforms.
Because we consider only unmasked reads, any compatibility graph G ′ M ′ ⃗ is fully transitive: a minimum path cover solves minimum clique cover, solving minimum coloring of the conflict connected component G M '.
Regarding the first point, solving a maximum unweighted matching on B M ' and computing connected components (after contracting left and right nodes representing the same node in G ′ M ′ ⃗ ) would give a minimum path cover of G ′ M ′ ⃗ [ 35].
Original edges are given weight of 1. Theorem 1. Computing connected components of a maximum weighted matching of B M ′ ε followed by contraction of nodes representing the same node in G ′ M ′ ⃗ produces a minimum path cover of G ′ M ′ ⃗, while secondarily maximizing the number of paths consisting of a single node.
As noted in [ 35], connected components in an unweighted matching of the original B M ' produce a minimum path cover of G ′ M ′ ⃗, where n - k is the number of paths and k is the number of edges selected in the matching.
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They were computed by the described optimal procedure with the amendment that, in the case of equal correlation paths, the minimum path was considered to cover the QSAR model with the highest correlation factor.
x3: Minimum path length (minimum number of edges/links from one of the nine external inputs).
In this paper we investigate the k-path cover problem for graphs, which is to find the minimum number of vertex disjoint k-paths that cover all the vertices of a graph.
The HSY physical map consists of 68 overlapped BACs on the minimum tiling path, and covers all four HSY-specific Knobs.
These were then used to 454-sequence a minimum tiling path which covered an entire chromosome arm from Oryza barthii [ 37].
We characterize the minimum forest cover along optimal paths (when deforestation is not optimal).
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