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efischer
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@@ -20,8 +20,8 @@ The problem of pairing TCRA/TCRB sequences thus reduces to the "assignment probl
matching on a bipartite graph--the subset of vertex-disjoint edges whose weights sum to the maximum possible value. matching on a bipartite graph--the subset of vertex-disjoint edges whose weights sum to the maximum possible value.
This is a well-studied combinatorial optimization problem, with many known solutions. This is a well-studied combinatorial optimization problem, with many known solutions.
The most efficient known algorithm for maximum weight matching is from Duan and Su (2012), and requires a bipartite graph The most efficient algorithm known to the author for maximum weight matching of a bipartite graph with strictly integral weights
with strictly integer edge weights. For a graph with m edges, n vertices per side, and maximum integer edge weight N, is from Duan and Su (2012). For a graph with m edges, n vertices per side, and maximum integer edge weight N,
their algorithm runs in **O(m sqrt(n) log(N))** time. As the graph representation of a pairSEQ experiment is their algorithm runs in **O(m sqrt(n) log(N))** time. As the graph representation of a pairSEQ experiment is
bipartite with integer weights, this algorithm is ideal for BiGpairSEQ. bipartite with integer weights, this algorithm is ideal for BiGpairSEQ.