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efischer
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### ABOUT
This program simulates BiGpairSEQ, a graph theory based adaptation
of the pairSEQ algorithm for pairing T cell receptor sequences.
of the [pairSEQ][1] algorithm for pairing T cell receptor sequences.
### USAGE
@@ -36,7 +36,7 @@ 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.
This is a very well-studied combinatorial optimization problem, with many known solutions.
The best currently-known algorithm for bipartite graphs with integer weights is from [Duan and Su][2].
The best currently-known algorithm for bipartite graphs with integer weights is from [Duan and Su][2](https://web.eecs.umich.edu/~pettie/matching/Duan-Su-scaling-bipartite-matching.pdf).
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. With its best-known efficiency and requirement of integer weights, this
algorithm is ideal for BiGpairSEQ.
@@ -67,8 +67,8 @@ runtime of O(n (n log(n) + m)).
### CITATIONS
* Howie, B., Sherwood, A. M., et. al. "High-throughput pairing of T cell receptor alpha and beta sequences." Sci. Transl. Med. 7, 301ra131 (2015)
[2](https://web.eecs.umich.edu/~pettie/matching/Duan-Su-scaling-bipartite-matching.pdf)
[1] Howie, B., Sherwood, A. M., et. al. "High-throughput pairing of T cell receptor alpha and beta sequences." Sci. Transl. Med. 7, 301ra131 (2015)
[2]: Duan, R. and Su H. "A Scaling Algorithm for Maximum Weight Matching in Bipartite Graphs." (2012)
### ACKNOWLEDGEMENTS
Conceived in collaboration with Dr. Alice MacQueen, who brought the original pairSEQ paper to the author's attention