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### ABOUT ### ABOUT
This program simulates BiGpairSEQ, a graph theory based adaptation This program simulates BiGpairSEQ, a graph theory based adaptation
of the [pairSEQ][1] algorithm for pairing T cell receptor sequences. of the pairSEQ algorithm for pairing T cell receptor sequences.
### USAGE ### 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. 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. 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](https://web.eecs.umich.edu/~pettie/matching/Duan-Su-scaling-bipartite-matching.pdf). The best currently-known algorithm for bipartite graphs with integer weights is from [Duan and Su][2]
For a graph with m edges, n vertices per side, and maximum integer edge weight N, their algorithm runs 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 in O(m sqrt(n) log(N)) time. With its best-known efficiency and requirement of integer weights, this
algorithm is ideal for BiGpairSEQ. algorithm is ideal for BiGpairSEQ.
@@ -68,7 +68,9 @@ runtime of O(n (n log(n) + m)).
### CITATIONS ### CITATIONS
[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) [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) [2]: https://web.eecs.umich.edu/~pettie/matching/Duan-Su-scaling-bipartite-matching.pdf
Duan, R. and Su H. "A Scaling Algorithm for Maximum Weight Matching in Bipartite Graphs." (2012)
### ACKNOWLEDGEMENTS ### ACKNOWLEDGEMENTS
Conceived in collaboration with Dr. Alice MacQueen, who brought the original pairSEQ paper to the author's attention Conceived in collaboration with Dr. Alice MacQueen, who brought the original pairSEQ paper to the author's attention