diff --git a/readme.md b/readme.md index 09499a9..f297326 100644 --- a/readme.md +++ b/readme.md @@ -57,10 +57,6 @@ a pairSEQ experiment is bipartite with integer weights, this algorithm seems ide fairly new algorithm, and not yet implemented by the graph theory library used in this simulator (JGraphT), nor has the author had time to implement it himself. -There have been some studies which show that [auction algorithms](https://en.wikipedia.org/wiki/Auction_algorithm) for the assignment problem can have superior performance in -real-world implementations, due to their simplicity, than more complex algorithms with better theoretical asymptotic -performance. But, again, there is no such algorithms implemented by JGraphT, nor has the author yet had time to implement one. - So this program instead uses the [Fibonacci heap](https://en.wikipedia.org/wiki/Fibonacci_heap) based algorithm of Fredman and Tarjan (1987) (essentially [the Hungarian algorithm](https://en.wikipedia.org/wiki/Hungarian_algorithm) augmented with a more efficeint priority queue) which has a worst-case runtime of **O(n (n log(n) + m))**. The algorithm is implemented as described in Melhorn and Näher (1999). (The simulator @@ -75,6 +71,15 @@ be balanced assignment problems, in practice sequence dropout can cause them to the Hungarian algorithm, graph doubling--which could be challenging with the computational resources available to the author--has not yet been necessary. +There have been some studies which show that [auction algorithms](https://en.wikipedia.org/wiki/Auction_algorithm) for the assignment problem can have superior performance in +real-world implementations, due to their simplicity, than more complex algorithms with better theoretical asymptotic +performance. The author has implemented a basic forward auction algorithm, which produces optimal assignment for unbalanced bipartite graphs with +integer weights. To allow for unbalanced assignment, this algorithim eschews epsilon-scaling, +and as a result is prone to "bidding-wars" which increase run time, making it less efficient than the implementation of +the Fredman-Tarjan algorithm in JGraphT. A forward/reverse auction algorithm as developed by Bertsekas and Castañon +should be able to handle unbalanced (or, as they call it, asymmetric) assignment much more efficiently, but has yet to be +implemented. + The relative time/space efficiencies of BiGpairSEQ when backed by different MWM algorithms remains an open problem. ## THE BiGpairSEQ ALGORITHM