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mention forward/reverse auction algorithms

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eugenefischer
2023-04-09 20:42:58 -05:00
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@@ -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 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. 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 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 [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 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 the Hungarian algorithm, graph doubling--which could be challenging with the computational resources available to the
author--has not yet been necessary. 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 relative time/space efficiencies of BiGpairSEQ when backed by different MWM algorithms remains an open problem.
## THE BiGpairSEQ ALGORITHM ## THE BiGpairSEQ ALGORITHM