867 research outputs found
Efficient Implementation of a Synchronous Parallel Push-Relabel Algorithm
Motivated by the observation that FIFO-based push-relabel algorithms are able
to outperform highest label-based variants on modern, large maximum flow
problem instances, we introduce an efficient implementation of the algorithm
that uses coarse-grained parallelism to avoid the problems of existing parallel
approaches. We demonstrate good relative and absolute speedups of our algorithm
on a set of large graph instances taken from real-world applications. On a
modern 40-core machine, our parallel implementation outperforms existing
sequential implementations by up to a factor of 12 and other parallel
implementations by factors of up to 3
Critical slowing down in polynomial time algorithms
Combinatorial optimization algorithms which compute exact ground state
configurations in disordered magnets are seen to exhibit critical slowing down
at zero temperature phase transitions. Using arguments based on the physical
picture of the model, including vanishing stiffness on scales beyond the
correlation length and the ground state degeneracy, the number of operations
carried out by one such algorithm, the push-relabel algorithm for the random
field Ising model, can be estimated. Some scaling can also be predicted for the
2D spin glass.Comment: 4 pp., 3 fig
- …