652 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
A New Push-Relabel Algorithm for Sparse Networks
In this paper, we present a new push-relabel algorithm for the maximum flow
problem on flow networks with vertices and arcs. Our algorithm computes
a maximum flow in time on sparse networks where . To our
knowledge, this is the first time push-relabel algorithm for the edge case; previously, it was known that push-relabel implementations
could find a max-flow in time when (King,
et. al., SODA `92). This also matches a recent flow decomposition-based
algorithm due to Orlin (STOC `13), which finds a max-flow in time on
sparse networks.
Our main result is improving on the Excess-Scaling algorithm (Ahuja & Orlin,
1989) by reducing the number of nonsaturating pushes to across all
scaling phases. This is reached by combining Ahuja and Orlin's algorithm with
Orlin's compact flow networks. A contribution of this paper is demonstrating
that the compact networks technique can be extended to the push-relabel family
of algorithms. We also provide evidence that this approach could be a promising
avenue towards an -time algorithm for all edge densities.Comment: 23 pages. arXiv admin note: substantial text overlap with
arXiv:1309.2525 - This version includes an extension of the result to the
O(n) edge cas
A Distributed Mincut/Maxflow Algorithm Combining Path Augmentation and Push-Relabel
We develop a novel distributed algorithm for the minimum cut problem. We
primarily aim at solving large sparse problems. Assuming vertices of the graph
are partitioned into several regions, the algorithm performs path augmentations
inside the regions and updates of the push-relabel style between the regions.
The interaction between regions is considered expensive (regions are loaded
into the memory one-by-one or located on separate machines in a network). The
algorithm works in sweeps - passes over all regions. Let be the set of
vertices incident to inter-region edges of the graph. We present a sequential
and parallel versions of the algorithm which terminate in at most
sweeps. The competing algorithm by Delong and Boykov uses push-relabel updates
inside regions. In the case of a fixed partition we prove that this algorithm
has a tight bound on the number of sweeps, where is the number of
vertices. We tested sequential versions of the algorithms on instances of
maxflow problems in computer vision. Experimentally, the number of sweeps
required by the new algorithm is much lower than for the Delong and Boykov's
variant. Large problems (up to vertices and edges) are
solved using under 1GB of memory in about 10 sweeps.Comment: 40 pages, 15 figure
Computational investigations of maximum flow algorithms
"April 1995."Includes bibliographical references (p. 55-57).by Ravindra K. Ahuja ... [et al.
Efficiently computing maximum flows in scale-free networks
We study the maximum-flow/minimum-cut problem on scale-free networks, i.e., graphs whose degree distribution follows a power-law. We propose a simple algorithm that capitalizes on the fact that often only a small fraction of such a network is relevant for the flow. At its core, our algorithm augments Dinitz’s algorithm with a balanced bidirectional search. Our experiments on a scale-free random network model indicate sublinear run time. On scale-free real-world networks, we outperform the commonly used highest-label Push-Relabel implementation by up to two orders of magnitude. Compared to Dinitz’s original algorithm, our modifications reduce the search space, e.g., by a factor of 275 on an autonomous systems graph.
Beyond these good run times, our algorithm has an additional advantage compared to Push-Relabel. The latter computes a preflow, which makes the extraction of a minimum cut potentially more difficult. This is relevant, for example, for the computation of Gomory-Hu trees. On a social network with 70000 nodes, our algorithm computes the Gomory-Hu tree in 3 seconds compared to 12 minutes when using Push-Relabel
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