Abstract
We present a novel distributed algorithm for the minimum s-t cut problem, suitable for solving large sparse instances. 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, which are passes over all regions. Let \(\mathcal B\) 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 \(2|{\mathcal B}|^2+1\) 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 O(n2) bound on the number of sweeps, where n 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 108 vertices and 6·108 edges) are solved using under 1GB of memory in about 10 sweeps.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Shekhovtsov, A., Hlavac, V.: A distributed mincut/maxflow algorithm combining path augmentation and push-relabel. Research Report K333–43/11, CTU–CMP–2011–03, Czech Technical University in Prague (2011)
Boykov, Y., Kolmogorov, V.: An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. PAMI 26 (2004)
Liu, J., Sun, J.: Parallel graph-cuts by adaptive bottom-up merging. In: CVPR (2010)
Strandmark, P., Kahl, F.: Parallel and distributed graph cuts by dual decomposition. In: CVPR (2010)
Goldberg, A.V., Tarjan, R.E.: A new approach to the maximum flow problem. Journal of the ACM 35 (1988)
Goldberg, A.V.: Processor-efficient implementation of a maximum flow algorithm. Inf. Process. Lett. 38 (1991)
Delong, A., Boykov, Y.: A scalable graph-cut algorithm for N-D grids. In: CVPR (2008)
Goldberg, A.V.: The partial augment–relabel algorithm for the maximum flow problem. In: Proceedings of the 16th Annual European Symposium on Algorithms (2008)
Goldberg, A.V., Rao, S.: Beyond the flow decomposition barrier. J. ACM (1998)
Cherkassky, B.V., Goldberg, A.V.: On implementing push-relabel method for the maximum flow problem. Technical report (1994)
Goldberg, A.: Efficient graph algorithms for sequential and parallel computers. PhD thesis, Massachusetts Institute of Technology (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Shekhovtsov, A., Hlavác̆, V. (2011). A Distributed Mincut/Maxflow Algorithm Combining Path Augmentation and Push-Relabel. In: Boykov, Y., Kahl, F., Lempitsky, V., Schmidt, F.R. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2011. Lecture Notes in Computer Science, vol 6819. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23094-3_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-23094-3_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23093-6
Online ISBN: 978-3-642-23094-3
eBook Packages: Computer ScienceComputer Science (R0)