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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 71, 2022 - Issue 7
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Articles

TBGMax: leveraging two-boundary graph pattern for lossless maximum-flow acceleration

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Pages 2047-2072 | Received 23 May 2020, Accepted 20 Oct 2020, Published online: 06 Dec 2020

References

  • Boykov Y, Kolmogorov V. An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. IEEE Trans Pattern Anal Mach Intell. 2004; 26: 1124–1137.
  • Goldberg AV, Tarjan RE. Efficient maximum flow algorithms. Comm. ACM. 2014;57:82–89.
  • Verma T, Dhruv B. MaxFlow revisited: an empirical comparison of maxflow algorithms for dense vision problems. Proc. British Machine Vision Conference; 2012. p. 1–12.
  • Zhang YP, Hua B, Jiang J, et al. Research on the maximum flow in large-scale network. Proc. Int. Conf. Computational Intelligence and Security; 2011. p. 482–486.
  • Zhang Y, Xu X, Hua B, et al. Contracting community for computing maximum flow. Proc. Int. Conf. Granular Computing; 2012. p. 651–656.
  • Zhao S, Xu X, Hua B, et al. Contraction network for solving maximum flow problem. Proc. ACM SIGKDD Workshop on Mining Data Semantics; 2012. p. 1–6.
  • Ford LR, Fulkerson DR. Maximal flow through a network. Canad J Math. 1956;8:399–404.
  • Edmonds J, Karp RM. Theoretical improvements in algorithmic efficiency for network flow problems. J ACM. 1972;19:248–264.
  • Goldberg AV, Tarjan RE. A new approach to the maximum flow problem. J ACM. 1988;35:921–940.
  • Even S, Tarjan RE. Network flow and testing graph connectivity. SIAM J Comput. 1975;4:507–518.
  • Borradaile G, Klein PN. An O(n log n) algorithm for maximum st-flow in a directed planar graph. J ACM. 2009;56:1–30.
  • Christiano P, Kelner J, Madry A. Electrical flows, Laplacian systems, and faster approximation of maximum flow in undirected graphs. Proc. ACM Symposium on Theory of Computing; 2010. p. 1–9.
  • Kelner A, Lee YT. An almost-linear-time algorithm for approximate max flow in undirected graphs, and its multicommodity generalizations. Proc. ACMSIAM Symposium on Discrete Algorithms; 2014. p. 217–226.
  • Sherman J. Nearly maximum flows in nearly linear time. Proc. IEEE Symposium on Foundations of Computer Science; 2013. p. 263–269.
  • Anderson R, Setubal JC. A parallel implementation of the push-relabel algorithm for the maximum flow problem. J Parallel Distrib Comput. 1995;1:17–26.
  • Shiloach Y, Vishkin U. An O(n2log n) parallel max-flow algorithm. J Algo. 1982;2:128–146.
  • Gomory RE, Hu TC. Multi-terminal network flows. J Soc Indust Appl Math. 1961;9:551–570.
  • Gusfield D. Very simple methods for all pairs network flow analysis. SIAM J Comput. 1990;19:143–155.
  • Scheuermann B, Rosenhahn B. Slimcuts: Graphcuts for high resolution images using graph reduction. Proc. Int. Workshop on energy minimization methods in computer vision and pattern recognition; 2011. p. 219–232.
  • Liers F, Pardella G. Simplifying maximum flow computations: the effect of shrinking and good initial flows. Discrete Appl Math. 2011; 159: 2187–2203.
  • Zhao S, Su J, Liu Q, et al. To solve maximum flow problem of network with a layering method. J Comput Res Develop. 2014;51:1845–1853.
  • Wei W, Liu Y, Zhang R. SPLMax: exploiting the simple path introduced locality for maximum flow acceleration. IEEE Comm Lett. 2018;22:1330–1333.
  • Hopcroft J, Tarjan R. Algorithm 447: efficient algorithms for graph manipulation. Comm ACM. 1973;16:372–378.
  • Goldberg AV. Homepage of Andrew Goldberg's network optimization library; 2006. Available from: http://www.avglab.com/andrew/soft.html
  • Hochbaum DS. Homepage of Hochbaum's pseudo-flow implementation. 2009. Available from: https://riot.ieor.berkeley.edu/Applications/Pseudoflow/maxflow.html
  • Shekhovtsov A. Homepage of a distributed algorithm for mincut/maxflow combining path augmentation and push-relabel; 2019. Available from: http://cmp.felk.cvut.cz/shekhovt/d_maxflow/index.html
  • Shekhovtsov A, Hlavac V. A distributed mincut/maxflow algorithm combining path augmentation and push-Relabel. Int J Comput Vis. 2013;104:315–342.
  • Wikipedia. Homepage of Edmonds–Karp algorithm in Wikipedia; 2019. Available from: https://en.wikipedia.org/wiki/Edmonds-Karp_algorithm
  • IBM Corporation. Homepage of CPLEX optimizer. 2019. Available from: https://www.ibm.com/analytics/cplex-optimizer
  • David SJ, Catherine CM. Network flows and matching: first DIMACS implementation challenge. AMS; 1993.
  • Naher S. Homepage of typical generators for max-flow problems; 2003. Available from: http://www.informatik.uni-trier.de/naeher/Professur/research/generators/maxflow/
  • Cherkassy BV, Goldberg AV. On implementing push-relabel method for the maximum flow problem. Proc. Int. Conf. Integer Programming and Combinatorial Optimization; 1995. p. 157–171.
  • Schultes D. United States road networks (TIGER/Line); 2019. Available from: http://www.dis.uniroma1.it/challenge9/data/tiger/
  • Karger DR. Minimum cuts in near-linear time. J ACM. 2000;47:46–76.
  • Karger DR, Stein C. A new approach to the minimum cut problem. J ACM. 1996;43:601–640.
  • Karzanov AV. Determining the maximal flow in a network by the method of preflows. Soviet Math Dokladi. 1974;15:434–437.
  • Padberg M, Rinaldi G. An efficient algorithm for the minimum capacity cut problem. Math Program. 1990;47:19–36.

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