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Graph Partitioning With Limited Moves (2402.15485v1)

Published 23 Feb 2024 in cs.DS

Abstract: In many real world networks, there already exists a (not necessarily optimal) $k$-partitioning of the network. Oftentimes, one aims to find a $k$-partitioning with a smaller cut value for such networks by moving only a few nodes across partitions. The number of nodes that can be moved across partitions is often a constraint forced by budgetary limitations. Motivated by such real-world applications, we introduce and study the $r$-move $k$-partitioning~problem, a natural variant of the Multiway cut problem. Given a graph, a set of $k$ terminals and an initial partitioning of the graph, the $r$-move $k$-partitioning~problem aims to find a $k$-partitioning with the minimum-weighted cut among all the $k$-partitionings that can be obtained by moving at most $r$ non-terminal nodes to partitions different from their initial ones. Our main result is a polynomial time $3(r+1)$ approximation algorithm for this problem. We further show that this problem is $W[1]$-hard, and give an FPTAS for when $r$ is a small constant.

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References (36)
  1. Introduction to the special section on graph algorithms in computer vision. IEEE Transactions on Pattern Analysis & Machine Intelligence, 23(10):1049–1052, 2001.
  2. Graph partitioning models for parallel computing. Parallel computing, 26(12):1519–1534, 2000.
  3. Thorsten Joachims. Transductive learning via spectral graph partitioning. In Proceedings of the 20th international conference on machine learning (ICML-03), pages 290–297, 2003.
  4. VLSI physical design: from graph partitioning to timing closure. Springer Science & Business Media, 2011.
  5. Geo-graphs: an efficient model for enforcing contiguity and hole constraints in planar graph partitioning. Operations Research, 60(5):1213–1228, 2012.
  6. Scalable network analytics for characterization of outbreak influence in voluminous epidemiology datasets. Concurrency and Computation: Practice and Experience, 31(7):e4998, 2019.
  7. The complexity of multiway cuts. In Proceedings of the twenty-fourth annual ACM symposium on Theory of computing, pages 241–251, 1992.
  8. The complexity of multiterminal cuts. SIAM Journal on Computing, 23(4):864–894, 1994.
  9. Fair disaster containment via graph-cut problems. In International Conference on Artificial Intelligence and Statistics, pages 6321–6333. PMLR, 2022.
  10. A local search approximation algorithm for the multiway cut problem. Discrete Applied Mathematics, 338:8–21, 2023.
  11. An improved approximation algorithm for multiway cut. In Proceedings of the thirtieth annual ACM symposium on Theory of computing, pages 48–52, 1998.
  12. An improved integrality gap for the călinescu-karloff-rabani relaxation for multiway cut. In International Conference on Integer Programming and Combinatorial Optimization, pages 39–50. Springer, 2017.
  13. Finding k cuts within twice the optimal. SIAM Journal on Computing, 24(1):101–108, 1995.
  14. Sdp gaps and ugc hardness for multiway cut, 0-extension, and metric labeling. In Proceedings of the fortieth annual ACM symposium on Theory of computing, pages 11–20, 2008.
  15. Multiway cut, pairwise realizable distributions, and descending thresholds. In Proceedings of the forty-sixth annual ACM symposium on Theory of computing, pages 724–733, 2014.
  16. Subhash Khot. On the power of unique 2-prover 1-round games. In Proceedings of the thiry-fourth annual ACM symposium on Theory of computing, pages 767–775, 2002.
  17. Improving the integrality gap for multiway cut. Mathematical Programming, 183(1):171–193, 2020.
  18. Peng Zhang. A new approximation algorithm for the unbalanced min s–t cut problem. Theoretical Computer Science, 609:658–665, 2016.
  19. On size-constrained minimum s–t cut problems and size-constrained dense subgraph problems. Theoretical Computer Science, 609:434–442, 2016.
  20. Clustering with local restrictions. Information and Computation, 222:278–292, 2013.
  21. Leizhen Cai. Parameterized complexity of cardinality constrained optimization problems. The Computer Journal, 51(1):102–121, 2008.
  22. A polynomial algorithm for the k-cut problem for fixed k. Mathematics of operations research, 19(1):24–37, 1994.
  23. Multicriteria global minimum cuts. Algorithmica, 46(1):15–26, 2006.
  24. Edge-connectivity augmentation problems. Journal of Computer and System Sciences, 35(1):96–144, 1987.
  25. A new approach to the minimum cut problem. Journal of the ACM (JACM), 43(4):601–640, 1996.
  26. On the parameterized complexity of cutting a few vertices from a graph. In International Symposium on Mathematical Foundations of Computer Science, pages 421–432. Springer, 2013.
  27. Peng Zhang. Unbalanced graph cuts with minimum capacity. Frontiers of Computer Science, 8:676–683, 2014.
  28. Harald Räcke. Optimal hierarchical decompositions for congestion minimization in networks. In Proceedings of the fortieth annual ACM symposium on Theory of computing, pages 255–264, 2008.
  29. On cutting a few vertices from a graph. Discrete Applied Mathematics, 127(3):643–649, 2003.
  30. Multi-parameter analysis for local graph partitioning problems: Using greediness for parameterization. Algorithmica, 71(3):566–580, 2015.
  31. Balanced partitions of trees and applications. Algorithmica, 71(2):354–376, 2015.
  32. Approximation algorithms and hardness of the k-route cut problem. ACM Transactions on Algorithms (TALG), 12(1):1–40, 2015.
  33. Unbalanced graph cuts. In European Symposium on Algorithms, pages 191–202. Springer, 2005.
  34. A fast parametric maximum flow algorithm and applications. SIAM Journal on Computing, 18(1):30–55, 1989.
  35. Richard T Wong. Combinatorial optimization: Algorithms and complexity (christos h. papadimitriou and kenneth steiglitz). SIAM Review, 25(3):424, 1983.
  36. Jue Leskovec. email-Eu-core network dataset.
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