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Faster Worst Case Deterministic Dynamic Connectivity

Authors Casper Kejlberg-Rasmussen, Tsvi Kopelowitz, Seth Pettie, Mikkel Thorup

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Casper Kejlberg-Rasmussen
Tsvi Kopelowitz
Seth Pettie
Mikkel Thorup

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Casper Kejlberg-Rasmussen, Tsvi Kopelowitz, Seth Pettie, and Mikkel Thorup. Faster Worst Case Deterministic Dynamic Connectivity. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 53:1-53:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.ESA.2016.53

Abstract

We present a deterministic dynamic connectivity data structure for undirected graphs with worst case update time O(sqrt{(n(log(log(n)))^2)/log(n)}) and constant query time. This improves on the previous best deterministic worst case algorithm of Frederickson (SIAM J. Comput., 1985) and Eppstein Galil, Italiano, and Nissenzweig (J. ACM, 1997), which had update time O(sqrt{n}). All other algorithms for dynamic connectivity are either randomized (Monte Carlo) or have only amortized performance guarantees.
Keywords
  • dynamic graph
  • spanning tree

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References

  1. U. A. Acar, G. E. Blelloch, R. Harper, J. L. Vittes, and S. L. M. Woo. Dynamizing static algorithms, with applications to dynamic trees and history independence. In Proceedings 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 531-540, 2004. Google Scholar
  2. S. Albers and T. Hagerup. Improved parallel integer sorting without concurrent writing. Information and Computation, 136(1):25-51, 1997. URL: http://dx.doi.org/10.1006/inco.1997.2632.
  3. S. Alstrup, J. Holm, K. de Lichtenberg, and M. Thorup. Maintaining information in fully dynamic trees with top trees. ACM Trans. on Algorithms, 1(2):243-264, 2005. URL: http://dx.doi.org/10.1145/1103963.1103966.
  4. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein. Introduction to Algorithms, 3rd ed. MIT Press, 2009. Google Scholar
  5. E. W. Dijkstra. A note on two problems in connexion with graphs. Numerische Mathematik, 1:269-271, 1959. Google Scholar
  6. D. Eppstein, Z. Galil, G. F. Italiano, and A. Nissenzweig. Sparsification-a technique for speeding up dynamic graph algorithms. In Proceedings 33rd Annual Symposium on Foundations of Computer Science (FOCS), pages 60-69, 1992. Google Scholar
  7. D. Eppstein, Z. Galil, G. F. Italiano, and A. Nissenzweig. Sparsification - a technique for speeding up dynamic graph algorithms. J. ACM, 44(5):669-696, 1997. Google Scholar
  8. D. Eppstein, G. F. Italiano, R. Tamassia, R. E. Tarjan, J. Westbrook, and M. Yung. Maintenance of a minimum spanning forest in a dynamic plane graph. J. Algor., 13(1):33-54, 1992. Google Scholar
  9. D. Eppstein, G. F. Italiano, R. Tamassia, R. E. Tarjan, J. Westbrook, and M. Yung. Corrigendum: Maintenance of a minimum spanning forest in a dynamic plane graph. J. Algor., 15(1):173, 1993. Google Scholar
  10. G. Frederickson. Data structures for on-line updating of minimum spanning trees, with applications. SIAM J. Comput., 14(4):781-798, 1985. Google Scholar
  11. M. L. Fredman and M. Saks. The cell probe complexity of dynamic data structures. In Proceedings 21st Annual ACM Symposium on Theory of Computing (STOC), pages 345-354, 1989. Google Scholar
  12. M. L. Fredman and R. E. Tarjan. Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM, 34(3):596-615, 1987. Google Scholar
  13. D. Gibb, B. M. Kapron, V. King, and N. Thorn. Dynamic graph connectivity with improved worst case update time and sublinear space. CoRR, abs/1509.06464, 2015. Google Scholar
  14. M. R. Henzinger and M. L. Fredman. Lower bounds for fully dynamic connectivity problems in graphs. Algorithmica, 22(3):351-362, 1998. Google Scholar
  15. M. R. Henzinger and V. King. Randomized fully dynamic graph algorithms with polylogarithmic time per operation. J. ACM, 46(4):502-516, 1999. Google Scholar
  16. M. R. Henzinger and M. Thorup. Sampling to provide or to bound: With applications to fully dynamic graph algorithms. J. Random Structures and Algs., 11(4):369-379, 1997. Google Scholar
  17. J. Holm, K. de Lichtenberg, and M. Thorup. Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity. J. ACM, 48(4):723-760, 2001. Google Scholar
  18. B. M. Kapron, V. King, and B. Mountjoy. Dynamic graph connectivity in polylogarithmic worst case time. In Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 1131-1142, 2013. Google Scholar
  19. P. B. Miltersen, S. Subramanian, J. S. Vitter, and R. Tamassia. Complexity models for incremental computation. Theoretical Computer Science, 130(1):203-236, 1994. Google Scholar
  20. M. Pǎtraşcu and E. Demaine. Logarithmic lower bounds in the cell-probe model. SIAM J. Comput., 35(4):932-963, 2006. Google Scholar
  21. M. Patrascu and M. Thorup. Don't rush into a union: take time to find your roots. In Proceedings of the 43rd ACM Symposium on Theory of Computing (STOC), pages 559-568, 2011. Technical report available as arXiv:1102.1783. Google Scholar
  22. D. D. Sleator and R. E. Tarjan. A data structure for dynamic trees. J. Comput. Syst. Sci., 26(3):362-391, 1983. Google Scholar
  23. R. E. Tarjan and R. F. Werneck. Self-adjusting top trees. In Proceedings 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 813-822, 2005. Google Scholar
  24. M. Thorup. Near-optimal fully-dynamic graph connectivity. In Proceedings 32nd ACM Symposium on Theory of Computing (STOC), pages 343-350, 2000. Google Scholar
  25. C. Wulff-Nilsen. Faster deterministic fully-dynamic graph connectivity. In Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 1757-1769, 2013. Google Scholar
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