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Multiple Source Dual Fault Tolerant BFS Trees

Authors Manoj Gupta, Shahbaz Khan



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Manoj Gupta
Shahbaz Khan

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Manoj Gupta and Shahbaz Khan. Multiple Source Dual Fault Tolerant BFS Trees. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 127:1-127:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.ICALP.2017.127

Abstract

Let G=(V,E) be a graph with n vertices and m edges, with a designated set of sigma sources S subseteq V. The fault tolerant subgraph for any graph problem maintains a sparse subgraph H=(V,E') of G with E' subseteq E, such that for any set F of k failures, the solution for the graph problem on G\F is maintained in its subgraph H\F. We address the problem of maintaining a fault tolerant subgraph for computing Breath First Search tree (BFS) of the graph from a single source s in V (referred as k FT-BFS) or multiple sources S subseteq V (referred as k FT-MBFS). We simply refer to them as FT-BFS (or FT-MBFS) for k=1, and dual FT-BFS (or dual FT-MBFS) for k=2. The problem of k FT-BFS was first studied by Parter and Peleg [ESA13]. They designed an algorithm to compute FT-BFS subgraph of size O(n^{3/2}). Further, they showed how their algorithm can be easily extended to FT-MBFS requiring O(sigma^{1/2}n^{3/2}) space. They also presented matching lower bounds for these results. The result was later extended to solve dual FT-BFS by Parter [PODC15] requiring (n^{5/3}) space, again with matching lower bounds. However, their result was limited to only edge failures in undirected graphs and involved very complex analysis. Moreover, their solution doesn't seems to be directly extendible for dual FT-MBFS problem. We present a similar algorithm to solve dual FT-BFS problem with a much simpler analysis. Moreover, our algorithm also works for vertex failures and directed graphs, and can be easily extended to handle dual FT-MBFS problem, matching the lower bound of O(sigma^{1/3}n^{5/3}) space described by Parter [PODC15]. The key difference in our approach is a much simpler classification of path interactions which formed the basis of the analysis by Parter [PODC15].
Keywords
  • BFS
  • fault-tolerant
  • graph
  • algorithms
  • data-structures

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References

  1. Surender Baswana, Shreejit Ray Chaudhury, Keerti Choudhary, and Shahbaz Khan. Dynamic DFS in Undirected Graphs: breaking the O(m) barrier. In Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016, Arlington, VA, USA, January 10-12, 2016, pages 730-739, 2016. Google Scholar
  2. Surender Baswana, Keerti Choudhary, and Liam Roditty. Fault tolerant reachability for directed graphs. In Distributed Computing - 29th International Symposium, DISC 2015, Tokyo, Japan, October 7-9, 2015, Proceedings, pages 528-543, 2015. Google Scholar
  3. Surender Baswana, Keerti Choudhary, and Liam Roditty. Fault tolerant subgraph for single source reachability: generic and optimal. In Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016, Cambridge, MA, USA, June 18-21, 2016, pages 509-518, 2016. Google Scholar
  4. Davide Bilò, Fabrizio Grandoni, Luciano Gualà, Stefano Leucci, and Guido Proietti. Improved purely additive fault-tolerant spanners. In Algorithms - ESA 2015 - 23rd Annual European Symposium, Patras, Greece, September 14-16, 2015, Proceedings, pages 167-178, 2015. Google Scholar
  5. Davide Bilò, Luciano Gualà, Stefano Leucci, and Guido Proietti. Multiple-edge-fault-tolerant approximate shortest-path trees. In 33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016, February 17-20, 2016, Orléans, France, pages 18:1-18:14, 2016. Google Scholar
  6. Gilad Braunschvig, Shiri Chechik, David Peleg, and Adam Sealfon. Fault tolerant additive and (μ, α)-spanners. Theor. Comput. Sci., 580:94-100, 2015. Google Scholar
  7. Shiri Chechik, Michael Langberg, David Peleg, and Liam Roditty. Fault Tolerant Spanners for General Graphs. SIAM J. Comput., 39(7):3403-3423, 2010. URL: http://dx.doi.org/10.1137/090758039.
  8. Camil Demetrescu, Mikkel Thorup, Rezaul Alam Chowdhury, and Vijaya Ramachandran. Oracles for distances avoiding a failed node or link. SIAM J. Comput., 37(5):1299-1318, 2008. Google Scholar
  9. Michael Dinitz and Robert Krauthgamer. Fault-tolerant spanners: better and simpler. In Proceedings of the 30th Annual ACM Symposium on Principles of Distributed Computing, PODC 2011, San Jose, CA, USA, June 6-8, 2011, pages 169-178, 2011. URL: http://dx.doi.org/10.1145/1993806.1993830.
  10. Ran Duan and Seth Pettie. Dual-failure distance and connectivity oracles. In Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2009, New York, NY, USA, January 4-6, 2009, pages 506-515, 2009. Google Scholar
  11. Manoj Gupta and Shahbaz Khan. Multiple Source Dual Fault Tolerant BFS Trees. CoRR, abs/1704.06907, 2017. Google Scholar
  12. Neelesh Khanna and Surender Baswana. Approximate shortest paths avoiding a failed vertex: Optimal size data structures for unweighted graphs. In 27th International Symposium on Theoretical Aspects of Computer Science, STACS 2010, March 4-6, 2010, Nancy, France, pages 513-524, 2010. Google Scholar
  13. Thomas Lengauer and Robert Endre Tarjan. A fast algorithm for finding dominators in a flowgraph. ACM Trans. Program. Lang. Syst., 1(1):121-141, 1979. Google Scholar
  14. Merav Parter. Vertex Fault Tolerant Additive Spanners. In Distributed Computing - 28th International Symposium, DISC 2014, Austin, TX, USA, October 12-15, 2014. Proceedings, pages 167-181, 2014. Google Scholar
  15. Merav Parter. Dual failure resilient BFS structure. In Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing, PODC 2015, Donostia-San Sebastián, Spain, July 21 - 23, 2015, pages 481-490, 2015. Google Scholar
  16. Merav Parter and David Peleg. Sparse fault-tolerant BFS trees. In Algorithms - ESA 2013 - 21st Annual European Symposium, Sophia Antipolis, France, September 2-4, 2013. Proceedings, pages 779-790, 2013. Google Scholar
  17. Merav Parter and David Peleg. Fault tolerant approximate BFS structures. In Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014, Portland, Oregon, USA, January 5-7, 2014, pages 1073-1092, 2014. Google Scholar
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