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Efficient Labeling for Reachability in Directed Acyclic Graphs

Authors Maciej Dulęba, Paweł Gawrychowski, Wojciech Janczewski

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ACM Subject Classification
  • Theory of computation → Data structures design and analysis
Keywords
  • informative labeling scheme
  • reachability
  • DAG

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Abstract

We consider labeling nodes of a directed graph for reachability queries. A reachability labeling scheme for such a graph assigns a binary string, called a label, to each node. Then, given the labels of nodes u and v and no other information about the underlying graph, it should be possible to determine whether there exists a directed path from u to v. By a simple information theoretical argument and invoking the bound on the number of partial orders, in any scheme some labels need to consist of at least n/4 bits, where n is the number of nodes. On the other hand, it is not hard to design a scheme with labels consisting of n/2+𝒪(log n) bits. In the classical centralised setting, where a single data structure is stored as a whole, Munro and Nicholson designed a structure for reachability queries consisting of n²/4+o(n²) bits (which is optimal, up to the lower order term). We extend their approach to obtain a scheme with labels consisting of n/3+o(n) bits.

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Maciej Dulęba, Paweł Gawrychowski, and Wojciech Janczewski. Efficient Labeling for Reachability in Directed Acyclic Graphs. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 27:1-27:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ISAAC.2020.27

Author Details

Maciej Dulęba
  • Institute of Computer Science, University of Wrocław, Poland
Paweł Gawrychowski
  • Institute of Computer Science, University of Wrocław, Poland
Wojciech Janczewski
  • Institute of Computer Science, University of Wrocław, Poland

References

  1. Noga Alon. Asymptotically optimal induced universal graph. Geometric and Functional Analysis, 27(1):1-32, 2017. Google Scholar
  2. Noga Alon and Rajko Nenadov. Optimal induced universal graphs for bounded-degree graphs. In 28th SODA, pages 1149-1157, 2017. Google Scholar
  3. Stephen Alstrup, Philip Bille, and Theis Rauhe. Labeling schemes for small distances in trees. SIAM Journal on Discrete Mathematics, 19(2):448-462, 2005. Google Scholar
  4. Stephen Alstrup, Søren Dahlgaard, and Mathias Bæk Tejs Knudsen. Optimal induced universal graphs and adjacency labeling for trees. In 56th FOCS, pages 1311-1326, 2015. Google Scholar
  5. Stephen Alstrup, Søren Dahlgaard, Mathias Bæk Tejs Knudsen, and Ely Porat. Sublinear distance labeling. In 24th ESA, pages 5:1-5:15, 2016. Google Scholar
  6. Stephen Alstrup, Esben Bistrup Halvorsen, and Kasper Green Larsen. Near-optimal labeling schemes for nearest common ancestors. In 25th SODA, pages 972-982, 2014. Google Scholar
  7. Stephen Alstrup, Haim Kaplan, Mikkel Thorup, and Uri Zwick. Adjacency labeling schemes and induced-universal graphs. In 47th STOC, pages 625-634. ACM, 2015. Google Scholar
  8. Marthe Bonamy, Cyril Gavoille, and Michal Pilipczuk. Shorter labeling schemes for planar graphs. In 31st SODA, pages 446-462, 2020. Google Scholar
  9. Vida Dujmovic, Louis Esperet, Gwenaël Joret, Cyril Gavoille, Piotr Micek, and Pat Morin. Adjacency labelling for planar graphs (and beyond). CoRR, abs/2003.04280, 2020. URL: http://arxiv.org/abs/2003.04280.
  10. Tomás Feder and Rajeev Motwani. Clique partitions, graph compression and speeding-up algorithms. In 23rd STOC, pages 123-133, 1991. Google Scholar
  11. Ofer Freedman, Paweł Gawrychowski, Patrick K. Nicholson, and Oren Weimann. Optimal distance labeling schemes for trees. In 36th PODC, pages 185-194, 2017. Google Scholar
  12. Cyril Gavoille, Michal Katz, Nir A. Katz, Christophe Paul, and David Peleg. Approximate distance labeling schemes. In 9th ESA, pages 476-487, 2001. Google Scholar
  13. Cyril Gavoille, David Peleg, Stéphane Pérennès, and Ran Raz. Distance labeling in graphs. In 12th SODA, pages 210-219, 2001. Google Scholar
  14. Paweł Gawrychowski, Adrian Kosowski, and Przemysław Uznański. Sublinear-space distance labeling using hubs. In 30th DISC, pages 230-242, 2016. Google Scholar
  15. Paweł Gawrychowski, Fabian Kuhn, Jakub Łopuszański, Konstantinos Panagiotou, and Pascal Su. Labeling schemes for nearest common ancestors through minor-universal trees. In 29th SODA, pages 2604-2619, 2018. Google Scholar
  16. Torben Hagerup, Peter Bro Miltersen, and Rasmus Pagh. Deterministic dictionaries. Journal of Algorithms, 41(1):69-85, 2001. Google Scholar
  17. Sampath Kannan, Moni Naor, and Steven Rudich. Implicit representation of graphs. SIAM Journal on Discrete Mathematics, 5(4):596-603, 1992. Google Scholar
  18. Michal Katz, Nir A. Katz, Amos Korman, and David Peleg. Labeling schemes for flow and connectivity. SIAM J. Comput., 34(1):23-40, 2004. Google Scholar
  19. D.J. Kleitman and B. L. Rothschild. The number of finite topologies. Proceedings of the American Mathematical Society, 25:276-282, 1970. Google Scholar
  20. Amos Korman. Labeling schemes for vertex connectivity. ACM Trans. Algorithms, 6(2):39:1-39:10, 2010. Google Scholar
  21. Adrian Kosowski, Przemysław Uznański, and Laurent Viennot. Hardness of exact distance queries in sparse graphs through hub labeling. In 38th PODC, pages 272-279, 2019. Google Scholar
  22. J. W. Moon. On minimal n-universal graphs. Proceedings of the Glasgow Mathematical Association, 7(1):32–33, 1965. Google Scholar
  23. D. Mubay and G. Turan. Finding bipartite subgraphs efficiently. Information Processing Letters, 110(5):174-177, 2010. Google Scholar
  24. J. Ian Munro and Patrick K. Nicholson. Succinct posets. Algorithmica, 76(2):445-473, 2016. Google Scholar
  25. David Peleg. Informative labeling schemes for graphs. Theor. Comput. Sci., 340(3):577-593, 2005. Google Scholar
  26. Noy Galil Rotbart. New Ideas on Labeling Schemes. PhD thesis, University of Copenhagen, 2016. Google Scholar
  27. Mikkel Thorup and Uri Zwick. Compact routing schemes. In 13th SPAA, pages 1-10, 2001. Google Scholar
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