On Sense of Direction and Mobile Agents

  • Paola FlocchiniEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11639)


An edge-labeled graph is said to have Sense of Direction if the labeling satisfies a particular set of global consistency properties. When the graph represents a system of communicating entities, the presence of sense of direction has been shown to have a strong impact on computability and complexity.

Since its introduction, sense of direction has been investigated from various view points, revealing interesting graph theoretical properties and providing useful tools for the design of efficient distributed algorithms; furthermore, its presence allows to solve some otherwise unsolvable problems.

Far from being exhausted, the study of sense of direction and other consistency properties of edge-labeled graphs is still filled with interesting questions, open problems, and important new research directions.

In this paper, we revisit sense of direction reviewing the main results in the context of message passing point-to-point models, showing its impact in the more recent mobile agents models, and indicating directions for future study.


  1. 1.
    Angluin, D.: Local and global properties in networks of processors. In: Proceedings of 12th ACM Symposium on Theory of Computing, pp. 82–93 (1980)Google Scholar
  2. 2.
    Attiya, H., van Leeuwen, J., Santoro, N., Zaks, S.: Efficient elections in chordal ring networks. Algorithmica 4, 437–446 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Barrière, L., Flocchini, P., Fraigniaud, P., Santoro, N.: Rendezvous and election of mobile agents: impact of sense of direction. Theory Comput. Syst. 40(2), 143–162 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Boldi, P., Vigna, S.: Minimal sense of direction and decision problems for Cayley graphs. Inf. Process. Lett. 64, 299–303 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Boldi, P., Vigna, S.: On the complexity of deciding sense of direction. SIAM J. Comput. 29(3), 779–789 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Boldi, P., Vigna, S.: Lower bounds for sense of direction in regular graphs. Distrib. Comput. 16(4), 279–286 (2003)zbMATHCrossRefGoogle Scholar
  7. 7.
    Boldi, P., Vigna, S.: Lower bounds for weak sense of direction. J. Discret. Algorithms 1(2), 119–128 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Borowiecki, P., Dereniowski, D., Kuszner, L.: Distributed graph searching with a sense of direction. Distrib. Comput. 155(3), 155–170 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Chalopin, J., Das, S., Labourel, A., Markou, E.: Black hole search with finite automata scattered in a synchronous torus. In: Peleg, D. (ed.) DISC 2011. LNCS, vol. 6950, pp. 432–446. Springer, Heidelberg (2011). Scholar
  10. 10.
    Cheng, C., Suzuki, I.: Weak sense of direction labelings and graph embeddings. Discret. Appl. Math. 159(5), 303–310 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Das, S., Santoro, N.: Moving and computing models: agents. In: Flocchini, P., Prencipe, G., Santoro, N. (eds.) Distributed Computing by Mobile Entities, pp. 15–34. Springer, Cham (2019). Scholar
  12. 12.
    Dobrev, S.: Leader election using any sense of direction. In: Proceedings of 6th International Colloquium on Structural Information and Communication Complexity (SIROCCO), pp. 93–104 (1999)Google Scholar
  13. 13.
    Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: Searching for a black hole in arbitrary networks: optimal mobile agent protocols. Distrib. Comput. 19(1), 1–19 (2006)zbMATHCrossRefGoogle Scholar
  14. 14.
    Dobrev, S., Královic, R., Santoro, N.: On the cost of waking up. Int. J. Netw. Comput. 7(2), 336–348 (2017)CrossRefGoogle Scholar
  15. 15.
    Flocchini, P.: Minimal sense of direction in regular networks. Inf. Process. Lett. 61, 331–338 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Flocchini, P., Huang, M., Luccio, F.L.: Decontamination of hypercubes by mobile agents. Networks 52(3), 167–178 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Flocchini, P., Luccio, F., Pagli, L., Santoro, N.: Network decontamination under m-immunity. Discret. Appl. Math. 201, 114–129 (2016)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Flocchini, P., Mans, B.: Optimal election in labeled hypercubes. J. Parallel Distrib. Comput. 33(1), 76–83 (1996)CrossRefGoogle Scholar
  19. 19.
    Flocchini, P., Mans, B., Santoro, N.: On the impact of sense of direction on message complexity. Inf. Process. Lett. 63(1), 23–31 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Flocchini, P., Mans, B., Santoro, N.: Sense of direction: definition, properties and classes. Networks 32(3), 165–180 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Flocchini, P., Mans, B., Santoro, N.: Sense of direction in distributed computing. Theor. Comput. Sci. 291(1), 29–53 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Flocchini, P., Roncato, A., Santoro, N.: Symmetries and sense of direction in labeled graphs. Discret. Appl. Math. 87, 99–115 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Flocchini, P., Roncato, A., Santoro, N.: Backward consistency and sense of direction in advanced distributed systems. SIAM J. Comput. 32(2), 281–306 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Flocchini, P., Roncato, A., Santoro, N.: Computing on anonymous networks with sense of direction. Theor. Comput. Sci. 301(1–3), 355–379 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Flocchini, P., Santoro, N.: Topological constraints for sense of direction. Int. J. Found. Comput. Sci. 9(2), 179–198 (1998)zbMATHCrossRefGoogle Scholar
  26. 26.
    Foldes, S., Urrutia, J.: Sense of direction, semigroups, and Cayley graphs. Manuscript (1998)Google Scholar
  27. 27.
    Hanusse, N., Ilcinkas, D., Kosowski, A., Nisse, N.: Locating a target with an agent guided by unreliable local advice: how to beat the random walk when you have a clock? In: Proceedings of 29th ACM Symposium on Principles of Distributed Computing (PODC), pp. 355–364 (2010)Google Scholar
  28. 28.
    Ilcinkas, D.: Setting port numbers for fast graph exploration. Theor. Comput. Sci 401(1–3), 236–242 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  29. 29.
    Kranakis, E., Krizanc, D., Markou, E.: Deterministic symmetric rendezvous with tokens in a synchronous torus. Discret. Appl. Math. 159(9), 896–923 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Leão, R.S.C., Barbosa, V.C.: Minimal chordal sense of direction and circulant graphs. In: Královič, R., Urzyczyn, P. (eds.) MFCS 2006. LNCS, vol. 4162, pp. 670–680. Springer, Heidelberg (2006). Scholar
  31. 31.
    Loui, M., Matsushita, T., West, D.: Election in complete networks with a sense of direction. Inf. Process. Lett. 22, 185–187 (1986)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Markou, E., Shi, W.: Dangerous graphs. In: Flocchini, P., Prencipe, G., Santoro, N. (eds.) Distributed Computing by Mobile Entities, vol. 11340, pp. 455–515. Springer, Cham (2019). Scholar
  33. 33.
    Pan, Y.: A near-optimal multi-stage distributed algorithm for finding leaders in clustered chordal rings. Inf. Sci. 76(1–2), 131–140 (1994)zbMATHCrossRefGoogle Scholar
  34. 34.
    Robbins, S., Robbins, K.: Choosing a leader on a hypercube. In: Proceedings of International Conference on Databases, Parallel Architectures and their Applications, pp. 469–471 (1990)Google Scholar
  35. 35.
    Singh, G.: Efficient leader election using sense of direction. Distrib. Comput. 10, 159–165 (1997)CrossRefGoogle Scholar
  36. 36.
    Tel, G.: Linear election in hypercubes. Parallel Proc. Lett. 5(1), 357–366 (1995)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Tel, G.: Sense of direction in processor networks. In: Bartosek, M., Staudek, J., Wiedermann, J. (eds.) SOFSEM 1995. LNCS, vol. 1012, pp. 50–82. Springer, Heidelberg (1995). Scholar
  38. 38.
    Yamashita, M., Kameda, T.: Computing on anonymous networks, part I: characterizing the solvable cases. IEEE Trans. Parallel Distrib. Comput. 7(1), 69–89 (1996)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of OttawaOttawaCanada

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