Abstract
The basic primitive for a mobile agent is the ability to visit all the nodes of the graph in a systematic manner. This chapter considers the exploration of unknown graphs in full detail, for the specific mobile agent model considered in this book. The graph is considered to be finite, undirected and connected. Other than this fact, no prior knowledge of the graph is assumed. Several exploration techniques are introduced and explained for either a single agent, or multiple agents, exploring either labelled or unlabelled graphs. We focus on the efficiency of exploration and consider three different complexity measures, the time taken, the amount of memory used by the agents and the storage needed at each node of the graph. For exploration by multiple agents, we consider collaborative exploration by a team of colocated agents as well as distributed exploration by agents scattered in a graph. The concluding section presents some brief ideas and references on more advanced topics on graph exploration that are not covered in this chapter.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
Note that since this is not a proper port labelling, the algorithm should have a default action of traversing port number 0 whenever there is no edge with the required port number.
References
Awerbuch, B., Betke, M., Singh, M.: Piecemeal graph learning by a mobile robot. Inf. Comput. 152, 155–172 (1999)
Bampas, E., Chalopin, J., Das, S., Hackfeld, J., Karousatou, C.: Maximal exploration of trees with energy-constrained agents. CoRR, abs/1802.06636 (2018)
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)
Becha, H., Flocchini, P.: Optimal construction of sense of direction in a torus by a mobile agent. Int. J. Found. Comput. Sci. 18(3), 529–546 (2007)
Bender, M., Fernandez, A., Ron, D., Sahai, A., Vadhan, S.: The power of a pebble: exploring and mapping directed graphs. In: Proceedings of the 30th ACM Symposium on Theory of Computing (STOC 1998), pp. 269–287 (1998)
Blum, M., Kozen, D.: On the power of the compass (or, why mazes are easier to search than graphs). In: 19th Symposium on Foundations of Computer Science (FOCS 1978), pp. 132–142 (1978)
Brass, P., Cabrera-Mora, F., Gasparri, A., Xiao, J.: Multirobot tree and graph exploration. IEEE Trans. Robot. 27(4), 707–717 (2011)
Budach, L.: Automata and labyrinths. Math. Nachrichten 86, 195–282 (1978)
Chalopin, J., Das, S., Kosowski, A.: Constructing a map of an anonymous graph: applications of universal sequences. In: Lu, C., Masuzawa, T., Mosbah, M. (eds.) OPODIS 2010. LNCS, vol. 6490, pp. 119–134. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17653-1_10
Chalopin, J., Das, S., Santoro, N.: Rendezvous of mobile agents in unknown graphs with faulty links. In: Proceedings of 21st International Symposium on Distributed Computing (DISC), pp. 108–122 (2007)
Cohen, R., Fraigniaud, P., Ilcinkas, D., Korman, A., Peleg, D.: Label-guided graph exploration by a finite automaton. ACM Trans. Algorithms 4(4), 42:1–42:18 (2008)
Czyzowicz, J., Dereniowski, D., Gasieniec, L., Klasing, R., Kosowski, A., Pajak, D.: Collision-free network exploration. J. Comput. Syst. Sci. 86, 70–81 (2017)
Czyzowicz, J., et al.: More efficient periodic traversal in anonymous undirected graphs. Theor. Comput. Sci. 444, 60–76 (2012)
Czyzowicz, J., Kosowski, A., Pelc, A.: How to meet when you forget: log-space rendezvous in arbitrary graphs. Distrib. Comput. 25(2), 165–178 (2012)
Das, S., Dereniowski, D., Karousatou, C.: Collaborative exploration of trees by energy-constrained mobile robots. Theory Comput. Syst. 62(5), 1223–1240 (2018)
Das, S., Dereniowski, D., Uznanski, P.: Energy constrained depth first search. CoRR, abs/1709.10146 (2017)
Das, S., Flocchini, P., Kutten, S., Nayak, A., Santoro, N.: Map construction of unknown graphs by multiple agents. Theor. Comput. Sci. 385(1–3), 34–48 (2007)
Das, S., Flocchini, P., Nayak, A., Santoro, N.: Effective elections for anonymous mobile agents. In: Asano, T. (ed.) ISAAC 2006. LNCS, vol. 4288, pp. 732–743. Springer, Heidelberg (2006). https://doi.org/10.1007/11940128_73
Das, S., Mihalák, M., Šrámek, R., Vicari, E., Widmayer, P.: Rendezvous of mobile agents when tokens fail anytime. In: Baker, T.P., Bui, A., Tixeuil, S. (eds.) OPODIS 2008. LNCS, vol. 5401, pp. 463–480. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-92221-6_29
Deng, X., Papadimitriou, C.H.: Exploring an unknown graph. J. Graph Theory 32(3), 265–297 (1999)
Dereniowski, D., Disser, Y., Kosowski, A., Pajak, D., Uznański, P.: Fast collaborative graph exploration. Inf. Comput. 243, 37–49 (2015)
Dieudonne, Y., Pelc, A., Peleg, D.: Gathering despite mischief. ACM Trans. Algorithms 11(1), 1 (2014)
Diks, K., Fraigniaud, P., Kranakis, E., Pelc, A.: Tree exploration with little memory. J. Algorithms 51, 38–63 (2004)
Disser, Y., Hackfeld, J., Klimm, M.: Undirected graph exploration with \((\log \log n)\) pebbles. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 25–39 (2016)
Dobrev, S., Flocchini, P., Kralovic, R., Ruzicka, P., Prencipe, G., Santoro, N.: Black hole search in common interconnection networks. Networks 47(2), 61–71 (2006)
Duncan, C.A., Kobourov, S.G., Kumar, V.S.A.: Optimal constrained graph exploration. In: 12th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 807–814 (2001)
Dynia, M., Łopuszański, J., Schindelhauer, C.: Why robots need maps. In: Prencipe, G., Zaks, S. (eds.) SIROCCO 2007. LNCS, vol. 4474, pp. 41–50. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72951-8_5
Flocchini, P., Huang, M.J., Luccio, F.L.: Decontamination of hypercubes by mobile agents. Networks 52(3), 167–178 (2008)
Fraigniaud, P., Gasieniec, L., Kowalski, D., Pelc, A.: Collective tree exploration. Networks 48(3), 166–177 (2006)
Fraigniaud, P., Ilcinkas, D., Peer, G., Pelc, A., Peleg, D.: Graph exploration by a finite automaton. Theor. Comput. Sci. 345(2–3), 331–344 (2005)
Kosowski, A., Navarra, A.: Graph decomposition for memoryless periodic exploration. Algorithmica 63(1–2), 26–38 (2012)
Menc, A., Pajak, D., Uznanski, P.: Time and space optimality of rotor-router graph exploration. Inf. Process. Lett. 127, 17–20 (2017)
Ortolf, C., Schindelhauer, C.: Online multi-robot exploration of grid graphs with rectangular obstacles. In: 24th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 27–36 (2012)
Panaite, P., Pelc, A.: Exploring unknown undirected graphs. J. Algorithms 33, 281–295 (1999)
Reingold, O.: Undirected connectivity in log-space. J. ACM 55(4), 17:1–17:24 (2008)
Rollik, H.A.: Automaten in planaren graphen. Acta Informatica 13(3), 287–298 (1980)
Shannon, C.E.: Presentation of a maze-solving machine. In: 8th Conference of the Josiah Macy Jr. Found. (Cybernetics), pp. 173–180 (1951)
Tarjan, R.: Depth first search and linear graph algorithms. SIAM J. Comput. 1(2), 146–160 (1972)
Yamashita, M., Kameda, T.: Computing on anonymous networks: part i-characterizing the solvable cases. IEEE Trans. Parallel Distrib. Syst. 7(1), 69–89 (1996)
Yanovski, V., Wagner, I.A., Bruckstein, A.M.: A distributed ant algorithm for efficiently patrolling a network. Algorithmica 37(3), 165–186 (2003)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Das, S. (2019). Graph Explorations with Mobile Agents. In: Flocchini, P., Prencipe, G., Santoro, N. (eds) Distributed Computing by Mobile Entities. Lecture Notes in Computer Science(), vol 11340. Springer, Cham. https://doi.org/10.1007/978-3-030-11072-7_16
Download citation
DOI: https://doi.org/10.1007/978-3-030-11072-7_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-11071-0
Online ISBN: 978-3-030-11072-7
eBook Packages: Computer ScienceComputer Science (R0)