Algorithmica

, Volume 74, Issue 1, pp 117–155 | Cite as

Convergecast and Broadcast by Power-Aware Mobile Agents

  • Julian Anaya
  • Jérémie Chalopin
  • Jurek Czyzowicz
  • Arnaud Labourel
  • Andrzej Pelc
  • Yann Vaxès
Article

Abstract

A set of identical, mobile agents is deployed in a weighted network. Each agent has a battery—a power source allowing it to move along network edges. An agent uses its battery proportionally to the distance traveled. We consider two tasks: convergecast, in which at the beginning, each agent has some initial piece of information, and information of all agents has to be collected by some agent; and broadcast in which information of one specified agent has to be made available to all other agents. In both tasks, the agents exchange the currently possessed information when they meet. The objective of this paper is to investigate what is the minimal value of power, initially available to all agents, so that convergecast or broadcast can be achieved. We study this question in the centralized and the distributed settings. In the centralized setting, there is a central monitor that schedules the moves of all agents. In the distributed setting every agent has to perform an algorithm being unaware of the network. In the centralized setting, we give a linear-time algorithm to compute the optimal battery power and the strategy using it, both for convergecast and for broadcast, when agents are on the line. We also show that finding the optimal battery power for convergecast or for broadcast is NP-hard for the class of trees. On the other hand, we give a polynomial algorithm that finds a 2-approximation for convergecast and a 4-approximation for broadcast, for arbitrary graphs.In the distributed setting, we give a 2-competitive algorithm for convergecast in trees and a 4-competitive algorithm for broadcast in trees. The competitive ratio of 2 is proved to be the best for the problem of convergecast, even if we only consider line networks. Indeed, we show that there is no (\(2-\epsilon \))-competitive algorithm for convergecast or for broadcast in the class of lines, for any \(\epsilon >0\).

Keywords

Convergecast Broadcast Mobile agent Power-aware Centralized algorithm Distributed algorithm Competitive ratio Graph 

References

  1. 1.
    Albers, S.: Energy-efficient algorithms. Commun. ACM 53(5), 86–96 (2010)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Albers, S., Henzinger, M.R.: Exploring unknown environments. In: Proceedings of the 29th Annual ACM Symposium on Theory of Computing (STOC), pp. 416–425 (1997)Google Scholar
  3. 3.
    Alpern, S., Gal, S.: The Theory of Search Games and Rendezvous, vol. 55. Springer, Berlin (2003)MATHGoogle Scholar
  4. 4.
    Ambühl, C.: An optimal bound for the mst algorithm to compute energy efficient broadcast trees in wireless networks. In: Proceedings of the International Colloquium on Automata, Languages, and Programming (ICALP), Lecture Notes in Computer Science, vol. 3580, pp. 1139–1150 (2005)Google Scholar
  5. 5.
    Ando, H., Oasa, Y., Suzuki, I., Yamashita, M.: Distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Trans. Robot. Autom. 15(5), 818–828 (1999)CrossRefGoogle Scholar
  6. 6.
    Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M., Peralta, R.: Computation in networks of passively mobile finite-state sensors. Distrib. Comput. 18(4), 235–253 (2006)MATHCrossRefGoogle Scholar
  7. 7.
    Annamalai, V., Gupta, S., Schwiebert, L.: On tree-based convergecasting in wireless sensor networks. IEEE Wirel. Commun. Netw. 3, 1942–1947 (2003)Google Scholar
  8. 8.
    Augustine, J., Irani, S., Swamy, C.: Optimal power-down strategies. In: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 530–539 (2004)Google Scholar
  9. 9.
    Averbakh, I., Berman, O.: A heuristic with worst-case analysis for minimax routing of two travelling salesmen on a tree. Discrete Appl. Math. 68(1–2), 17–32 (1996)MATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Awerbuch, B., Betke, M., Rivest, R.L., Singh, M.: Piecemeal graph exploration by a mobile robot. Inf. Comput. 152(2), 155–172 (1999)MATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Awerbuch, B., Goldreich, O., Vainish, R., Peleg, D.: A trade-off between information and communication in broadcast protocols. J. ACM 37(2), 238–256 (1990)MATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Azar, Y.: On-line load balancing. In: Fiat A., Woeginger G. (eds.) Online Algorithms Lecture notes in Computer Science, vol. 1442, pp. 178–195 (1998)Google Scholar
  13. 13.
    Baezayates, R., Culberson, J., Rawlins, G.: Searching in the plane. Inf. Comput. 106(2), 234–252 (1993)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Bar-Yehuda, R., Goldreich, O., Itai, A.: On the time-complexity of broadcast in multi-hop radio networks: an exponential gap between determinism and randomization. J. Comput. Syst. Sci. 45(1), 104–126 (1992)MATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Bender, M., Slonim, D.: The power of team exploration: two robots can learn unlabeled directed graphs. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science (FOCS), pp. 75–85 (1994)Google Scholar
  16. 16.
    Bender, M.A., Fernández, A., Ron, D., Sahai, A., Vadhan, S.: The power of a pebble: exploring and mapping directed graphs. Inf. Comput. 176(1), 1–21 (2002)MATHCrossRefGoogle Scholar
  17. 17.
    Betke, M., Rivest, R., Singh, M.: Piecemeal learning of an unknown environment. Mach. Learn. 18(2–3), 231–254 (1995)Google Scholar
  18. 18.
    Blum, A., Raghavan, P., Schieber, B.: Navigating in unfamiliar geometric terrain. SIAM J. Comput. 26(1), 110–137 (1997)MATHMathSciNetCrossRefGoogle Scholar
  19. 19.
    Bunde, D.: Power-aware scheduling for makespan and flow. J. Sched. 12(5), 489–500 (2009)MATHMathSciNetCrossRefGoogle Scholar
  20. 20.
    Chen, F., Johnson, M., Alayev, Y., Bar-Noy, A., La Porta, T.: Who, when, where: timeslot assignment to mobile clients. IEEE Trans. Mob. Comput. 11(1), 73–85 (2012)CrossRefGoogle Scholar
  21. 21.
    Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Solving the robots gathering problem. In: Proceedings of the International Colloquium of Automata. Languages and Programming (ICALP), Lecture Notes in Computer Science, vol. 2719 pp. 1181–1196. Springer, Berlin (2003)Google Scholar
  22. 22.
    Cohen, R., Peleg, D.: Convergence properties of the gravitational algorithm in asynchronous robot systems. SIAM J. Comput. 34(6), 1516–1528 (2005)MATHMathSciNetCrossRefGoogle Scholar
  23. 23.
    Cord-Landwehr, A., Degener, B., Fischer, M., Hüllmann, M., Kempkes, B., Klaas, A., Kling, P., Kurras, S., Märtens, M., Meyer auf der Heide, F., Raupach, C., Swierkot, K., Warner, D., Weddemann, C., Wonisch, D.: A new approach for analyzing convergence algorithms for mobile robots. In: Aceto L., Henzinger M., Sgall J. (eds.) Proceedings of the International Colloquium of Automata, Languages and Programming (ICALP), Lecture Notes in Computer Science, vol. 6756 pp. 650–661 (2011)Google Scholar
  24. 24.
    Das, S., Flocchini, P., Santoro, N., Yamashita, M.: On the computational power of oblivious robots: forming a series of geometric patterns. In: Proceedings of the 29th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC), pp. 267–276 (2010)Google Scholar
  25. 25.
    Deng, X., Papadimitriou, C.H.: Exploring an unknown graph. J. Graph Theory 32(3), 265–297 (1999)MATHMathSciNetCrossRefGoogle Scholar
  26. 26.
    Dynia, M., Korzeniowski, M., Schindelhauer, C.: Power-aware collective tree exploration. In: Architecture of Computing Systems (ARCS), Lecture Notes in Computer Science, vol. 3894, pp. 341–351 (2006)Google Scholar
  27. 27.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of asynchronous robots with limited visibility. Theor. Comput. Sci. 337(1–3), 147–168 (2005)MATHMathSciNetCrossRefGoogle Scholar
  28. 28.
    Fraigniaud, P., Gasieniec, L., Kowalski, D.R., Pelc, A.: Collective tree exploration. Networks 48(3), 166–177 (2006)MATHMathSciNetCrossRefGoogle Scholar
  29. 29.
    Frederickson, G., Hecht, M., Kim, C.: Approximation algorithms for some routing problems. SIAM J. Comput. 7(2), 178–193 (1978)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)MATHGoogle Scholar
  31. 31.
    Irani, S., Shukla, S., Gupta, R.: Algorithms for power savings. ACM Trans. Algorithms 3(4), 41 (2007)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Kesselman, A., Kowalski, D.R.: Fast distributed algorithm for convergecast in ad hoc geometric radio networks. J. Parallel Distrib. Comput. 66(4):578–585, 2006. Algorithms for Wireless and Ad-Hoc NetworksGoogle Scholar
  33. 33.
    Krishnamachari, B., Estrin, D., Wicker, S.: The impact of data aggregation in wireless sensor networks. In: Proceedings of the 22nd International Conference on Distributed Computing Systems Workshops, pp. 575–578 (2002)Google Scholar
  34. 34.
    Megow, N., Mehlhorn, K., Schweitzer, P.: Online graph exploration: new results on old and new algorithms. Theor. Comput. Sci. 463, 62–72 (2012)MATHMathSciNetCrossRefGoogle Scholar
  35. 35.
    Rajagopalan, R., Varshney, P.: Data-aggregation techniques in sensor networks: a survey. IEEE Commun. Surv. Tutor. 8(4), 48–63 (2006)CrossRefGoogle Scholar
  36. 36.
    Santoro, N.: Design and Analysis of Distributed Algorithms, vol. 56. Wiley, New York (2006)CrossRefGoogle Scholar
  37. 37.
    Stojmenovic, I., Lin, X.: Power-aware localized routing in wireless networks. IEEE Trans. Parallel Distrib. Syst. 12(11), 1122–1133 (2001)CrossRefGoogle Scholar
  38. 38.
    Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)MATHMathSciNetCrossRefGoogle Scholar
  39. 39.
    Yamashita, M., Suzuki, I.: Characterizing geometric patterns formable by oblivious anonymous mobile robots. Theor. Comput. Sci. 411(26–28), 2433–2453 (2010)MATHMathSciNetCrossRefGoogle Scholar
  40. 40.
    Yao, F., Demers, A., Shenker, S.: A scheduling model for reduced cpu energy. In: Proceedings of the 36th Annual Symposium on Foundations of Computer Science, pp. 374–382 (1995)Google Scholar

Copyright information

© European Union 2014

Authors and Affiliations

  • Julian Anaya
    • 1
  • Jérémie Chalopin
    • 2
  • Jurek Czyzowicz
    • 1
  • Arnaud Labourel
    • 2
  • Andrzej Pelc
    • 1
  • Yann Vaxès
    • 2
  1. 1.Université du Québec en OutaouaisGatineauCanada
  2. 2.LIFCNRS & Aix-Marseille UniversityMarseilleFrance

Personalised recommendations