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Convergecast and Broadcast by Power-Aware Mobile Agents

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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 \(\epsilon >0\).

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References

  1. Albers, S.: Energy-efficient algorithms. Commun. ACM 53(5), 86–96 (2010)

    Article  MathSciNet  Google Scholar 

  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)

  3. Alpern, S., Gal, S.: The Theory of Search Games and Rendezvous, vol. 55. Springer, Berlin (2003)

    MATH  Google Scholar 

  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)

  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)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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. 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)

  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)

    Article  MATH  MathSciNet  Google Scholar 

  10. Awerbuch, B., Betke, M., Rivest, R.L., Singh, M.: Piecemeal graph exploration by a mobile robot. Inf. Comput. 152(2), 155–172 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

  13. Baezayates, R., Culberson, J., Rawlins, G.: Searching in the plane. Inf. Comput. 106(2), 234–252 (1993)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

  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)

    Article  MATH  Google Scholar 

  17. Betke, M., Rivest, R., Singh, M.: Piecemeal learning of an unknown environment. Mach. Learn. 18(2–3), 231–254 (1995)

    Google Scholar 

  18. Blum, A., Raghavan, P., Schieber, B.: Navigating in unfamiliar geometric terrain. SIAM J. Comput. 26(1), 110–137 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  19. Bunde, D.: Power-aware scheduling for makespan and flow. J. Sched. 12(5), 489–500 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

  22. Cohen, R., Peleg, D.: Convergence properties of the gravitational algorithm in asynchronous robot systems. SIAM J. Comput. 34(6), 1516–1528 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  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)

  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)

  25. Deng, X., Papadimitriou, C.H.: Exploring an unknown graph. J. Graph Theory 32(3), 265–297 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  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)

  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)

    Article  MATH  MathSciNet  Google Scholar 

  28. Fraigniaud, P., Gasieniec, L., Kowalski, D.R., Pelc, A.: Collective tree exploration. Networks 48(3), 166–177 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  29. Frederickson, G., Hecht, M., Kim, C.: Approximation algorithms for some routing problems. SIAM J. Comput. 7(2), 178–193 (1978)

    Article  MathSciNet  Google Scholar 

  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)

    MATH  Google Scholar 

  31. Irani, S., Shukla, S., Gupta, R.: Algorithms for power savings. ACM Trans. Algorithms 3(4), 41 (2007)

    Article  MathSciNet  Google Scholar 

  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 Networks

  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)

  34. Megow, N., Mehlhorn, K., Schweitzer, P.: Online graph exploration: new results on old and new algorithms. Theor. Comput. Sci. 463, 62–72 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  35. Rajagopalan, R., Varshney, P.: Data-aggregation techniques in sensor networks: a survey. IEEE Commun. Surv. Tutor. 8(4), 48–63 (2006)

    Article  Google Scholar 

  36. Santoro, N.: Design and Analysis of Distributed Algorithms, vol. 56. Wiley, New York (2006)

    Book  Google Scholar 

  37. Stojmenovic, I., Lin, X.: Power-aware localized routing in wireless networks. IEEE Trans. Parallel Distrib. Syst. 12(11), 1122–1133 (2001)

    Article  Google Scholar 

  38. Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  39. Yamashita, M., Suzuki, I.: Characterizing geometric patterns formable by oblivious anonymous mobile robots. Theor. Comput. Sci. 411(26–28), 2433–2453 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  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)

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Authors and Affiliations

  1. Université du Québec en Outaouais, C.P. 1250, succ. Hull, Gatineau, J8X 3X7, QC, Canada

    Julian Anaya, Jurek Czyzowicz & Andrzej Pelc

  2. LIF, CNRS & Aix-Marseille University, 13288, Marseille, France

    Jérémie Chalopin, Arnaud Labourel & Yann Vaxès

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  1. Julian Anaya
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  2. Jérémie Chalopin
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  3. Jurek Czyzowicz
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  4. Arnaud Labourel
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Correspondence to Arnaud Labourel.

Additional information

Jérémie Chalopin and Arnaud Labourel were partially supported by the ANR project MACARON (anr-13-js02-0002).

Andrzej Pelc was partially supported by NSERC discovery Grant and by the Research Chair in Distributed Computing at the Université du Québec en Outaouais.

A preliminary version of this paper appeared in Proc. 26th International Symposium of Distributed Computing (DISC 2012).

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Anaya, J., Chalopin, J., Czyzowicz, J. et al. Convergecast and Broadcast by Power-Aware Mobile Agents. Algorithmica 74, 117–155 (2016). https://doi.org/10.1007/s00453-014-9939-8

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