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Collecting Information by Power-Aware Mobile Agents

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Distributed Computing (DISC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7611))

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Abstract

A set of identical, mobile agents is deployed in a weighted network. Each agent possesses a battery - a power source allowing the agent to move along network edges. Agents use their batteries proportionally to the distance traveled. At the beginning, each agent has its initial information. Agents exchange the actually possessed information when they meet. The agents collaborate in order to perform an efficient convergecast , where the initial information of all agents must be eventually transmitted to some agent.

The objective of this paper is to investigate what is the minimal value of power, initially available to all agents, so that convergecast may be achieved. We study the question in the centralized and the distributed settings. In the distributed setting every agent has to perform an algorithm being unaware of the network. We give a linear-time centralized algorithm solving the problem for line networks. We give a 2-competitive distributed algorithm achieving convergecast for tree networks. The competitive ratio of 2 is proved to be the best possible for this problem, even if we only consider line networks. We show that already for the case of tree networks the centralized problem is strongly NP-complete. We give a 2-approximation centralized algorithm for general graphs.

Partially supported by NSERC discovery grant and by the Research Chair in Distributed Computing at the Université du Québec en Outaouais.

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References

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

    Article  MathSciNet  Google Scholar 

  2. Albers, S., Henzinger, M.R.: Exploring unknown environments. SIAM J. on Comput. 29(4),1164–1188

    Google Scholar 

  3. Alpern, S., Gal, S.: The theory of search games and rendezvous. Kluwer Academic Publ. (2002)

    Google Scholar 

  4. Ambühl, C.: An Optimal Bound for the MST Algorithm to Compute Energy Efficient Broadcast Trees in Wireless Networks. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1139–1150. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Ando, H., Oasa, Y., Suzuki, I., Yamashita, M.: Distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Trans. on Robotics and Automation 15(5), 818–828 (1999)

    Article  Google Scholar 

  6. Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. In: Distributed Computing, pp. 235–253 (2006)

    Google Scholar 

  7. Annamalai, V., Gupta, S.K.S., Schwiebert, L.: On Tree-Based Convergecasting in Wireless Sensor Networks. IEEE Wireless Communications and Networking 3, 1942–1947 (2003)

    Google Scholar 

  8. Augustine, J., Irani, S., Swamy, C.: Optimal powerdown strategies. SIAM J. Comput. 37, 1499–1516 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Averbakh, I., Berman, O.: A heuristic with worst-case analysis for minimax routing of two traveling salesmen on a tree. Discrete Applied Mathematics 68, 17–32 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  10. Azar, Y.: On-line Load Balancing. In: Fiat, A., Woeginger, G. (eds.) Online Algorithms 1996. LNCS, vol. 1442, pp. 178–195. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  11. Awerbuch, B., Betke, M., Rivest, R., Singh, M.: Piecemeal graph exploration by a mobile robot. Information and Computation 152, 155–172 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  12. Baeza Yates, R.A., Culberson, J.C., Rawlins, G.J.E.: Searching in the Plane. Information and Computation 106(2), 234–252 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  13. Bender, M., Fernandez, A., Ron, D., Sahai, A., Vadhan, S.: The power of a pebble: exploring and mapping directed graphs. In: Proc. 30th STOC, pp. 269–278 (1998)

    Google Scholar 

  14. Bender, M., Slonim, D.: The power of team exploration: two robots can learn unlabeled directed graphs. In: Proc. 35th FOCS, pp. 75–85 (1994)

    Google Scholar 

  15. Betke, M., Rivest, R.L., Singh, M.: Piecemeal learning of an unknown environment. Machine Learning 18(2/3), 231–254 (1995)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  17. Bunde, D.P.: Power-aware scheduling for makespan and flow. In: SPAA, pp. 190–196 (2006)

    Google Scholar 

  18. Chen, F., Johnson, M.P., Alayev, Y., Bar-Noy, A., La Porta, T.F.: Who, When, Where: Timeslot Assignment to Mobile Clients. IEEE Transactions on Mobile Computing 11(1), 73–85 (2012)

    Article  Google Scholar 

  19. Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Solving the Robots Gathering Problem. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 1181–1196. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  20. Cohen, R., Peleg, D.: Convergence Properties of the Gravitational Algorithm in Asynchronous Robot Systems. SIAM J. on Comput. 34(6), 1516–1528 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  21. 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.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 650–661. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  22. Deng, X., Papadimitriou, C.H.: Exploring an unknown graph. In: Proc. 31st FOCS, vol. I, pp. 355–361 (1990)

    Google Scholar 

  23. Das, S., Flocchini, P., Santoro, N., Yamashita, M.: On the Computational Power of Oblivious Robots: Forming a Series of Geometric Patterns. In: Proc. PODC, pp. 267–276 (2010)

    Google Scholar 

  24. Dynia, M., Korzeniowski, M., Schindelhauer, C.: Power-Aware Collective Tree Exploration. In: Grass, W., Sick, B., Waldschmidt, K. (eds.) ARCS 2006. LNCS, vol. 3894, pp. 341–351. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  25. Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of asynchronous robots with limited visibility. Th. Comp. Science 337, 147–168 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  26. Fraigniaud, P., Gąsieniec, L., Kowalski, D.R., Pelc, A.: Collective Tree Exploration. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 141–151. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  27. Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of NP-Completeness, 96–105, 224 (1979)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  29. Heinzelman, W.B., Chandrakasan, A.P., Balakrishnan, H.: An Application-Specific Protocol Architecture for Wireless Microsensor Networks. Transactions on Wireless Communication 1(4), 660–670 (2002)

    Article  Google Scholar 

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

    Google Scholar 

  31. Kesselman, A., Kowalski, D.R.: Fast distributed algorithm for convergecast in ad hoc geometric radio networks. Journal of Parallel and Distributed Computing 66(4), 578–585 (2006)

    Article  MATH  Google Scholar 

  32. Krishnamachari, L., Estrin, D., Wicker, S.: The impact of data aggregation in wireless sensor networks. In: ICDCS Workshops, pp. 575–578 (2002)

    Google Scholar 

  33. Megow, N., Mehlhorn, K., Schweitzer, P.: Online Graph Exploration: New Results on Old and New Algorithms. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 478–489. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  34. Nikoletseas, S., Spirakis, P.G.: Distributed Algorithms for Energy Efficient Routing and Tracking in Wireless Sensor Networks. Algorithms 2, 121–157 (2009)

    Article  MathSciNet  Google Scholar 

  35. Rajagopalan, R., Varshney, P.K.: Data-aggregation techniques in sensor networks: a survey. IEEE Communications Surveys and Tutorials 8(4), 48–63 (2006)

    Article  Google Scholar 

  36. Stojmenovic, I., Lin, X.: Power-Aware Localized Routing in Wireless Networks. IEEE Trans. Parallel Distrib. Syst. 12(11), 1122–1133 (2001)

    Article  Google Scholar 

  37. Suzuki, I., Yamashita, M.: Distributed Anonymous Mobile Robots: Formation of Geometric Patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  38. Yamashita, M., Suzuki, I.: Characterizing geometric patterns formable by oblivious anonymous mobile robots. Th. Comp. Science 411(26-28), 2433–2453 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  39. Yao, F.F., Demers, A.J., Shenker, S.: A scheduling model for reduced CPU energy. In: Proc. of 36th FOCS, pp. 374–382 (1995)

    Google Scholar 

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Anaya, J., Chalopin, J., Czyzowicz, J., Labourel, A., Pelc, A., Vaxès, Y. (2012). Collecting Information by Power-Aware Mobile Agents. In: Aguilera, M.K. (eds) Distributed Computing. DISC 2012. Lecture Notes in Computer Science, vol 7611. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33651-5_4

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  • DOI: https://doi.org/10.1007/978-3-642-33651-5_4

  • Publisher Name: Springer, Berlin, Heidelberg

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