Abstract
We design a formal model of an amorphous computer suitable for theoretical investigation of its computational properties. The model consists of a finite set of nodes created by RAMs with restricted memory, which are dispersed uniformly in a given area. Within a limited radius the nodes can communicate with their neighbors via a single-channel radio. The assumptions on low-level communication abilities are among the weakest possible: the nodes work asynchronously, there is no broadcasting collision detection mechanism and no network addresses. For the underlying network we design a randomized communication protocol and analyze its efficiency. The subsequent experiments and combinatorial analysis of random networks show that the expectations under which our protocol was designed are met by the vast majority of the instances of our amorphous computer model.
This research was carried out within the institutional research plan AV0Z10300504 and partially supported by the GA ČR grant No. 1ET100300419 and GD201/05/H014.
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References
Abelson, H., et al.: Amorphous Computing. Communications of the ACM 43(5), 74–82 (2000)
Abelson, H., et al.: Amorphous Computing. MIT Artificial Intelligence Laboratory Memo No. 1665 (August 1999)
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)
Coore, D.: Introduction to Amorphous Computing. In: Banâtre, J.-P., Fradet, P., Giavitto, J.-L., Michel, O. (eds.) UPP 2004. LNCS, vol. 3566, pp. 99–109. Springer, Heidelberg (2005)
D’Hondt, E.: Exploring the Amorphous Computing Paradigm. Master’s Thesis, Vrije University (2000)
Ellis, R.B., et al.: Random Geometric Graph Diameter in the Unit Disk with ℓ p Metric. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 167–172. Springer, Heidelberg (2005)
Glauche, I., et al.: Continuum Percolation of Wireless Ad Hoc Communication Networks. Physica A 325, 577–600 (2003)
Grimmett, G.: Percolation, 2nd edn. Springer, Heidelberg (1999)
Gupta, P., Kumar, P.R.: Critical Power for Asymptotic Connectivity in Wireless Networks. In: Stochastic Analysis, Control, Optimization and Applications, pp. 547–566. Birkhäuser, Basel (1998)
Li, K.: Topological Characteristics of Random Multihop Wireless Networks. Cluster Computing 8(2–3), 119–126 (2005)
Nikoletseas, S.E.: Models and Algorithms for Wireless Sensor Networks (Smart Dust). In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds.) SOFSEM 2006. LNCS, vol. 3831, pp. 64–83. Springer, Heidelberg (2006)
Spirakis, P.G.: Algorithmic and Foundational Aspects of Sensor Systems. In: Nikoletseas, S.E., Rolim, J.D.P. (eds.) ALGOSENSORS 2004. LNCS, vol. 3121, pp. 3–8. Springer, Heidelberg (2004)
Warneke, B., et al.: Smart Dust: Communicating with a Cubic-Millimeter Computer. Computer 34(1), 44–51 (2001)
Weisstein, E.W.: Percolation Threshold. From MathWorld — A Wolfram Web Resource, http://mathworld.wolfram.com/PercolationThreshold.html
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Petrů, L., Wiedermann, J. (2007). A Model of an Amorphous Computer and Its Communication Protocol. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds) SOFSEM 2007: Theory and Practice of Computer Science. SOFSEM 2007. Lecture Notes in Computer Science, vol 4362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69507-3_38
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DOI: https://doi.org/10.1007/978-3-540-69507-3_38
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