Assume a grid of nodes where each node is occupied with probability p and empty with probability (1-p). Percolation theory is a quantitative (statistical-theoretical) and conceptual model for understanding and analyzing the statistical properties (e.g., size, diameter, shape, etc.) of the clusters of occupied nodes as the value of p changes. Many concepts associated with complex systems such as clustering, fractals, diffusion, and particularly phase transitions are modeled as percolation problem. The significance of the percolation model is that many different problems can be mapped to the percolation problem; e.g., forest-fire spread, oil field density estimation, diffusion in disordered media, etc.
Published in Chapter:
Querical Data Networks
Cyrus Shahabi (University of Southern California, USA) and Farnoush Banaei-Kashani (University of Southern California, USA)
Copyright: © 2009
|Pages: 10
DOI: 10.4018/978-1-60566-242-8.ch083
Abstract
Recently, a family of massive self-organizing data networks has emerged. These networks mainly serve as large-scale distributed query processing systems. We term these networks Querical Data Networks (QDN). A QDN is a federation of a dynamic set of peer, autonomous nodes communicating through a transient-form interconnection. Data is naturally distributed among the QDN nodes in extra-fine grain, where a few data items are dynamically created, collected, and/or stored at each node. Therefore, the network scales linearly to the size of the dataset. With a dynamic dataset, a dynamic and large set of nodes, and a transient-form communication infrastructure, QDNs should be considered as the new generation of distributed database systems with significantly less constraining assumptions as compared to their ancestors. Peer-to-peer networks (Daswani, 2003) and sensor networks (Estrin, 1999, Akyildiz, 2002) are well-known examples of QDN.