Using Heterogeneity to Enhance Random Walk-based Queries

It is a well-known property of random walks that nodes with higher degree are visited more frequently. Based on this property, we propose the use of cluster-heads (high-degree nodes) together with a simple push-pull mechanism to enhance the performance of random walk-based querying: events are pushed towards high-degree nodes (cluster-heads) and pulled from the cluster-heads by a random-walk originated at the sink. Following this simple mechanism, we show that having even a small percentage of clusterheads (degree-heterogeneity) can provide significant improvements in query performance. For linear topologies, we use connections between random walks and electrical resistances to prove that placing uniformly a fraction of 4/5k cluster-heads (where 2k is the degree This work was supported in part by NSF through grants numbered CNS-0325875, CNS-0347621, CNS-0435505, and CCF-0430061. The work was done while the second author was a PostDoc at USC M. Zuniga (B) · B. Krishnamachari Department of Electrical Engineering—Systems, University of Southern California, Los Angeles, CA 90089-0781 USA e-mail: [email protected] B. Krishnamachari e-mail: [email protected] C. Avin Department of Communication Systems Engineering, Ben Gurion University of The Negev, Beer Sheva, 84105, Israel e-mail: [email protected] of each cluster-head), can reduce querying costs from (n2) to (n2/k2), an improvement of (k2). For more realistic two-dimensional topologies, we use Markov chain analysis and simulations to show a similar trend— using about 10% of the nodes as cluster-heads provides a query cost improvement between 30% and 70% depending on the coverage of the high-degree nodes.