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 cluster-heads (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 of each cluster-head), can reduce querying costs from Θ(n ²) to Θ(n ²/k ²), an improvement of Θ(k ²). 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.