Scalable clustering of Internet paths by shared congestion

Internet paths sharing the same bottleneck can be identified using several shared congestion detection techniques. However, all of these techniques have been designed to detect shared congestion between a pair of paths. To cluster N paths by shared congestion, a straightforward approach of using pairwise tests would require O(N²) time complexity. In this paper, we present a scalable approach to cluster Internet paths based on DCW (Delay Correlation with Wavelet denoising) which does not require a common end point between paths. We present a function to map each path's measurement data into a point in a multidimensional space such that points are close to each other if and only if the corresponding paths share congestion. Because points in the space are indexed using a tree-like structure, the computational complexity of clustering N paths can be reduced to O(N log N). The indexing overhead can be further improved by reducing dimensionality of the space through wavelet transform. Computation cost is kept low by reusing for dimensionality reduction the same wavelet coefficients obtained in DCW. Our approach is evaluated by simulations and found to be effective for a large N. The tradeoff between dimensionality and clustering accuracy is shown empirically.