28 research outputs found
Efficiently computing maximum flows in scale-free networks
We study the maximum-flow/minimum-cut problem on scale-free networks, i.e., graphs whose degree distribution follows a power-law. We propose a simple algorithm that capitalizes on the fact that often only a small fraction of such a network is relevant for the flow. At its core, our algorithm augments Dinitz’s algorithm with a balanced bidirectional search. Our experiments on a scale-free random network model indicate sublinear run time. On scale-free real-world networks, we outperform the commonly used highest-label Push-Relabel implementation by up to two orders of magnitude. Compared to Dinitz’s original algorithm, our modifications reduce the search space, e.g., by a factor of 275 on an autonomous systems graph.
Beyond these good run times, our algorithm has an additional advantage compared to Push-Relabel. The latter computes a preflow, which makes the extraction of a minimum cut potentially more difficult. This is relevant, for example, for the computation of Gomory-Hu trees. On a social network with 70000 nodes, our algorithm computes the Gomory-Hu tree in 3 seconds compared to 12 minutes when using Push-Relabel
Efficient Estimation of Heat Kernel PageRank for Local Clustering
Given an undirected graph G and a seed node s, the local clustering problem
aims to identify a high-quality cluster containing s in time roughly
proportional to the size of the cluster, regardless of the size of G. This
problem finds numerous applications on large-scale graphs. Recently, heat
kernel PageRank (HKPR), which is a measure of the proximity of nodes in graphs,
is applied to this problem and found to be more efficient compared with prior
methods. However, existing solutions for computing HKPR either are
prohibitively expensive or provide unsatisfactory error approximation on HKPR
values, rendering them impractical especially on billion-edge graphs.
In this paper, we present TEA and TEA+, two novel local graph clustering
algorithms based on HKPR, to address the aforementioned limitations.
Specifically, these algorithms provide non-trivial theoretical guarantees in
relative error of HKPR values and the time complexity. The basic idea is to
utilize deterministic graph traversal to produce a rough estimation of exact
HKPR vector, and then exploit Monte-Carlo random walks to refine the results in
an optimized and non-trivial way. In particular, TEA+ offers practical
efficiency and effectiveness due to non-trivial optimizations. Extensive
experiments on real-world datasets demonstrate that TEA+ outperforms the
state-of-the-art algorithm by more than four times on most benchmark datasets
in terms of computational time when achieving the same clustering quality, and
in particular, is an order of magnitude faster on large graphs including the
widely studied Twitter and Friendster datasets.Comment: The technical report for the full research paper accepted in the
SIGMOD 201