Douglas de Jager | Imperial College London

Papers

Asynchronous Iterative Solution for State-Based Performance Metrics

Sigmetrics paper

Solution of large sparse fixed-point problems, Mx = x and Mx + b =x, may be seen as underpinning many important performance analysis calculations. These calculations include steady-state, passage-time and transient-time calculations in discrete-time Markov chains, continuous-time Markov chains and semi-Markov processes. In recent years, much work has been done to extend the application of asynchronous iterative fixed-point solutions methods to many different contexts. This work has been motivated by the potential for faster solution, more efficient suse of the communication channel and/or access to memory, and simplification of task management and programming. In this paper, we present theoretical developments which allow us to extend the application of asynchronous iterative solution methods to solve for the key performance metrics mentioned above—such that we may employ the full breadth of Chazan and Miranker’s classes of asynchronous iterations.

Hypergraph Partitioning for Faster Parallel PageRank Computation

EPEW paper

The PageRank algorithm is used by search engines such as
Google to order Web pages. It uses an iterative numerical method to
compute the maximal eigenvector of a transition matrix derived from
the Web’s hyperlink structure and a user-centred model of Web-surfing
behaviour. As the web has expanded and as demand for user-tailored
web page ordering metrics has grown, scalable parallel computation of
PageRank has become a focus of considerable research effort.
In this paper, we seek a scalable problem decomposition for parallel
PageRank computation, through the use of state-of-the-art hypergraph-
based partitioning schemes. These have not been previously applied in
this context. We consider both one and two-dimensional hypergraph de-
composition models. Exploiting the recent availability of the Parkway 2.1
parallel hypergraph partitioner, we present empirical results on a gigabit
PC cluster for three publicly available web graphs. Our results show that
hypergraph-based partitioning substantially reduces communication vol-
ume over conventional partitioning schemes (by up to three orders of
magnitude), while still maintaining computational load balance. They
also show a halving of the per-iteration runtime cost when compared to
the most effective alternative approach used to date.