PageRank is one of the principle criteria according to which Google ranks Web pages. PageRank can be interpreted as the frequency that a random surfer visits a Web page, and thus it reflects the popularity of a Web page. We study the effect of newly created links on Google PageRank. We discuss to what extent a page can control its PageRank. Using the asymptotic analysis we provide simple conditions that show whether or not new links result in increased PageRank for a Web page and its neighbors. Furthermore, we show that there exists an optimal (although impractical) linking strategy. We conclude that a Web page benefits from links inside its Web community and on the other hand irrelevant links penalize the Web pages and their Web communities.

Near-optimal decomposition is central to the efficient solution of numerous prob-lems in scientific computing and computer-aided design. In particular, intelligent a priori partitioning of input data can greatly improve the runtime and scalabil-ity of large-scale parallel computations. Discrete data structures such as graphs and hypergraphs are used to formalise such partitioning problems, with hyper-graphs typically preferred for their greater expressiveness. Optimal graph and hypergraph partitioning are NP-complete problems; however, serial heuristic al-gorithms that run in low-order polynomial time have been studied extensively and good tool support exists. Yet, to date, only graph partitioning algorithms have been parallelised. This thesis presents the first parallel hypergraph partitioning algorithms, enabling both partitioning of much larger hypergraphs, and computation of partitions with significantly reduced runtimes. In the multilevel approach which we adopt, the coarsening and refinement phases are performed in parallel while the initial

Abstract. The efficiency of the PageRank computation is important since the constantly evolving nature of the Web requires this computation to be repeated many times. Due to the enormous size of the Web’s hyperlink structure, PageRank computations are usually carried out on parallel computers. Recently, a hypergraph-partitioning-based formulation for parallel sparse-matrix vector multiplication is proposed as a preprocessing step which will minimize the communication overhead of the parallel PageRank computations. Based on this work, we propose Website-based partitioning approaches in order to reduce the overhead of this preprocessing step. The conducted experiments show that the proposed approach produces comparable performance results for PageRank computation while achieving lower preprocessing overheads. 1

BinRank is a system that approximates object rank results by utilizing a hybrid approach inspired by materialized views in traditional query processing. Number of relatively small subsets of the data graph are materialized in such a way that any keyword query can be answered by running ObjectRank on only one of the subgraphs. BinRank generates the subgraphs by partitioning all the terms in the corpus based on their co-occurrence, executing ObjectRank for each partition using the terms to generate a set of random walk starting points, and keeping only those objects that receive non-negligible scores. The intuition is that a subgraph that contains all objects and links relevant to a set of related terms should have all the information needed to rank objects with respect to one of these terms. We demonstrate that BinRank can achieve subsecond query execution time on the English Wikipedia data set, while producing high-quality search results that closely approximate the results of ObjectRank on the original graph. The Wikipedia link graph contains about 108 edges, which is at least two orders of magnitude larger than what prior state of the art dynamic authority-based search systems have been able to demonstrate. Experimental evaluation investigates the trade-off between query execution time, quality of the results, and storage requirements of BinRank.