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Centre for Mathematical Sciences  -  Faculty of Engineering  -  Lund University


Master's Theses

Curious about the mathematics that lie at the foundation of today's search engines?

Here, we present some ideas for interesting Master's Thesis projects. They are suitable for students majoring in e.g. mathematics or computer science (typically F, Π, D, E programs). If you are interested, please contact Sergei Silvestrov for more information.

PageRank as a Power Series

The PageRank ranking method, the de facto algorithm for ranking web pages, is often formulated as a fixed-point iteration method. It has been shown that it can also be expressed as a power series. In this master's thesis, the power series formulation will be investigated more closely, particularly in relation to various block matrix expansions of the graph's transition matrix.
Keywords: PageRank, Theoretical, Matrix theory

Simulation of Link Graphs

It is known that in large-scale link networks, such as the ones found on the World Wide Web, the distribution of rank values in common models such as PageRank normally follows a so-called Zipfian distribution. This master's thesis aims at finding methods for simulating/constructing link graphs, such that the induced rank values of the nodes therein are distributed as if the link graph actually came from e.g. the topology of the WWW.
Keywords: Simulation, PageRank, Matrix theory, Statistics, Numerical experiments

Significance of Local Links

The group has access to very large-scale World Wide Web link graphs. This master's thesis aims at investigating the effects of separating the links into local links (links within a web server) and external links (links between servers or server IP addresses), and assigning different weights to these two groups of links. The hope is to be able to augment e.g. the PageRank algorithm by lowering the significance of the local links, which are under direct control by the webmasters.
Keywords:PageRank, Matrix theory, Statistics, Numerical experiments, WWW concepts

Address: The Mathematics in IR Group, Centre for Mathematical Sciences, Faculty of Engineering, Lund University
Box 118, SE-221 00 Lund, Sweden
Phone: +46 46 222 88 54, Fax: +46 46 222 xx xx