Exploration on and of networks

Güldas, H. (2019)

Doctoral Thesis

This dissertation consists of two parts, with the common theme "Exploration on and of Networks". In Part I we investigate the theme "exploration on networks" by studying random walks on dynamic random graphs. Random walks can be seen as a model for exploration on networks. In particular, we study the "mixing times" of random walks which is a measure of how fast the random walk explores the graph. In Part II we investigate the theme "exploration of networks" by studying the problem of union-complexity of random disk regions. This problem is related to the frequency assignment on wireless networks. In particular, we study average-case behaviour of union-complexity of random disk regions, which can be seen as a measure of complexity of a 'typical' wireless network.

• Complex networks
• Random graphs
• Random walks
• Mixing times
• Union complexity

• All authors: Güldas, H.
• Supervisor: Hollander, W.T.F. den; Hofstad, R.M. van der
• Committee: Vaart, A. van der; Stevenhagen, P.; Cerny, J.; Salez, J.; Valesin, D.
• Qualification: Doctor (dr.)
• Awarding Institution: Mathematical Institute, Science, Leiden
• Date: 2019-07-03