Generating networks for performance evaluation of P2P trust path search algorithms

Abstract

Trust has become central in computing science research. The problem of nding trust paths and estimating the trust one can place in a partner arises in various application areas, including virtual organisations, authentication systems and reputation-based trust systems. We study the use of peer-to-peer algorithms for nding trust paths and probabilistically assessing trust values in systems where trust is organised similar to the `web of trust'. Many empirical results demonstrate that many real-life large networks and systems are scale-free, that is, the node degree follows a power law distribution. To be able to analyse such networks, \growth algorithms" have been devised that generate scale-free networks by growing the size of the network in a manner that intuitively resembles real networks. Interestingly, generation of scale-free networks with directed arcs has not been researched extensively, especially for the case that avoids duplicate arcs as well as arcs that connect a node with itself (self loops). Being able to easily generate scale-free networks with these properties allows more accurate and e cient evaluation and simulation of routing algorithms and applications. We consider various di erent graph algorithms, which modify existing network generating models for directed graphs. A mathematical framework is presented to prove under which conditions the algorithm can generate networks with the scale-free feature. Since a complete proof is not feasible, we evaluate if these algorithms generate scale-free networks using statistical tests. We nd that removing multiple arcs and self loops after an entire network has been generated does not a ect the scale-free character, but at the cost of the growth nature of the algorithm. To obtain reliable results with small enough con dence intervals through simulation, one needs to run many simulations and generate many networks and it is therefore of importance to generate networks with the desired properties in reasonable time. We implement a set of algorithms and compare them with respect to CPU time and memory use, in terms of both theoretical complexity analysis and experimental results. We show through experiments that using relatively standard equipment networks with a million or more nodes can be generated in mere seconds. ii Finally, we explore the suitability of using peer-to-peer algorithms for nding trust paths and inferring the trust value of a set of trust paths discovered. We employ discrete event simulation and Monte Carlo techniques to evaluate these search algorithms. We implement all the relevant methods and search protocols in the Peersim simulation environment. Our main conclusion is that many peer-to-peer algorithms perform similarly, and only di er through (and are sensitive to) parameter choices, such as the number of nodes to which a query is forwarded. We also conclude that ooding is the most practical method if one stresses the requirement for nding all the trust paths, and if networks are less densely connected.