textThe emergence of large scale distributed computing networks has given increased
prominence to a number of algorithmic concerns, including the need to
handle dynamic membership, selfishness, and incomplete information. In this document,
we outline our explorations into these algorithmic issues.
We first present our results on the analysis of a graph-based coupon collecvi
tor process related to load balancing for networks with dynamic membership. In
addition to extending the study of the coupon collector process, our results imply
load balancing properties of certain distributed hash tables.
Second, we detail our results on worst case payoffs when playing buyersupplier
games, against many selfish, collaborating opponents. We study optimization
over the set of core vectors. We show both positive and negative results on
optimizing over the cores of such games. Furthermore, we introduce and study the
concept of focus point price, which answers the question: If we are constrained to
play in equilibrium, how much can we lose by playing the wrong equilibrium?
Finally, we present our analysis of a revenue management problem with incomplete
information, the online weighted transversal matroid matching problem.
In specific, we present an algorithm that delivers expected revenue within a constant
of optimal in the online setting. Our results use a novel algorithm to generalize
several results known for special cases of transversal matroids.Computer Science