Improved distributed algorithms for fundamental graph problems

Abstract

Distributed graph algorithms provide efficient and theoretically sound methods for solving graph problems in distributed settings and more generally for performing distributed computation in networks. These algorithms are applicable in a wide variety of settings, ranging from computer networks to massively parallel computing and beyond. This thesis addresses a number of the central problems of distributed graph algorithms. These problems generally revolve around two of the principal challenges of the area, locality and congestion. The problems include computing maximal independent set, minimum spanning tree, minimum edge cut and minimum vertex cut, graph connectivity decompositions, network information dissemination, minimum-weight connected dominating set, and scheduling distributed protocols. We develop novel techniques, concepts, and tools for these problems, and present algorithms and impossibility results which improve considerably on the state of the art, in several cases resolving or advancing long-standing open problems.