Distributed broadcast and minimum spanning tree algorithms with low communication complexity




Mashreghi, Ali

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In distributed computing, a set of processors that have their own input collaborate to compute a function. Processors can communicate by exchanging messages of limited size over links available on a predetermined communication network. In this thesis, we consider the problems of broadcast and minimum spanning tree construction in a distributed setting. These problems are of fundamental importance. Efficient solutions for these problems can lead to improvements in algorithms for a number of other distributed problems such as leader election. Since 1990, due to the ``folk theorem" mentioned in Awerbuch et al. JACM, it was believed that to construct a minimum spanning tree (or even broadcast tree) in a network with n processors and m communication links, Omega(m) messages are needed. However, in 2015, King, Kutten, and Thorup \cite{king2015construction} showed that if the nodes initially know the identity of their neighbors, the communication can be brought down to O(n log n) which is o(m) for sufficiently dense graphs. Our research has been focused on obtaining algorithms for constructing minimum spanning and broadcast trees that use only o(m) messages. At the same time, we have tried to improve the time complexity of our algorithms. We provide time improvements to the algorithms of King et al. in the synchronous network. Also, we provide the first asynchronous minimum spanning tree algorithm that achieves o(m) message complexity. This research will help to highlight the limitations imposed by asynchrony. It also shows that when nodes initially know the identities of their neighbors, we can design algorithms that break the barrier of Omega(m) messages proved in models where nodes do not have this knowledge.



distributed computing, minimum spanning tree, broadcast tree