General mathematical foundations for modeling and analyzing distributed systems.Impossibility results and lower bounds, expressing inherent limitations of distributed systems,.Rigorous proofs of algorithm correctness and performance properties (also some error discoveries),.Abstract models for problems that are solved by distributed systems, and for the algorithms used to solve them.This work has produced many different kinds of results, including: ACM Sigact News, 32(4), pp.18-25.Talk Abstract: For several decades, my collaborators, students, and I have worked on theory for distributed systems in order to understand their capabilities and limitations in a rigorous, mathematical way. This ranking method was used in Google in its early days of establishments. Ranking a set of pages that have links to each other.
The dataset consists of rows that show friends of an individual. These new friends have the most common friends with that person but are not his/her friends. Suggesting some, for example 10, new friends to a person using Spark.
This algorithm is explained in 1 in detail. At the end, evey node should know its neighbor in the tree. In this algorithm, nodes talk to each other to find a minimum spanning tree between themeselves. 2 Gallager-Humblet-Spira (GHS) Minimum Spanning Tree Algorithm Nodes in a a given topology exchange messages in an asynchronous manner until they come to a consensus on their valuse.
Bellman-Ford Shortest Path Algorithmĭesired topology is fed into the code with a predefined format, then message passing starts so that finally a specified node, that does not have a central view of the network, knows the shortest path to evey other nodes. IDs and link delays are passed to the nodes in a circular topology in clockwise order, then they start to exchange required messages until a leader is founded with the help of LCR algorithm explained in Distributed Algorithms by Nancy A. Implementation LCR leader election, Bellman-Ford shortest path, Paxos consensus algorithm, and GHS minimum spanning tree algorithms using socket programming as well as distributed computation of a page rank and a friend suggestion method using Spark. These assignments were part of my undergrad coursework at Sharif UT.
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