The Effects of Locality on Efficient Distributed Computation

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We live in an era of increasing connectivity. The days where computation happens at a single machine are coming to an end, and now our systems often comprise of a set of independent devices that have to interact to accomplish a goal without a central coordinator. This shift has introduced many new challenges and has forced us to think about algorithms and computation in a different way. One central issue that is unique to distributed algorithm design is that of "locality", a term that means that each device might have very limited information about the entire system, or can only view and communicate with other nearby devices. Our goal in this research is to better understand how different degrees of locality affect how efficient distributed algorithms can be. We consider the notion of efficiency in a broad sense, since different applications have different priorities with respect to resource consumption. Three important measures of efficiency are: time (how fast is the algorithm), cost (how much money or fuel does it take to run the algorithm), and communication (what are the network bandwidth requirements). Our main contributions will be to formally and precisely analyze the tradeoff between the efficiency of algorithms (with respect to the three measures listed above) and locality constraints. More specifically, this involves producing two kinds of results: (1) describing efficient algorithms when information and/or device capabilities are restricted, and, (2) proving impossibility results that give the best efficiency bounds that we can hope for under such restrictions. We have identified four application areas where we will focus our efforts in producing these kinds of results: (Area 1) Static Networks with Synchronous Communication(Area 2) Networks of Mobile Nodes with Wireless Radio Communication(Area 3) Autonomous Robots in Unknown Environments(Area 4) Routing Packets in Networks with Bounded BuffersIn the next 5 years, I plan to complete the following projects within each of the above application areas:(Area 1) Determining the optimal leader election algorithms under all possible ranges of information locality.(Area 2) Determining the optimal neighbour discovery algorithms for vehicles traveling on simple road networks, both under information restrictions and communication/sensing restrictions.(Area 3) Determining the optimal rendezvous algorithms for autonomous robots in an unknown environment with limited communication and vision.(Area 4) Determining the best strategy for forwarding packets in a network where each router has a small memory buffer and limited information about the rest of the network.I plan to directly train 8-10 HQP in the next 5 years, and I will be indirectly involved in the training of other HQP in our newly-formed collaborative research lab.