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Electrical Flows over Spanning Trees

Series: Theory Seminar

Speaker: Dr. Swati Gupta, Assistant Professor and Fouts Family Early Career Professor, H. Milton Stewart School of Industrial & Systems Engineering, Georgia Institute of Technology.

Date/Time: Mar 03 18:30:00

Location: Microsoft Teams - ON-LINE

Abstract:
The network reconfiguration problem seeks to find a rooted tree T such that the energy of the (unique) feasible electrical flow over T is minimized. The tree requirement on the support of the flow is motivated by operational constraints in electricity distribution networks. The bulk of existing results on convex optimization over vertices of polytopes and on the structure of electrical flows do not easily give guarantees for this problem, while many heuristic methods have been developed in the power systems community as early as 1989. Our main contribution is to give the first provable approximation guarantees for the network reconfiguration problem. We provide novel lower bounds and corresponding approximation factors for various settings ranging from min(O(m-n), O(n)) for general graphs, to O(sqrt{n}) over grids with uniform resistances on edges, and O(1) for grids with uniform edge resistances and demands. To obtain the result for general graphs, we propose a new method for (approximate) spectral graph sparsification, which may be of independent interest. Using insights from our theoretical results, we propose a general heuristic for the network reconfiguration problem that is orders of magnitude faster than existing methods in the literature, while obtaining comparable performance.
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Microsoft Teams Link:
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For more details about the seminar please visit the website at Link

Host Faculty: Dr. Anand Louis