David Durfee

Algorithms, Combinatorics and Optimization

School of Computer Science

Georgia Institute of Technology

Date: Wednesday, Aug 22, 2018

Time: 10am (EST)

Location: Klaus 2100

Committee:

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Dr. Richard Peng (Advisor), School of Computer Science, Georgia Institute of Technology

Dr. Santosh Vempala, School of Computer Science, Georgia Institute of Technology

Dr. Xi Chen, Department of Computer Science, Columbia University

Dr. Eric Vigoda, School of Computer Science, Georgia Institute of Technology

Dr. Alejandro Toriello, School of Industrial and Systems Engineering,
Georgia Institute of Technology

Abstract:

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In this thesis we present four different works that solve problems in
dynamic graph algorithms, spectral graph algorithms, computational
economics, and differential privacy. While these areas are not all
strongly correlated, there were similar techniques integral to each of
the results. In particular, a key to each result was carefully
constructing probability distributions that interact with fast
algorithms on networks or mechanisms for economic games and private data
output. For the fast algorithms on networks this required utilizing
essential graph properties for each network to determine sampling
probabilities for sparsification procedures that we often recursively
applied to achieve runtime speedups. For mechanisms in economic games we
construct a gadget game mechanism by carefully manipulating the expected
payoff resulting from the probability distribution on the strategy space
to give a correspondence between two economic games and imply a hardness
equivalence. For mechanisms on private data output we construct a
smoothing framework for input data that allows private output from known
mechanisms while still maintaining certain levels of accuracy.