Final doctoral examination and defense of dissertation of David Durfee

Wednesday, August 22, 2018 - 10:00am
Klaus 2100
Title: Algorithmic Manipulation of Probability Distributions for Networks and Mechanisms
Advisor: Dr. Richard Peng, School of Computer Science, Georgia Institute of Technology
Committee: Dr. Xi Chen, Computer Science, Columbia University
  Dr. Alejandro Toriello, School of Industrial and Systems Engineering, Georgia Institute of Technology
  Dr. Santosh Vempala, School of Computer Science, Georgia Institute of Technology
  Dr. Eric Vigoda, School of Computer Science, Georgia Institute of Technology
Reader: Dr. Santosh Vempala, School of Computer Science, Georgia Institute of Technology

Summary: 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.