*********************************
There is now a CONTENT FREEZE for Mercury while we switch to a new platform. It began on Friday, March 10 at 6pm and will end on Wednesday, March 15 at noon. No new content can be created during this time, but all material in the system as of the beginning of the freeze will be migrated to the new platform, including users and groups. Functionally the new site is identical to the old one. webteam@gatech.edu
*********************************
Title: Algorithmic Manipulation of Probability Distributions for
Networks and Mechanisms
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:
--------------
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:
--------------
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.
