Ph. D. Defense
Algorithms for Geometric Matching, Clustering, and Covering
jwpan at cs.duke.edu
||Wednesday, July 20, 2016
||1:00pm - 3:00pm
||D344 LSRC, Duke
With the popularization of GPS-enabled devices such as mobile phones, location data are becoming available at an unprecedented scale. The locations may be collected from vehicles moving around a city, user check-ins in social networks, and geo-tagged micro-blogging photos or messages. Besides the longitude and latitude, each location record may also have a timestamp and additional information such as the name of the location. Time-ordered sequences of these locations form trajectories, which contain useful information about people's movement patterns.
The first part of this thesis focuses on a few geometric problems motivated by the matching and clustering of trajectories. We first give a new algorithm for computing the matching between a pair of curves under existing models such as dynamic time warping (DTW). The algorithm is more efficient than standard dynamic programming algorithms both theoretically and practically. We then propose a new matching model for trajectories that avoids the drawbacks of existing models. For trajectory clustering, we present an algorithm that computes clusters of subtrajectories, which correspond to common movement patterns. We also consider trajectories of check-ins, and propose a statistical generative model, which identifies check-in clusters as well as the transition patterns between the clusters. The second part of the thesis considers the problem of covering shortest paths in a road network, motivated by an EV charging station placement problem. We first introduce a general technique for the geometric set cover problem. This technique leads to near-linear-time approximation algorithms, which are the state-of-the-art algorithms for this problem in either running time or approximation ratio. We then use this technique to develop a near-linear-time algorithm for this shortest-path cover problem.
Advisor(s): Pankaj Agarwal
Committee: Jun Yang, Kamesh Munagala, Alan Gelfand