Delay Minimizing User Association in Cellular Networks via Hierarchically Well-Separated Trees

We study downlink delay minimization within the context of cellular user association policies that map mobile users to base stations. We note the delay minimum user association problem fits within a broader class of network utility maximization and can be posed as a non-convex quadratic program. This non-convexity motivates a split quadratic objective function that captures the original problem's inherent tradeoff: association with a station that provides the highest signal-to-interference-plus-noise ratio (SINR) vs. a station that is least congested. We find the split-term formulation is amenable to linearization by embedding the base stations in a hierarchically well-separated tree (HST), which offers a linear approximation with constant distortion. We provide a numerical comparison of several problem formulations and find that with appropriate optimization parameter selection, the quadratic reformulation produces association policies with sum delays that are close to that of the original network utility maximization. We also comment on the more difficult problem when idle base stations (those without associated users) are deactivated.Comment: 6 pages, 5 figures. Submitted on 2013-10-03 to the 2015 IEEE International Conference on Communications (ICC). Accepted on 2015-01-09 to the 2015 IEEE International Conference on Communications (ICC

On the Applications of Metric Trees and Metric Labeling to Hard Combinatorial Optimization Problems

Matching of metric distributions is a fundamental problem in computer science having numerous real life applications including computer vision, pattern recognition, and natural language processing. The problem can be reduced to graph matching since arbitrary metrics can be represented using graphs.Exact graph matching is known to be computationally intractable which motivates inexact matching approaches. Although graphs structurally represent metric data without losing information, processing data over graphs is prone to entail performance problems. Specifically, running time of many graph algorithms depend on the number of edges and vertices of the input graph which increases quadratically by the number of nodes on the extreme case of complete graphs. Thus, it is desirable to obtain a sparse representation of the data while preserving the quality of information. A common technique to achieve this is through representing graphs by metric trees which recently became defacto metric structures for embedding problems. In this dissertation, we focus on problems involving data that can be represented by graphs. As a general theme, we concentrate on approximation of graphs by trees for improving the performance of certain algorithms using topological structure of trees. We also focus on the fundamental problem of inexact graph matching, efficient approximation algorithms for the problem and its applications. Specifically, we present an inexact graph matching problem referred to as multilayer matching, which utilizes the structure of hierarchical metric trees. We represent graphs as trees and achieve matching over the trees to improve the performance and accuracy of inexact matching. We also establish a relationship between the well known metric labeling problem and inexact graph matching. We propose efficient approximation algorithms for both multilayer matching and metric labeling using the primal-dual approximation scheme. We provide application of the proposed methods to image matching, pattern recognition, and question answering problems. Finally, we present a novel motion segmentation method utilizing metric trees which provides tracking of objects in a video sequence without a priori knowledge of number of objects in the scene.Ph.D., Computer Science -- Drexel University, 201