Design of Scheduling Algorithms Using Game Theoretic Ideas

Scheduling a set of jobs over a collection of machines to optimize a certain quality-of-service measure is one of the most important research topics in both computer science theory and practice. In this thesis, we design algorithms that optimize {\em flow-time} (or delay) of jobs for scheduling problems that arise in a wide range of applications. We consider the classical model of unrelated machine scheduling and resolve several long standing open problems; we introduce new models that capture the novel algorithmic challenges in scheduling jobs in data centers or large clusters; we study the effect of selfish behavior in distributed and decentralized environments; we design algorithms that strive to balance the energy consumption and performance.

The technically interesting aspect of our work is the surprising connections we establish between approximation and online algorithms, economics, game theory, and queuing theory. It is the interplay of ideas from these different areas that lies at the heart of most of the algorithms presented in this thesis.

The main contributions of the thesis can be placed in one of the following categories.

1. Classical Unrelated Machine Scheduling: We give the first polygorithmic approximation algorithms for minimizing the average flow-time and minimizing the maximum flow-time in the offline setting. In the online and non-clairvoyant setting, we design the first non-clairvoyant algorithm for minimizing the weighted flow-time in the resource augmentation model. Our work introduces iterated rounding technique for the offline flow-time optimization, and gives the first framework to analyze non-clairvoyant algorithms for unrelated machines.

2. Polytope Scheduling Problem: To capture the multidimensional nature of the scheduling problems that arise in practice, we introduce Polytope Scheduling Problem (\psp). The \psp problem generalizes almost all classical scheduling models, and also captures hitherto unstudied scheduling problems such as routing multi-commodity flows, routing multicast (video-on-demand) trees, and multi-dimensional resource allocation. We design several competitive algorithms for the \psp problem and its variants for the objectives of minimizing the flow-time and completion time. Our work establishes many interesting connections between scheduling and market equilibrium concepts, fairness and non-clairvoyant scheduling, and queuing theoretic notion of stability and resource augmentation analysis.

3. Energy Efficient Scheduling: We give the first non-clairvoyant algorithm for minimizing the total flow-time + energy in the online and resource augmentation model for the most general setting of unrelated machines.

4. Selfish Scheduling: We study the effect of selfish behavior in scheduling and routing problems. We define a fairness index for scheduling policies called {\em bounded stretch}, and show that for the objective of minimizing the average (weighted) completion time, policies with small stretch lead to equilibrium outcomes with small price of anarchy. Our work gives the first linear/ convex programming duality based framework to bound the price of anarchy for general equilibrium concepts such as coarse correlated equilibrium.

Biologically Inspired Design of Protein-Silica Hybrid Nanoparticles for Drug Delivery Applications

The design and application of effective drug carriers is a fundamental concern in the delivery of therapeutics for the treatment of cancer and other vexing health problems. Traditionally utilized chemotherapeutics are limited in efficacy due to poor bioavailability as a result of their size and solubility as well as significant deleterious effects to healthy tissue through their inability to preferentially target pathological cells and tissues, especially in treatment of cancer. Thus, a major effort in the development of nanoscopic drug delivery vehicles for cancer treatment has focused on exploiting the inherent differences in tumor physiology and limiting the exposure of drugs to non-tumorous tissue, which is commonly achieved by encapsulation of chemotherapeutics within macromolecular or supramolecular carriers that incorporate targeting ligands and that enable controlled release. The overall aim of this work is to engineer a hybrid nanomaterial system comprised of protein and silica and to characterize its potential as an encapsulating drug carrier. The synthesis of silica, an attractive nanomaterial component because it is both biocompatible as well as structurally and chemically stable, within this system is catalyzed by self-assembled elastin-like polypeptide (ELP) micelles that incorporate of a class of biologically-inspired, silica-promoting peptides, silaffins. Furthermore, this methodology produces near-monodisperse, hybrid inorganic/micellar materials under mild reaction conditions such as temperature, pH and solvent. This work studies this material system along three avenues: 1) proof-of-concept silicification (i.e. the formation and deposition of silica upon organic materials) of ELP micellar templates, 2) encapsulation and pH-triggered release of small, hydrophobic chemotherapeutics, and 3) selective silicification of templates to potentiate retention of peptide targeting ability.