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.

Prenatal protease inhibitor use and risk of preterm birth among HIV-infected women initiating antiretroviral drugs during pregnancy.

BACKGROUND: Conflicting results have been reported among studies of protease inhibitor (PI) use during pregnancy and preterm birth. Uncontrolled confounding by indication may explain some of the differences among studies. METHODS: In total, 777 human immunodeficiency virus (HIV)-infected pregnant women in a prospective cohort who were not receiving antiretroviral (ARV) treatment at conception were studied. Births <37 weeks gestation were reviewed, and deliveries due to spontaneous labor and/or rupture of membranes were identified. Risk of preterm birth and low birth weight (<2500 g) were evaluated by using multivariable logistic regression. RESULTS: Of the study population, 558 (72%) received combination ARV with PI during pregnancy, and a total of 130 preterm births were observed. In adjusted analyses, combination ARV with PI was not significantly associated with spontaneous preterm birth, compared to ARV without PI (odds ratio [OR], 1.22; 95% confidence interval [CI], 0.70-2.12). Sensitivity analyses that included women who received ARV prior to pregnancy also did not identify a significant association (OR, 1.34; 95% CI, 0.84-2.16). Low birth weight results were similar. CONCLUSIONS: No evidence of an association between use of combination ARV with PI during pregnancy and preterm birth was found. Our study supports current guidelines that promote consideration of combination ARV for all HIV-infected pregnant women.

Contracting Freedom: Governance and East Indian Indenture in the British Atlantic, 1838-1917

This is a dissertation about identity and governance, and how they are mutually constituted. Between 1838 and 1917, the British brought approximately half a million East Indian laborers to the Atlantic to work on sugar plantations. The dissertation argues that contrary to previous historiographical assumptions, indentured East Indians were an amorphous mass of people drawn from various regions of British India. They were brought together not by their innate "Indian-ness" upon their arrival in the Caribbean, but by the common experience of indenture recruitment, transportation and plantation life. Ideas of innate "Indian-ness" were products of an imperial discourse that emerged from and shaped official approaches to governing East Indians in the Atlantic. Government officials and planters promoted visions of East Indians as "primitive" subjects who engaged in child marriage and wife murder. Officials mobilized ideas about gender to sustain racialized stereotypes of East Indian subjects. East Indian women were thought to be promiscuous, and East Indian men were violent and depraved (especially in response to East Indian women's promiscuity). By pointing to these stereotypes about East Indians, government officials and planters could highlight the promise of indenture as a civilizing mechanism. This dissertation links the study of governance and subject formation to complicate ideas of colonial rule as static. It uncovers how colonial processes evolved to handle the challenges posed by migrant populations.

The primary architects of indenture, Caribbean governments, the British Colonial Office, and planters hoped that East Indian indentured laborers would form a stable and easily-governed labor force. They anticipated that the presence of these laborers would undermine the demands of Afro-Creole workers for higher wages and shorter working hours. Indenture, however, was controversial among British liberals who saw it as potentially hindering the creation of a free labor market, and abolitionists who also feared that indenture was a new form of slavery. Using court records, newspapers, legislative documents, bureaucratic correspondence, memoirs, novels, and travel accounts from archives and libraries in Britain, Guyana, and Trinidad and Tobago, this dissertation explores how indenture was envisioned and constantly re-envisioned in response to its critics. It chronicles how the struggles between the planter class and the colonial state for authority over indentured laborers affected the way that indenture functioned in the British Atlantic. In addition to focusing on indenture's official origins, this dissertation examines the actions of East Indian indentured subjects as they are recorded in the imperial archive to explore how these people experienced indenture.

Indenture contracts were central to the justification of indenture and to the creation of a pliable labor force in the Atlantic. According to English common law, only free parties could enter into contracts. Indenture contracts limited the period of indenture and affirmed that laborers would be remunerated for their labor. While the architects of indenture pointed to contracts as evidence that indenture was not slavery, contracts in reality prevented laborers from participating in the free labor market and kept the wages of indentured laborers low. Further, in late nineteenth-century Britain, contracts were civil matters. In the British Atlantic, indentured laborers who violated the terms of their contracts faced criminal trials and their associated punishments such as imprisonment and hard labor. Officials used indenture contracts to exploit the labor and limit the mobility of indentured laborers in a manner that was reminiscent of slavery but that instead established indentured laborers as subjects with limited rights. The dissertation chronicles how indenture contracts spawned a complex inter-imperial bureaucracy in British India, Britain, and the Caribbean that was responsible for the transportation and governance of East Indian indentured laborers overseas.