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.

Botulinum toxin type A injections for the management of muscle tightness following total hip arthroplasty: a case series.

BACKGROUND: Development of hip adductor, tensor fascia lata, and rectus femoris muscle contractures following total hip arthroplasties are quite common, with some patients failing to improve despite treatment with a variety of non-operative modalities. The purpose of the present study was to describe the use of and patient outcomes of botulinum toxin injections as an adjunctive treatment for muscle tightness following total hip arthroplasty. METHODS: Ten patients (14 hips) who had hip adductor, abductor, and/or flexor muscle contractures following total arthroplasty and had been refractory to physical therapeutic efforts were treated with injection of botulinum toxin A. Eight limbs received injections into the adductor muscle, 8 limbs received injections into the tensor fascia lata muscle, and 2 limbs received injection into the rectus femoris muscle, followed by intensive physical therapy for 6 weeks. RESULTS: At a mean final follow-up of 20 months, all 14 hips had increased range in the affected arc of motion, with a mean improvement of 23 degrees (range, 10 to 45 degrees). Additionally all hips had an improvement in hip scores, with a significant increase in mean score from 74 points (range, 57 to 91 points) prior to injection to a mean of 96 points (range, 93 to 98) at final follow-up. There were no serious treatment-related adverse events. CONCLUSION: Botulinum toxin A injections combined with intensive physical therapy may be considered as a potential treatment modality, especially in difficult cases of muscle tightness that are refractory to standard therapy.

Nurse-led behavioral management of diabetes and hypertension in community practices: a randomized trial.

BACKGROUND: Several trials have demonstrated the efficacy of nurse telephone case management for diabetes (DM) and hypertension (HTN) in academic or vertically integrated systems. Little is known about the real-world potency of these interventions. OBJECTIVE: To assess the effectiveness of nurse behavioral management of DM and HTN in community practices among patients with both diseases. DESIGN: The study was designed as a patient-level randomized controlled trial. PARTICIPANTS: Participants included adult patients with both type 2 DM and HTN who were receiving care at one of nine community fee-for-service practices. Subjects were required to have inadequately controlled DM (hemoglobin A1c [A1c] ≥ 7.5%) but could have well-controlled HTN. INTERVENTIONS: All patients received a call from a nurse experienced in DM and HTN management once every two months over a period of two years, for a total of 12 calls. Intervention patients received tailored DM- and HTN- focused behavioral content; control patients received non-tailored, non-interactive information regarding health issues unrelated to DM and HTN (e.g., skin cancer prevention). MAIN OUTCOMES AND MEASURES: Systolic blood pressure (SBP) and A1c were co-primary outcomes, measured at 6, 12, and 24 months; 24 months was the primary time point. RESULTS: Three hundred seventy-seven subjects were enrolled; 193 were randomized to intervention, 184 to control. Subjects were 55% female and 50% white; the mean baseline A1c was 9.1% (SD = 1%) and mean SBP was 142 mmHg (SD = 20). Eighty-two percent of scheduled interviews were conducted; 69% of intervention patients and 70% of control patients reached the 24-month time point. Expressing model estimated differences as (intervention--control), at 24 months, intervention patients had similar A1c [diff = 0.1 %, 95 % CI (-0.3, 0.5), p = 0.51] and SBP [diff = -0.9 mmHg, 95% CI (-5.4, 3.5), p = 0.68] values compared to control patients. Likewise, DBP (diff = 0.4 mmHg, p = 0.76), weight (diff = 0.3 kg, p = 0.80), and physical activity levels (diff = 153 MET-min/week, p = 0.41) were similar between control and intervention patients. Results were also similar at the 6- and 12-month time points. CONCLUSIONS: In nine community fee-for-service practices, telephonic nurse case management did not lead to improvement in A1c or SBP. Gains seen in telephonic behavioral self-management interventions in optimal settings may not translate to the wider range of primary care settings.