Coping with dynamic membership, selfishness, and incomplete information: applications of probabilistic analysis and game theory

textThe emergence of large scale distributed computing networks has given increased prominence to a number of algorithmic concerns, including the need to handle dynamic membership, selfishness, and incomplete information. In this document, we outline our explorations into these algorithmic issues. We first present our results on the analysis of a graph-based coupon collecvi tor process related to load balancing for networks with dynamic membership. In addition to extending the study of the coupon collector process, our results imply load balancing properties of certain distributed hash tables. Second, we detail our results on worst case payoffs when playing buyersupplier games, against many selfish, collaborating opponents. We study optimization over the set of core vectors. We show both positive and negative results on optimizing over the cores of such games. Furthermore, we introduce and study the concept of focus point price, which answers the question: If we are constrained to play in equilibrium, how much can we lose by playing the wrong equilibrium? Finally, we present our analysis of a revenue management problem with incomplete information, the online weighted transversal matroid matching problem. In specific, we present an algorithm that delivers expected revenue within a constant of optimal in the online setting. Our results use a novel algorithm to generalize several results known for special cases of transversal matroids.Computer Science

Feedback Allocation For OFDMA Systems With Slow Frequency-domain Scheduling

We study the problem of allocating limited feedback resources across multiple users in an orthogonal-frequency-division-multiple-access downlink system with slow frequency-domain scheduling. Many flavors of slow frequency-domain scheduling (e.g., persistent scheduling, semi-persistent scheduling), that adapt user-sub-band assignments on a slower time-scale, are being considered in standards such as 3GPP Long-Term Evolution. In this paper, we develop a feedback allocation algorithm that operates in conjunction with any arbitrary slow frequency-domain scheduler with the goal of improving the throughput of the system. Given a user-sub-band assignment chosen by the scheduler, the feedback allocation algorithm involves solving a weighted sum-rate maximization at each (slow) scheduling instant. We first develop an optimal dynamic-programming-based algorithm to solve the feedback allocation problem with pseudo-polynomial complexity in the number of users and in the total feedback bit budget. We then propose two approximation algorithms with complexity further reduced, for scenarios where the problem exhibits additional structure.Comment: Accepted to IEEE Transactions on Signal Processin

Mathematical Approaches to Infectious Disease Prediction and Control

Mathematics has long been an important tool for understanding and controlling the spread of infectious diseases. Here, we begin with an overview of compartmental models, the traditional approach to modeling infectious disease dynamics, and then introduce contact network epidemi- ology, a relatively new approach that applies bond percolation on random graphs to model the spread of infectious disease through heterogeneous populations. As we illustrate, these methods can be used to address public health challenges and have recently been coupled with powerful computational methods to optimize epidemic control strategies

A real-world network modeling project

The Operations Research Department at the Naval Postgraduate School educates experienced junior military officers in state-of-the-art operations research methods. As part of the educational program all officers go through a standard graduate course on network modeling. Within that course, students complete a class-long network modeling project of a real-world infrastructure system that solidifies their understanding of operations research concepts and moves the learning experience beyond the classroom. Through the project, students abstract their real-world problems into mathematics, repeatedly evaluate the connection between the mathematics and reality, and reason about the model results. The project has educational, re- search, and practical benefits. On occasion, students make discoveries of such significance that we have contacted the infrastructure system operators with briefings on the student analysis results. Some student projects have eventually influenced Department of Homeland Security and Department of Defense policy. We detail what makes the network modeling project work, and how to implement it in other universities

Bayes Linear Methods for Large-Scale Network Search

Consider the problem of searching a large set of items, such as emails, for a small set which are relevant to a given query. This can be implemented in a sequential manner whereby we use knowledge from earlier items that we have screened to help us choose future items in an informed way. Often the items we are searching have an underlying network structure: for example emails can be related to a network of participants, where an edge in the network relates to the presence of a communication between those two participants. Recent work by Dimitrov, Kress and Nevo has shown that using the information about the network structure together with a modelling assumption that relevant items and participants are likely to cluster together, can greatly increase the rate of screening relevant items. However their approach is computationally expensive and thus limited in applicability to small networks. Here we show how Bayes Linear methods provide a natural approach to modelling such data; that they output posterior summaries that are most relevant to heuristic policies for choosing future items; and that they can easily be applied to large-scale networks. Both on simulated data, and data from the Enron Corpus, Bayes Linear approaches are shown to be applicable to situations where the method of Dimitrov et al. is infeasible; and give substantially better performance than methods that ignore the network structure

Pyomo - Optimization Modeling in Python

INFORMS Journal of Computing, November 2012The article of record as published may be located at http://dx.doi.org/10.1287/ijoc.2012.4.brIf a simple, intuitive tool for a task exists, the task is done more often, by more people. This basic principle is as true for gardening and gadgets, as it is for computation in operations research. The book, Pyomo { Optimization Modeling in Python, documents a simple, yet versatile tool for modeling and solving optimization problems

Optimizing Provider Recruitment for Influenza Surveillance Networks

The increasingly complex and rapid transmission dynamics of many infectious diseases necessitates the use of new, more advanced methods for surveillance, early detection, and decision-making. Here, we demonstrate that a new method for optimizing surveillance networks can improve the quality of epidemiological information produced by typical provider-based networks. Using past surveillance and Internet search data, it determines the precise locations where providers should be enrolled. When applied to redesigning the provider-based, influenza-like-illness surveillance network (ILINet) for the state of Texas, the method identifies networks that are expected to significantly outperform the existing network with far fewer providers. This optimized network avoids informational redundancies and is thereby more effective than networks designed by conventional methods and a recently published algorithm based on maximizing population coverage. We show further that Google Flu Trends data, when incorporated into a network as a virtual provider, can enhance but not replace traditional surveillance methods

Robust decomposable Markov decision processes motivated by allocating school budgets

Motivated by an application to school funding, we introduce the notion of a robust decomposable Markov decision process (MDP). A robust decomposable MDP model applies to situations where several MDPs, with the transition probabilities in each only known through an uncertainty set, are coupled together by joint resource constraints. Robust decomposable MDPs are different than both decomposable MDPs, and robust MDPs and can not be solved by a direct application of the solution methods from either of those areas. In fact, to the best of our knowledge, there is no known method to tractably compute optimal policies in robust, decomposable MDPs. We show how to tractably compute good policies for this model, and apply the derived method to a stylized school funding example.Stanko Dimitrov would like to acknowledge the funding he received from Natural Sciences and Engineering Research Council of Canada (NSERC) that partially supported his work on this manuscrip

Analysis of Humanitarian Assistance Cargo Transportation

Naval Postgraduate School Technical Report, NPS-OR-11-007, January 2012Humanitarian assistance is of growing importance to the United States and the Department of Defense's strategic objectives. Thus, United States combatant commands increasingly rely on humanitarian assistance cargo transportation programs to deliver materiel to people in need in their areas of responsibility. This report analyzes the options available to these commands in seeking humanitarian assistance cargo transportation. The report offers a description of current operations, with a specific focus on the European area of responsibility, where these programs have had limited activity. The analysis reaches the following conclusions: (1) currently no transportation program exists that focuses on providing a quality of service to combatant commands and humanitarian assistance transportation needs, (2) legal, fiscal, and operational mechanisms exist and are outlined to create such a program, and (3) exclusively space-available transportation is generally insufficient for providing the quality of service that may be required for relationship-building through humanitarian assistance cargo transportation, and contract shipping may be necessary. These conclusions are placed in the context of current humanitarian assistance operations, and relevant operational considerations are highlighted throughout the report. The analysis is based on both a quantitative model of transportation, as well as detailed conversations with humanitarian assistance personnel throughout key Department of Defense organizations