Three Puzzles on Mathematics, Computation, and Games

In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear programming. The second puzzle is about errors made when votes are counted during elections. The third puzzle is: are quantum computers possible?Comment: ICM 2018 plenary lecture, Rio de Janeiro, 36 pages, 7 Figure

Resource allocation in mobile cellular systems.

by Sung Chi Wan.Thesis (M.Phil.)--Chinese University of Hong Kong, 1995.Includes bibliographical references (leaves 59-[63]).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Design Issues in Mobile Communication Systems --- p.1Chapter 1.2 --- Radio Resource Management --- p.2Chapter 1.2.1 --- Constraint: Radio Interference --- p.2Chapter 1.2.2 --- Objective: High Capacity and Good Quality --- p.3Chapter 1.3 --- Channel Assignment --- p.3Chapter 1.3.1 --- Static Channel Assignment --- p.4Chapter 1.3.2 --- Dynamic Channel Assignment --- p.5Chapter 1.4 --- Review of Previous Results and Motivation --- p.6Chapter 1.5 --- Outline of the Thesis --- p.8Chapter 2 --- Static Channel Assignment --- p.9Chapter 2.1 --- Introduction --- p.9Chapter 2.2 --- Problem Formulation --- p.10Chapter 2.3 --- Pure Co channel Interference Case --- p.12Chapter 2.4 --- Systems of Special Structure --- p.16Chapter 2.5 --- Generalization of SP --- p.22Chapter 2.6 --- A Lower Bound for the General Case --- p.23Chapter 2.7 --- Numerical Examples --- p.25Chapter 2.8 --- Summary --- p.29Chapter 3 --- Dynamic Channel Assignment --- p.30Chapter 3.1 --- Introduction --- p.30Chapter 3.2 --- Distributed Packing Algorithm --- p.31Chapter 3.3 --- Performance Evaluation --- p.33Chapter 3.4 --- Summary --- p.38Chapter 4 --- Single-Channel User-Capacity Calculations --- p.39Chapter 4.1 --- Introduction --- p.39Chapter 4.2 --- Capacity as a Performance Measure --- p.40Chapter 4.3 --- Capacity of a Linear Celluar System --- p.41Chapter 4.4 --- Capacity of a 3-stripe Cellular System --- p.44Chapter 4.5 --- Summary --- p.46Chapter 5 --- Conclusion --- p.47Chapter 5.1 --- Summary of Results --- p.47Chapter 5.2 --- Suggestions for Further Research --- p.48Appendix --- p.49Chapter A --- On the Optimality of Sequential Packing --- p.49Chapter A.1 --- Graph Multi-coloring Problem --- p.49Chapter A.2 --- Sequential Packing Algorithm --- p.51Chapter A.3 --- Optimality of Sequential Packing --- p.52Chapter A.4 --- Concluding Remarks --- p.55Chapter B --- Derivation of the Capacity of 3-stripe system --- p.56Bibliography --- p.5

Cost-optimal constrained correlation clustering via weighted partial Maximum Satisfiability

Peer reviewe

A constraint solver for software engineering : finding models and cores of large relational specifications

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 105-120).Relational logic is an attractive candidate for a software description language, because both the design and implementation of software often involve reasoning about relational structures: organizational hierarchies in the problem domain, architectural configurations in the high level design, or graphs and linked lists in low level code. Until recently, however, frameworks for solving relational constraints have had limited applicability. Designed to analyze small, hand-crafted models of software systems, current frameworks perform poorly on specifications that are large or that have partially known solutions. This thesis presents an efficient constraint solver for relational logic, with recent applications to design analysis, code checking, test-case generation, and declarative configuration. The solver provides analyses for both satisfiable and unsatisfiable specifications--a finite model finder for the former and a minimal unsatisfiable core extractor for the latter. It works by translating a relational problem to a boolean satisfiability problem; applying an off-the-shelf SAT solver to the resulting formula; and converting the SAT solver's output back to the relational domain. The idea of solving relational problems by reduction to SAT is not new. The core contributions of this work, instead, are new techniques for expanding the capacity and applicability of SAT-based engines. They include: a new interface to SAT that extends relational logic with a mechanism for specifying partial solutions; a new translation algorithm based on sparse matrices and auto-compacting circuits; a new symmetry detection technique that works in the presence of partial solutions; and a new core extraction algorithm that recycles inferences made at the boolean level to speed up core minimization at the specification level.by Emina Torlak.Ph.D

Novel gradient-based methods for data distribution and privacy in data science

With an increase in the need of storing data at different locations, designing algorithms that can analyze distributed data is becoming more important. In this thesis, we present several gradient-based algorithms, which are customized for data distribution and privacy. First, we propose a provably convergent, second order incremental and inherently parallel algorithm. The proposed algorithm works with distributed data. By using a local quadratic approximation, we achieve to speed-up the convergence with the help of curvature information. We also illustrate that the parallel implementation of our algorithm performs better than a parallel stochastic gradient descent method to solve a large-scale data science problem. This first algorithm solves the problem of using data that resides at different locations. However, this setting is not necessarily enough for data privacy. To guarantee the privacy of the data, we propose differentially private optimization algorithms in the second part of the thesis. The first one among them employs a smoothing approach which is based on using the weighted averages of the history of gradients. This approach helps to decrease the variance of the noise. This reduction in the variance is important for iterative optimization algorithms, since increasing the amount of noise in the algorithm can harm the performance. We also present differentially private version of a recent multistage accelerated algorithm. These extensions use noise related parameter selection and the proposed stepsizes are proportional to the variance of the noisy gradient. The numerical experiments show that our algorithms show a better performance than some well-known differentially private algorithm