Efficient algorithms for robustness in resource allocation and scheduling problems

AbstractThe robustness function of an optimization (minimization) problem measures the maximum increase in the value of its optimal solution that can be produced by spending a given amount of resources increasing the values of the elements in its input. We present efficient algorithms for computing the robustness function of resource allocation and scheduling problems that can be modeled with partition and scheduling matroids. For the case of scheduling matroids, we give an O(m2n2) time algorithm for computing a complete description of the robustness function, where m is the number of elements in the matroid and n is its rank. For partition matroids, we give two algorithms: one that computes the complete robustness function in O(mlogm) time, and other that optimally evaluates the robustness function at only a specified point

Scheduling to minimize power consumption using submodular functions

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 59-64).We develop logarithmic approximation algorithms for extremely general formulations of multiprocessor multi-interval offline task scheduling to minimize power usage. Here each processor has an arbitrary specified power consumption to be turned on for each possible time interval, and each job has a specified list of time interval/processor pairs during which it could be scheduled. (A processor need not be in use for an entire interval it is turned on.) If there is a feasible schedule, our algorithm finds a feasible schedule with total power usage within an O(log n) factor of optimal, where n is the number of jobs. (Even in a simple setting with one processor, the problem is Set-Cover hard.) If not all jobs can be scheduled and each job has a specified value, then our algorithm finds a schedule of value at least (1 - c)Z and power usage within an O(log(1/E)) factor of the optimal schedule of value at least Z, for any specified Z and c > 0. At the foundation of our work is a general framework for logarithmic approximation to maximizing any submodular function subject to budget constraints. We also introduce the online version of this scheduling problem, and show its relation to the classical secretary problem. In order to obtain constant competitive algorithms for this online version, we study the secretary problem with submodular utility function. We present several constant competitive algorithms for the secretary problem with different kinds of utility functions.by Morteza Zadimoghaddam.S.M

Jointly Optimal Routing and Caching for Arbitrary Network Topologies

We study a problem of fundamental importance to ICNs, namely, minimizing routing costs by jointly optimizing caching and routing decisions over an arbitrary network topology. We consider both source routing and hop-by-hop routing settings. The respective offline problems are NP-hard. Nevertheless, we show that there exist polynomial time approximation algorithms producing solutions within a constant approximation from the optimal. We also produce distributed, adaptive algorithms with the same approximation guarantees. We simulate our adaptive algorithms over a broad array of different topologies. Our algorithms reduce routing costs by several orders of magnitude compared to prior art, including algorithms optimizing caching under fixed routing.Comment: This is the extended version of the paper "Jointly Optimal Routing and Caching for Arbitrary Network Topologies", appearing in the 4th ACM Conference on Information-Centric Networking (ICN 2017), Berlin, Sep. 26-28, 201

A Unified And Green Platform For Smartphone Sensing

Smartphones have become key communication and entertainment devices in people\u27s daily life. Sensors on (or attached to) smartphones can enable attractive sensing applications in different domains, including environmental monitoring, social networking, healthcare, transportation, etc. Most existing smartphone sensing systems are application-specific. How to leverage smartphones\u27 sensing capability to make them become unified information providers for various applications has not yet been fully explored. This dissertation presents a unified and green platform for smartphone sensing, which has the following desirable features: 1) It can support various smartphone sensing applications; 2) It is personalizable; 2) It is energy-efficient; and 3) It can be easily extended to support new sensors. Two novel sensing applications are built and integrated into this unified platform: SOR and LIPS. SOR is a smartphone Sensing based Objective Ranking (SOR) system. Different from a few subjective online review and recommendation systems (such as Yelp and TripAdvisor), SOR ranks a target place based on data collected via smartphone sensing. LIPS is a system that learns the LIfestyles of mobile users via smartPhone Sensing (LIPS). Combining both unsupervised and supervised learning, a hybrid scheme is proposed to characterize lifestyle and predict future activities of mobile users. This dissertation also studies how to use the cloud as a coordinator to assist smartphones for sensing collaboratively with the objective of reducing sensing energy consumption. A novel probabilistic model is built to address the GPS-less energy-efficient crowd sensing problem. Provably-good approximation algorithms are presented to enable smartphones to sense collaboratively without accurate locations such that sensing coverage requirements can be met with limited energy consumption