Improved algorithms and analysis for the laminar matroid secretary problem

In a matroid secretary problem, one is presented with a sequence of objects of various weights in a random order, and must choose irrevocably to accept or reject each item. There is a further constraint that the set of items selected must form an independent set of an associated matroid. Constant-competitive algorithms (algorithms whose expected solution weight is within a constant factor of the optimal) are known for many types of matroid secretary problems. We examine the laminar matroid and show an algorithm achieving provably 0.053 competitive ratio

On Correcting Inputs: Inverse Optimization for Online Structured Prediction

Algorithm designers typically assume that the input data is correct, and then proceed to find "optimal" or "sub-optimal" solutions using this input data. However this assumption of correct data does not always hold in practice, especially in the context of online learning systems where the objective is to learn appropriate feature weights given some training samples. Such scenarios necessitate the study of inverse optimization problems where one is given an input instance as well as a desired output and the task is to adjust the input data so that the given output is indeed optimal. Motivated by learning structured prediction models, in this paper we consider inverse optimization with a margin, i.e., we require the given output to be better than all other feasible outputs by a desired margin. We consider such inverse optimization problems for maximum weight matroid basis, matroid intersection, perfect matchings, minimum cost maximum flows, and shortest paths and derive the first known results for such problems with a non-zero margin. The effectiveness of these algorithmic approaches to online learning for structured prediction is also discussed.Comment: Conference version to appear in FSTTCS, 201

Determination of Natural Frequency of Aerofoil Section Blades Using Finite Element Approach, Study of Effect of Aspect Ratio and Thickness on Natural Frequency

In this paper an attempt has been made to calculate the natural frequencies of aerofoil section blades using the finite element method. The effect of varying the aspect ratio and thickness on the frequencies has also been studied. It is observed that by increasing the value of aspect ratio, the natural frequency in all the modes is increased. It is also concluded that, there is some optimum value of thickness at which the natural frequencies in different modes of vibration are minimum

Data-Aware Scheduling in Datacenters

Datacenters have emerged as the dominant form of computing infrastructure over the last two decades. The tremendous increase in the requirements of data analysis has led to a proportional increase in power consumption and datacenters are now one of the fastest growing electricity consumers in the United States. Another rising concern is the loss of throughput due to network congestion. Scheduling models that do not explicitly account for data placement may lead to a transfer of large amounts of data over the network causing unacceptable delays. In this dissertation, we study different scheduling models that are inspired by the dual objectives of minimizing energy costs and network congestion in a datacenter. As datacenters are equipped to handle peak workloads, the average server utilization in most datacenters is very low. As a result, one can achieve huge energy savings by selectively shutting down machines when demand is low. In this dissertation, we introduce the network-aware machine activation problem to find a schedule that simultaneously minimizes the number of machines necessary and the congestion incurred in the network. Our model significantly generalizes well-studied combinatorial optimization problems such as hard-capacitated hypergraph covering and is thus strongly NP-hard. As a result, we focus on finding good approximation algorithms. Data-parallel computation frameworks such as MapReduce have popularized the design of applications that require a large amount of communication between different machines. Efficient scheduling of these communication demands is essential to guarantee efficient execution of the different applications. In the second part of the thesis, we study the approximability of the co-flow scheduling problem that has been recently introduced to capture these application-level demands. Finally, we also study the question, "In what order should one process jobs?'' Often, precedence constraints specify a partial order over the set of jobs and the objective is to find suitable schedules that satisfy the partial order. However, in the presence of hard deadline constraints, it may be impossible to find a schedule that satisfies all precedence constraints. In this thesis we formalize different variants of job scheduling with soft precedence constraints and conduct the first systematic study of these problems

Revenue Maximization in Transportation Networks

We study the joint optimization problem of pricing trips in a transportation network and serving the induced demands by routing a fleet of available service vehicles to maximize revenue. Our framework encompasses applications that include traditional transportation networks (e.g., airplanes, buses) and their more modern counterparts (e.g., ride-sharing systems). We describe a simple combinatorial model, in which each edge in the network is endowed with a curve that gives the demand for traveling between its endpoints at any given price. We are supplied with a number of vehicles and a time budget to serve the demands induced by the prices that we set, seeking to maximize revenue. We first focus on a (preliminary) special case of our model with unit distances and unit time horizon. We show that this version of the problem can be solved optimally in polynomial time. Switching to the general case of our model, we first present a two-stage approach that separately optimizes for prices and routes, achieving a logarithmic approximation to revenue in the process. Next, using the insights gathered in the first two results, we present a constant factor approximation algorithm that jointly optimizes for prices and routes for the supply vehicles. Finally, we discuss how our algorithms can handle capacitated vehicles, impatient demands, and selfish (wage-maximizing) drivers

Introduction of web based e-learning in pharmacology: an innovative way

Background: In current scenario, poor attendances in classes and poor performances of students are a stimulus to think beyond the conventional teaching approach. Being current digital generation, students may show their affection to e-learning. Aim of this study was to introduce the e-learning in Pharmacology with objectives to evaluate its acceptability by students and faculties and learning gain of studentsMethods: Four inter-related e- modules for a topic “drugs used in treatment of bronchial asthma” were prepared and provided to the students. Pre-test was conducted before giving E-modules. Students were instructed to complete the e-modules in seven days and post-test was conducted on last day. Feedbacks from students and faculties were collected. Learning gain of students was evaluated along with their acceptability for e-modules.Results: Total of 147 students participated in the study but, 130 students completed pre-test and post-test, both. The absolute learning gain (% post-test score - % pre-test score) was found 23.3±19.2%. The class average normalized learning gain was found 0.32 (32%) that was significant, as per Hake’s criteria for the effectiveness of educational interventions. Slow speed of internet, background noise in modules, and size of e-modules were some technical problem faced by students. The most of students perceived the modules positively and demanded the e-modules for other topics. The faculties also perceived it positively and suggested to use e-modules additionally to classroom lectures.Conclusions: E-learning modules were taken positively by students and faculties and resulted in significant learning gain.