The Metric Nearness Problem

Metric nearness refers to the problem of optimally restoring metric properties to distance measurements that happen to be nonmetric due to measurement errors or otherwise. Metric data can be important in various settings, for example, in clustering, classification, metric-based indexing, query processing, and graph theoretic approximation algorithms. This paper formulates and solves the metric nearness problem: Given a set of pairwise dissimilarities, find a “nearest” set of distances that satisfy the properties of a metric—principally the triangle inequality. For solving this problem, the paper develops efficient triangle fixing algorithms that are based on an iterative projection method. An intriguing aspect of the metric nearness problem is that a special case turns out to be equivalent to the all pairs shortest paths problem. The paper exploits this equivalence and develops a new algorithm for the latter problem using a primal-dual method. Applications to graph clustering are provided as an illustration. We include experiments that demonstrate the computational superiority of triangle fixing over general purpose convex programming software. Finally, we conclude by suggesting various useful extensions and generalizations to metric nearness

Coverage & cooperation: Completing complex tasks as quickly as possible using teams of robots

As the robotics industry grows and robots enter our homes and public spaces, they are increasingly expected to work in cooperation with each other. My thesis focuses on multirobot planning, specifically in the context of coverage robots, such as robotic lawnmowers and vacuum cleaners. Two problems unique to multirobot teams are task allocation and search. I present a task allocation algorithm which balances the workload amongst all robots in the team with the objective of minimizing the overall mission time. I also present a search algorithm which robots can use to find lost teammates. It uses a probabilistic belief of a target robot’s position to create a planning tree and then searches by following the best path in the tree. For robust multirobot coverage, I use both the task allocation and search algorithms. First the coverage region is divided into a set of small coverage tasks which minimize the number of turns the robots will need to take. These tasks are then allocated to individual robots. During the mission, robots replan with nearby robots to rebalance the workload and, once a robot has finished its tasks, it searches for teammates to help them finish their tasks faster

Energy-efficient routing for mobile data collectors in wireless sensor networks with obstacles

This paper proposes an energy-efficient routing mechanism by introducing intentional mobility to wireless sensor networks (WSNs) with obstacles. In the sensing field, Mobile Data Collectors (MDCs) can freely move for collecting data from sensors. An MDC begins its periodical movement from the base station and finally returns and transports the data to the base station. In physical environments, the sensing field may contain various obstacles. A research challenge is how to find an obstacle-avoiding shortest tour for the MDC. Firstly, we obtain the same size grid cells by dividing the network region. Secondly, according to the line sweep technique, the spanning graph is easily constructed. The spanning graph composed of some grid cells usually includes the shortest search path for the MDC. Then, based on the spanning graph, we can construct a complete graph by Warshall-Floyd algorithm. Finally, we present a heuristic tour-planning algorithm on the basis of the complete graph. Through simulation, the validity of our method is verified. This paper contributes in providing an energy-efficient routing mechanism for the WSNs with obstacles

Travel Package Recommendation

Location Based SocialNetworks (LBSN) benefit the users by allowing them to share their locations and life moments with their friends. The users can also review the locations they have visited. Classical recommender systems provide users a ranked list of single items. This is not suitable for applications like trip planning,where the recommendations should contain multiple items in an appropriate sequence. The problem of generating such recommendations is challenging due to various critical aspects, which includes user interest, budget constraints and high sparsity in the available data used to solve the problem. In this paper, we propose a graph based approach to recommend a set of personalized travel packages. Each recommended package comprises of a sequence of multiple Point of Interests (POIs). Given the current location and spatio-temporal constraints, our goal is to recommend a package which satisfies the constraints. This approach utilizes the data collected fromLBSNs to learn user preferences and also models the location popularity

Simulating The Impact of Emissions Control on Economic Productivity Using Particle Systems and Puff Dispersion Model

A simulation platform is developed for quantifying the change in productivity of an economy under passive and active emission control mechanisms. The program uses object-oriented programming to code a collection of objects resembling typical stakeholders in an economy. These objects include firms, markets, transportation hubs, and boids which are distributed over a 2D surface. Firms are connected using a modified Prim’s Minimum spanning tree algorithm, followed by implementation of an all-pair shortest path Floyd Warshall algorithm for navigation purposes. Firms use a non-linear production function for transformation of land, labor, and capital inputs to finished product. A GA-Vehicle Routing Problem with multiple pickups and drop-offs is implemented for efficient delivery of commodities across multiple nodes in the economy. Boids are autonomous agents which perform several functions in the economy including labor, consumption, renting, saving, and investing. Each boid is programmed with several microeconomic functions including intertemporal choice models, Hicksian and Marshallian demand function, and labor-leisure model. The simulation uses a Puff Dispersion model to simulate the advection and diffusion of emissions from point and mobile sources in the economy. A dose-response function is implemented to quantify depreciation of a Boid’s health upon contact with these emissions. The impact of emissions control on productivity and air quality is examined through a series of passive and active emission control scenarios. Passive control examines the impact of various shutdown times on economic productivity and rate of emissions exposure experienced by boids. The active control strategy examines the effects of acceptable levels of emissions exposure on economic productivity. The key findings on 7 different scenarios of passive and active emissions controls indicate that rate of productivity and consumption in an economy declines with increased scrutiny of emissions from point sources. In terms of exposure rates, the point sources may not be the primary source of average exposure rates, however they significantly impact the maximum exposure rate experienced by a boid. Tightening of emissions control also negatively impacts the transportation sector by reducing the asset utilization rate as well as reducing the total volume of goods transported across the economy