Tour recommendation for groups

Consider a group of people who are visiting a major touristic city, such as NY, Paris, or Rome. It is reasonable to assume that each member of the group has his or her own interests or preferences about places to visit, which in general may differ from those of other members. Still, people almost always want to hang out together and so the following question naturally arises: What is the best tour that the group could perform together in the city? This problem underpins several challenges, ranging from understanding people’s expected attitudes towards potential points of interest, to modeling and providing good and viable solutions. Formulating this problem is challenging because of multiple competing objectives. For example, making the entire group as happy as possible in general conflicts with the objective that no member becomes disappointed. In this paper, we address the algorithmic implications of the above problem, by providing various formulations that take into account the overall group as well as the individual satisfaction and the length of the tour. We then study the computational complexity of these formulations, we provide effective and efficient practical algorithms, and, finally, we evaluate them on datasets constructed from real city data

Drone Base Station Trajectory Management for Optimal Scheduling in LTE-Based Sparse Delay-Sensitive M2M Networks

Providing connectivity in areas out of reach of the cellular infrastructure is a very active area of research. This connectivity is particularly needed in case of the deployment of machine type communication devices (MTCDs) for critical purposes such as homeland security. In such applications, MTCDs are deployed in areas that are hard to reach using regular communications infrastructure while the collected data is timely critical. Drone-supported communications constitute a new trend in complementing the reach of the terrestrial communication infrastructure. In this study, drones are used as base stations to provide real-time communication services to gather critical data out of a group of MTCDs that are sparsely deployed in a marine environment. Studying different communication technologies as LTE, WiFi, LPWAN and Free-Space Optical communication (FSOC) incorporated with the drone communications was important in the first phase of this research to identify the best candidate for addressing this need. We have determined the cellular technology, and particularly LTE, to be the most suitable candidate to support such applications. In this case, an LTE base station would be mounted on the drone which will help communicate with the different MTCDs to transmit their data to the network backhaul. We then formulate the problem model mathematically and devise the trajectory planning and scheduling algorithm that decides the drone path and the resulting scheduling. Based on this formulation, we decided to compare between an Ant Colony Optimization (ACO) based technique that optimizes the drone movement among the sparsely-deployed MTCDs and a Genetic Algorithm (GA) based solution that achieves the same purpose. This optimization is based on minimizing the energy cost of the drone movement while ensuring the data transmission deadline missing is minimized. We present the results of several simulation experiments that validate the different performance aspects of the technique

A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms

Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results. We survey developments in the area both from the algorithmic and hardness perspectives, with emphasis on new techniques and potential future research directions

Approximation Algorithms for Geometric Networks

The main contribution of this thesis is approximation algorithms for several computational geometry problems. The underlying structure for most of the problems studied is a geometric network. A geometric network is, in its abstract form, a set of vertices, pairwise connected with an edge, such that the weight of this connecting edge is the Euclidean distance between the pair of points connected. Such a network may be used to represent a multitude of real-life structures, such as, for example, a set of cities connected with roads. Considering the case that a specific network is given, we study three separate problems. In the first problem we consider the case of interconnected `islands' of well-connected networks, in which shortest paths are computed. In the second problem the input network is a triangulation. We efficiently simplify this triangulation using edge contractions. Finally, we consider individual movement trajectories representing, for example, wild animals where we compute leadership individuals. Next, we consider the case that only a set of vertices is given, and the aim is to actually construct a network. We consider two such problems. In the first one we compute a partition of the vertices into several subsets where, considering the minimum spanning tree (MST) for each subset, we aim to minimize the largest MST. The other problem is to construct a $t$-spanner of low weight fast and simple. We do this by first extending the so-called gap theorem. In addition to the above geometric network problems we also study a problem where we aim to place a set of different sized rectangles, such that the area of their corresponding bounding box is minimized, and such that a grid may be placed over the rectangles. The grid should not intersect any rectangle, and each cell of the grid should contain at most one rectangle. All studied problems are such that they do not easily allow computation of optimal solutions in a feasible time. Instead we consider approximation algorithms, where near-optimal solutions are produced in polynomial time. In addition to the above geometric network problems we also study a problem where we aim to place a set of different sized rectangles, such that the area of their corresponding bounding box is minimized, and such that a grid may be placed over the rectangles. The grid should not intersect any rectangle, and each cell of the grid should contain at most one rectangle. All studied problems are such that they do not easily allow computation of optimal solutions in a feasible time. Instead we consider approximation algorithms, where near-optimal solutions are produced in polynomial time

Approximation in Multiobjective Optimization with Applications

Over the last couple of decades, the field of multiobjective optimization has received much attention in solving real-life optimization problems in science, engineering, economics and other fields where optimal decisions need to be made in the presence of trade-offs between two or more conflicting objective functions. The conflicting nature of objective functions implies a solution set for a multiobjective optimization problem. Obtaining this set is difficult for many reasons, and a variety of approaches for approximating it either partially or entirely have been proposed. In response to the growing interest in approximation, this research investigates developing a theory and methodology for representing and approximating solution sets of multiobjective optimization problems. The concept of the tolerance function is proposed as a tool for modeling representation quality. Two types of subsets of the set being represented, covers and approximations, are defined, and their properties are examined. In addition, approximating the solution set of the multiobjective set covering problem (MOSCP), one of the challenging combinatorial optimization problems that has seen limited study, is investigated. Two algorithms are proposed for approximating the solution set of the MOSCP, and their approximation quality is derived. A heuristic algorithm is also proposed to approximate the solution set of the MOSCP. The performance of each algorithm is evaluated using test problems. Since the MOSCP has many real-life applications, and in particular designing reserve systems for ecological species is a common field for its applications, two optimization models are proposed in this dissertation for preserving reserve sites for species and their natural habitats

Metaheuristics for NP-hard combinatorial optimization problems

Ph.DDOCTOR OF PHILOSOPH