Visibility Domains and Complexity

Two problems in discrete and computational geometry are considered that are related to questions about the combinatorial complexity of arrangements of visibility domains and about the hardness of path planning under cost measures defined using visibility domains. The first problem is to estimate the VC-dimension of visibility domains. The VC-dimension is a fundamental parameter of every range space that is typically used to derive upper bounds on the size of hitting sets. Better bounds on the VC-dimension directly translate into better bounds on the size of hitting sets. Estimating the VC-dimension of visibility domains has proven to be a hard problem. In this thesis, new tools to tackle this problem are developed. Encircling arguments are combined with decomposition techniques of a new kind. The main ingredient of the novel approach is the idea of relativization that makes it possible to replace in the analysis of intersections the complicated visibility domains by simpler geometric ranges. The main result here is the new upper bound of 14 on the VC-dimension of visibility polygons in simple polygons that improves significantly upon the previously known best upper bound of 23. For the VC-dimension of perimeter visibility domains, the new techniques yield an upper bound of 7 that leaves only a very small gap to the best known lower bound of 5. The second problem considered is to compute the barrier resilience of visibility domains. In barrier resilience problems, one is given a set of barriers and two points s and t in R^d. The task is to find the minimum number of barriers one has to remove such that there is a way between s and t that does not cross a barrier. In the field of sensor networks, the barriers are interpreted as sensor ranges and the barrier resilience of a network is a measure for its vulnerability. In this thesis the very natural special case where the barriers are visibility domains is investigated. It can also be formulated in terms of finding a so-called minimum witness path. For visibility domains in simple polygons it is shown that one can find an optimal path efficiently. For polygons with holes an approximation hardness result is shown that is stronger than previous hardness results in geometric settings. Two different three-dimensional settings are considered and their respective relations to the Minimum Neighborhood Path problem and the Minimum Color Path problem in graphs are demonstrated. For one of the three-dimensional problems a 2-approximation algorithm is designed. For the general problem of finding minimum witness paths among polyhedral obstacles it turns out that it is not approximable in a strong sense

Sensor networks and distributed CSP: communication, computation and complexity

We introduce SensorDCSP, a naturally distributed benchmark based on a real-world application that arises in the context of networked distributed systems. In order to study the performance of Distributed CSP (DisCSP) algorithms in a truly distributed setting, we use a discrete-event network simulator, which allows us to model the impact of different network traffic conditions on the performance of the algorithms. We consider two complete DisCSP algorithms: asynchronous backtracking (ABT) and asynchronous weak commitment search (AWC), and perform performance comparison for these algorithms on both satisfiable and unsatisfiable instances of SensorDCSP. We found that random delays (due to network traffic or in some cases actively introduced by the agents) combined with a dynamic decentralized restart strategy can improve the performance of DisCSP algorithms. In addition, we introduce GSensorDCSP, a plain-embedded version of SensorDCSP that is closely related to various real-life dynamic tracking systems. We perform both analytical and empirical study of this benchmark domain. In particular, this benchmark allows us to study the attractiveness of solution repairing for solving a sequence of DisCSPs that represent the dynamic tracking of a set of moving objects.This work was supported in part by AFOSR (F49620-01-1-0076, Intelligent Information Systems Institute and MURI F49620-01-1-0361), CICYT (TIC2001-1577-C03-03 and TIC2003-00950), DARPA (F30602-00-2- 0530), an NSF CAREER award (IIS-9734128), and an Alfred P. Sloan Research Fellowship. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the US Government

Multi-robot team formation control in the GUARDIANS project

Purpose The GUARDIANS multi-robot team is to be deployed in a large warehouse in smoke. The team is to assist firefighters search the warehouse in the event or danger of a fire. The large dimensions of the environment together with development of smoke which drastically reduces visibility, represent major challenges for search and rescue operations. The GUARDIANS robots guide and accompany the firefighters on site whilst indicating possible obstacles and the locations of danger and maintaining communications links. Design/methodology/approach In order to fulfill the aforementioned tasks the robots need to exhibit certain behaviours. Among the basic behaviours are capabilities to stay together as a group, that is, generate a formation and navigate while keeping this formation. The control model used to generate these behaviours is based on the so-called social potential field framework, which we adapt to the specific tasks required for the GUARDIANS scenario. All tasks can be achieved without central control, and some of the behaviours can be performed without explicit communication between the robots. Findings The GUARDIANS environment requires flexible formations of the robot team: the formation has to adapt itself to the circumstances. Thus the application has forced us to redefine the concept of a formation. Using the graph-theoretic terminology, we can say that a formation may be stretched out as a path or be compact as a star or wheel. We have implemented the developed behaviours in simulation environments as well as on real ERA-MOBI robots commonly referred to as Erratics. We discuss advantages and shortcomings of our model, based on the simulations as well as on the implementation with a team of Erratics.</p

Success for pacific learners : the impact of tertiary education strategies

This project examined the impact of the 3 successive tertiary education strategies (2002-2007; 2007-2012 and 2010-2015) on how tertiary education institutions have developed their support for Pacific learners. Findings show that the Pasifika objectives within each of the 3 strategies are considered to be an important signal to Tertiary Education Institutions (TEIs) that success for Pasifika learners is a significant and continuing government priority and that the strategies are seen as an important enabler of change. These objectives have raised the priority for action to support Pasifika learners, unlocked resources for Pasifika initiatives and promoted the inclusion of Pasifika priorities on the strategic agendas of TEIs. It was noted however, this influence is only one of a number of internal and external, and local and national influences on enhancing success for Pasifika learners

Toward a Mathematical Theory of Behavioral-Social Dynamics for Pedestrian Crowds

This paper presents a new approach to behavioral-social dynamics of pedestrian crowds by suitable development of methods of the kinetic theory. It is shown how heterogeneous individual behaviors can modify the collective dynamics, as well as how local unusual behaviors can propagate in the crowd. The main feature of this approach is a detailed analysis of the interactions between dynamics and social behaviors.Comment: 22 pages, 5 figure