Locality and Bounding-Box Quality of Two-Dimensional Space-Filling Curves

Space-filling curves can be used to organise points in the plane into bounding-box hierarchies (such as R-trees). We develop measures of the bounding-box quality of space-filling curves that express how effective different space-filling curves are for this purpose. We give general lower bounds on the bounding-box quality measures and on locality according to Gotsman and Lindenbaum for a large class of space-filling curves. We describe a generic algorithm to approximate these and similar quality measures for any given curve. Using our algorithm we find good approximations of the locality and the bounding-box quality of several known and new space-filling curves. Surprisingly, some curves with relatively bad locality by Gotsman and Lindenbaum's measure, have good bounding-box quality, while the curve with the best-known locality has relatively bad bounding-box quality.Comment: 24 pages, full version of paper to appear in ESA. Difference with first version: minor editing; Fig. 2(m) correcte

Content-Addressable Network for Distributed Simulations

The development of distributed systems, parallel computation technology, and Peer-to-Peer systems facilitates the realization of a distributed interactive world model. Thereby, we can implement a worldwide distributed simulation and virtual community, e.g., city traffic simulation and Massively Multiuser Virtual Environments (MMVE). In this thesis, we present Content-Addressable Network for Simulations (CANS), which is based on CAN. Thus, it incorporates all the advantages of CAN, such as self-organization, scalability, and fault-tolerance. The peers in CANS carry out the simulation for the zone assigned to them, and the zones are allocated in such a way that there is as little communication between the peers as possible. We propose two approaches for reorganizing zone-assignments after peers churn. These approaches are based on the distributed tree structure and prefix code. In comparison to existing approaches, our proposed approaches are more efficient and reliable. Since CANS is used to simulate “city traffic” and MMVE, it requires a low-dimensional key space, i.e., a two-dimensional or three-dimensional key space. Thus, we propose CAN tree routing and zone code routing, both of which adopt long links. CAN tree routing has a hierarchical design that is based on the CAN tree. Each peer equips two long links on average. Zone code routing is based on B*-tree. Each peer equips long links and shares the load evenly. Both of these routing solutions achieve routing hops on average. Consequently, the existing CAN can be optimized to perform simulations efficiently and reliably

Logarithmic Path-Length in Space-Filling Curves

Data structures based on space-filling curves have shown to be a good approach in several applications. For the monitoring of moving objects, e. g. necessary for the contact detection in finite-element simulations, we need a special metrics to compare the quality of different curves. This pape

Geostry - a Peer-to-Peer System for Location-based Information

An interesting development is summarized by the notion of ”Ubiquitous Computing”: In this area, miniature systems are integrated into everyday objects making these objects ”smart” and able to communicate. Thereby, everyday objects can gather information about their state and their environment. By embedding this information into a model of the real world, which nowadays can be modeled very realistically using sophisticated 3D modeling techniques, it is possible to generate powerful digital world models. Not only can existing objects of the real world and their state be mapped into these world models, but additional information can be linked to these objects as well. The result is a symbiosis of the real world and digital information spaces. In this thesis, we present a system that allows for an easy access to this information. In contrast to existing solutions our approach is not based on a server-client architecture. Geostry bases on a peer-to-peer system and thus incorporates all the advantages, such as self-organization, fairness (in terms of costs), scalability and many more. Setting up the network is realized through a decentralized bootstrapping protocol based on an existing Internet service to provide robustness and availability. To selectively find geographic-related information Geostry supports spatial queries. They - among other things - enable the user to search for information e.g. in a certain district only. Sometimes, a certain piece of information raises particular interest. To cope with the run on the single computer that provides this specific information, Geostry offers dynamic replication mechanisms. Thereby, the information is replicated for as long as the rush lasts. Thus, Geostry offers all aspects from setting up a network, providing access to geo-related information and replication methods to provide accessibility in times of high loads

Logarithmic Path-Length in Space-Filling Curves

Abstract. Data structures based on space-filling curves have shown to be a good approach in several applications. For the monitoring of moving objects, e. g. necessary for the contact detection in finite-element simulations, we need a special metrics to compare the quality of different curves. This paper proposes the logarithmic index-range as a suitable quality metrics. It is based on the distance over the path of a space-filling curve to adjacent cells in the 2-dimensional grid. We present analytical results for the Hilbert, the Lebesgue curve, and the fi\Omega-indexing and experimental results for the H-indexing. 1 Introduction The performance of algorithms in computational geometry mainly depends on the efficiency of the underlying data structures. One problem is the representation of spatial moving objects in memory. Efficient sorting and searching is not easy because there is no unique sorting criterion in higher dimensions. There are two possibilities to circumvent this problem: Using complex data structures like trees which include several sorting criterions or mapping of the data into 1-dimensional structures to use efficient well known algorithms. Trees for higher dimensional spaces are much more sophisticated to implement if they should obtain given efficiency constraints

Path planning algorithms for atmospheric science applications of autonomous aircraft systems

Among current techniques, used to assist the modelling of atmospheric processes, is an approach involving the balloon or aircraft launching of radiosondes, which travel along uncontrolled trajectories dependent on wind speed. Radiosondes are launched daily from numerous worldwide locations and the data collected is integral to numerical weather prediction.This thesis proposes an unmanned air system for atmospheric research, consisting of multiple, balloon-launched, autonomous gliders. The trajectories of the gliders are optimised for the uniform sampling of a volume of airspace and the efficient mapping of a particular physical or chemical measure. To accomplish this we have developed a series of algorithms for path planning, driven by the dual objectives of uncertainty andinformation gain.Algorithms for centralised, discrete path planning, a centralised, continuous planner and finally a decentralised, real-time, asynchronous planner are presented. The continuous heuristics search a look-up table of plausible manoeuvres generated by way of an offline flight dynamics model, ensuring that the optimised trajectories are flyable. Further to this, a greedy heuristic for path growth is introduced alongside a control for search coarseness, establishing a sliding control for the level of allowed global exploration, local exploitation and computational complexity. The algorithm is also integrated with a flight dynamics model, and communications and flight systems hardware, enabling software and hardware-in-the-loop simulations. The algorithm outperforms random search in two and three dimensions. We also assess the applicability of the unmanned air system in ‘real’ environments, accounting for the presence of complicated flow fields and boundaries. A case study based on the island South Georgia is presented and indicates good algorithm performance in strong, variable winds. We also examine the impact of co-operation within this multi-agent system of decentralised, unmanned gliders, investigating the threshold for communication range, which allows for optimal search whilst reducing both the cost of individual communication devices and the computational resources associated with the processing of data received by each aircraft. Reductions in communication radius are found to have a significant, negative impact upon the resulting efficiency of the system. To somewhat recover these losses, we utilise a sorting algorithm, determining information priority between any two aircraft in range. Furthermore, negotiation between aircraft is introduced, allowing aircraft to resolve any possible conflicts between selected paths, which helps to counteractany latency in the search heuristic