I/O-efficient dynamic point location in monotone planar subdivisions

We present an efficient external-memory dynamic data structure for point location in monotone planar subdivisions. Our data structure uses O(N/B) disk blocks to store a monotone subdivision of size N, where B is the size of a disk block. It supports queries in O(logi N) I/OS (worst-case) and updates in O(lo& N) I/OS (amortized). We also propose a new variant of B-trees, called leuelbalanced B-trees, which allow insert, delete, merge, and split operations in O((l+ $logM,B f) log, N) I/OS (amortized), 2 5 b 2 B/2, even if each node stores a pointer to its parent. Here M is the size of main memory. Besides being essential to our point-location data structure, we believe that level-balanced B-trees are of significant independent interest. They can, for example, be used to dynamically maintain a planar St-graph using O((1 +$10g~,~ $$) log, N) = O(logi N) I/OS (amortized) per update, so that reachability queries can be answered in O(log, N) I/OS (worst case)

A new layout optimization technique for interferometric arrays, applied to the MWA

Antenna layout is an important design consideration for radio interferometers because it determines the quality of the snapshot point spread function (PSF, or array beam). This is particularly true for experiments targeting the 21 cm Epoch of Reionization signal as the quality of the foreground subtraction depends directly on the spatial dynamic range and thus the smoothness of the baseline distribution. Nearly all sites have constraints on where antennas can be placed---even at the remote Australian location of the MWA (Murchison Widefield Array) there are rock outcrops, flood zones, heritages areas, emergency runways and trees. These exclusion areas can introduce spatial structure into the baseline distribution that enhance the PSF sidelobes and reduce the angular dynamic range. In this paper we present a new method of constrained antenna placement that reduces the spatial structure in the baseline distribution. This method not only outperforms random placement algorithms that avoid exclusion zones, but surprisingly outperforms random placement algorithms without constraints to provide what we believe are the smoothest constrained baseline distributions developed to date. We use our new algorithm to determine antenna placements for the originally planned MWA, and present the antenna locations, baseline distribution, and snapshot PSF for this array choice.Comment: 12 pages, 6 figures, 1 table. Accepted for publication in MNRA

Geo-Skip List Data Structure ? Implementation and Solving Spatial Queries

A major portion of the queries fired on the internet have spatial keywords in them, the storage and retrieval of spatial data has become an important task in today?s era. Given a geographic query that is composed of query keywords and a location, a geographic search engine retrieves documents that are the most textually and spatially relevant to the query keywords and the location, respectively, and ranks the retrieved documents according to their joint textual and spatial relevance to the query. The lack of an efficient index that can simultaneously handle both the textual and spatial aspects of the documents makes existing geographic search engines inefficient in answering geographic queries. There are data structures which facilitate storage and retrieval of geographical data like R-trees, R* trees, KD trees etc. We propose Geo-Skip list data structure which is also one such data structure which is inspired from the skip list data structure. It is simple, dynamic, partly deterministic and partly randomized data structure. This structure brings out the hierarchy of administrative divisions of a region very well. Also it shows an improvement in the search efficiency as compared with R-trees. In this paper, we propose algorithms for the implementation of basic spatial queries with the help of Geo-Skip List data structure ? namely, point query, range query, finding the nearest neighbour query and kth nearest neighbour query

Towards a Scalable Dynamic Spatial Database System

With the rise of GPS-enabled smartphones and other similar mobile devices, massive amounts of location data are available. However, no scalable solutions for soft real-time spatial queries on large sets of moving objects have yet emerged. In this paper we explore and measure the limits of actual algorithms and implementations regarding different application scenarios. And finally we propose a novel distributed architecture to solve the scalability issues.Comment: (2012

A Static Optimality Transformation with Applications to Planar Point Location

Over the last decade, there have been several data structures that, given a planar subdivision and a probability distribution over the plane, provide a way for answering point location queries that is fine-tuned for the distribution. All these methods suffer from the requirement that the query distribution must be known in advance. We present a new data structure for point location queries in planar triangulations. Our structure is asymptotically as fast as the optimal structures, but it requires no prior information about the queries. This is a 2D analogue of the jump from Knuth's optimum binary search trees (discovered in 1971) to the splay trees of Sleator and Tarjan in 1985. While the former need to know the query distribution, the latter are statically optimal. This means that we can adapt to the query sequence and achieve the same asymptotic performance as an optimum static structure, without needing any additional information.Comment: 13 pages, 1 figure, a preliminary version appeared at SoCG 201

Analysis of Performance of Dynamic Multicast Routing Algorithms

In this paper, three new dynamic multicast routing algorithms based on the greedy tree technique are proposed; Source Optimised Tree, Topology Based Tree and Minimum Diameter Tree. A simulation analysis is presented showing various performance aspects of the algorithms, in which a comparison is made with the greedy and core based tree techniques. The effects of the tree source location on dynamic membership change are also examined. The simulations demonstrate that the Source Optimised Tree algorithm achieves a significant improvement in terms of delay and link usage when compared to the Core Based Tree, and greedy algorithm

Managing Unbounded-Length Keys in Comparison-Driven Data Structures with Applications to On-Line Indexing

This paper presents a general technique for optimally transforming any dynamic data structure that operates on atomic and indivisible keys by constant-time comparisons, into a data structure that handles unbounded-length keys whose comparison cost is not a constant. Examples of these keys are strings, multi-dimensional points, multiple-precision numbers, multi-key data (e.g.~records), XML paths, URL addresses, etc. The technique is more general than what has been done in previous work as no particular exploitation of the underlying structure of is required. The only requirement is that the insertion of a key must identify its predecessor or its successor. Using the proposed technique, online suffix tree can be constructed in worst case time $O(\log n)$ per input symbol (as opposed to amortized $O(\log n)$ time per symbol, achieved by previously known algorithms). To our knowledge, our algorithm is the first that achieves $O(\log n)$ worst case time per input symbol. Searching for a pattern of length $m$ in the resulting suffix tree takes $O(\min(m\log |\Sigma|, m + \log n) + tocc)$ time, where $tocc$ is the number of occurrences of the pattern. The paper also describes more applications and show how to obtain alternative methods for dealing with suffix sorting, dynamic lowest common ancestors and order maintenance

GENERATION OF FORESTS ON TERRAIN WITH DYNAMIC LIGHTING AND SHADOWING

The purpose of this research project is to exhibit an efficient method of creating dynamic lighting and shadowing for the generation of forests on terrain. In this research project, I use textures which contain images of trees from a bird’s eye view in order to create a high scale forest. Furthermore, by manipulating the transparency and color of the textures according to the algorithmic calculations of light and shadow on terrain, I provide the functionality of dynamic lighting and shadowing. Finally, by analyzing the OpenGL pipeline, I design my code in order to allow efficient rendering of the forest