A linear lower bound for incrementing a space-optimal integer representation in the bit-probe model

We present the first linear lower bound for the number of bits required to be accessed in the worst case to increment an integer in an arbitrary space- optimal binary representation. The best previously known lower bound was logarithmic. It is known that a logarithmic number of read bits in the worst case is enough to increment some of the integer representations that use one bit of redundancy, therefore we show an exponential gap between space-optimal and redundant counters. Our proof is based on considering the increment procedure for a space optimal counter as a permutation and calculating its parity. For every space optimal counter, the permutation must be odd, and implementing an odd permutation requires reading at least half the bits in the worst case. The combination of these two observations explains why the worst-case space-optimal problem is substantially different from both average-case approach with constant expected number of reads and almost space optimal representations with logarithmic number of reads in the worst case.Comment: 12 pages, 4 figure

On the size of quadtrees generalized to d-dimensional binary pictures

AbstractSome results about the size of quadtrees and linear quadtrees, used to represent binary 2n × 2n digital pictures, are generalized to d-dimensional 2n × … × 2n pictures. Among these results are a comparison of the space-efficiency of linear vs regular trees, in terms of both the number of nodes of the tree and the number of bits needed to store each node, and an upper bound on the number of nodes as a function of n and the perimeter of the picture

The Representation of symmetric patterns using the quadtree data structure

Hierarchical data structures for image representation have been widely explored in recent years. These data structures are based on the principle of recursive decomposition of an image region. The most commonly mentioned picture data structure for two-dimensional data is referred to as a quadtree . The purpose of this thesis is to investigate the use of a general quadtree scheme as a means of representing symmetric images. Specifically, images are generated according to the rules of selected two-dimensional plane symmetry groups

Automated equivalence checking of concurrent quantum systems

The novel field of quantum computation and quantum information has gathered significant momentum in the last few years. It has the potential to radically impact the future of information technology and in influence the development of modern society. The construction of practical, general purpose quantum computers has been challenging, but quantum cryptographic and communication devices have been available in the commercial marketplace for several years. Quantum networks have been built in various cities around the world and a dedicated satellite has been launched by China to provide secure quantum communication. Such new technologies demand rigorous analysis and verification before they can be trusted in safety- and security- critical applications. Experience with classical hardware and software systems has shown the difficulty of achieving robust and reliable implementations. We present CCSq, a concurrent language for describing quantum systems, and develop verification techniques for checking equivalence between CCSq processes. CCSq has well-defined operational and superoperator semantics for protocols that are functional, in the sense of computing a deterministic input-output relation for all interleavings arising from concurrency in the system. We have implemented QEC (Quantum Equivalence Checker), a tool which takes the specification and implementation of quantum protocols, described in CCSq, and automatically checks their equivalence. For efficiency purposes, we restrict ourselves to Clifford operators in the stabilizer formalism, but we are able to verify protocols over all input states. We have specified and verified a collection of interesting and practical quantum protocols ranging from quantum communication and quantum cryptography to quantum error correction

The contour tree image encoding technique and file format

The process of contourization is presented which converts a raster image into a discrete set of plateaux or contours. These contours can be grouped into a hierarchical structure, defining total spatial inclusion, called a contour tree. A contour coder has been developed which fully describes these contours in a compact and efficient manner and is the basis for an image compression method. Simplification of the contour tree has been undertaken by merging contour tree nodes thus lowering the contour tree's entropy. This can be exploited by the contour coder to increase the image compression ratio. By applying general and simple rules derived from physiological experiments on the human vision system, lossy image compression can be achieved which minimises noticeable artifacts in the simplified image. The contour merging technique offers a complementary lossy compression system to the QDCT (Quantised Discrete Cosine Transform). The artifacts introduced by the two methods are very different; QDCT produces a general blurring and adds extra highlights in the form of overshoots, whereas contour merging sharpens edges, reduces highlights and introduces a degree of false contouring. A format based on the contourization technique which caters for most image types is defined, called the contour tree image format. Image operations directly on this compressed format have been studied which for certain manipulations can offer significant operational speed increases over using a standard raster image format. A couple of examples of operations specific to the contour tree format are presented showing some of the features of the new format.Science and Engineering Research Counci

Advanced Map Matching Technologies and Techniques for Pedestrian/Wheelchair Navigation

Due to the constantly increasing technical advantages of mobile devices (such as smartphones), pedestrian/wheelchair navigation recently has achieved a high level of interest as one of smartphones’ potential mobile applications. While vehicle navigation systems have already reached a certain level of maturity, pedestrian/wheelchair navigation services are still in their infancy. By comparing vehicle navigation systems, a set of map matching requirements and challenges unique in pedestrian/wheelchair navigation is identified. To provide navigation assistance to pedestrians and wheelchair users, there is a need for the design and development of new map matching techniques. The main goal of this research is to investigate and develop advanced map matching technologies and techniques particular for pedestrian/wheelchair navigation services. As the first step in map matching, an adaptive candidate segment selection algorithm is developed to efficiently find candidate segments. Furthermore, to narrow down the search for the correct segment, advanced mathematical models are applied. GPS-based chain-code map matching, Hidden Markov Model (HMM) map matching, and fuzzy-logic map matching algorithms are developed to estimate real-time location of users in pedestrian/wheelchair navigation systems/services. Nevertheless, GPS signal is not always available in areas with high-rise buildings and even when there is a signal, the accuracy may not be high enough for localization of pedestrians and wheelchair users on sidewalks. To overcome these shortcomings of GPS, multi-sensor integrated map matching algorithms are investigated and developed in this research. These algorithms include a movement pattern recognition algorithm, using accelerometer and compass data, and a vision-based positioning algorithm to fill in signal gaps in GPS positioning. Experiments are conducted to evaluate the developed algorithms using real field test data (GPS coordinates and other sensors data). The experimental results show that the developed algorithms and the integrated sensors, i.e., a monocular visual odometry, a GPS, an accelerometer, and a compass, can provide high-quality and uninterrupted localization services in pedestrian/wheelchair navigation systems/services. The map matching techniques developed in this work can be applied to various pedestrian/wheelchair navigation applications, such as tracking senior citizens and children, or tourist service systems, and can be further utilized in building walking robots and automatic wheelchair navigation systems