Hypercube-Based Topologies With Incremental Link Redundancy.

Hypercube structures have received a great deal of attention due to the attractive properties inherent to their topology. Parallel algorithms targeted at this topology can be partitioned into many tasks, each of which running on one node processor. A high degree of performance is achievable by running every task individually and concurrently on each node processor available in the hypercube. Nevertheless, the performance can be greatly degraded if the node processors spend much time just communicating with one another. The goal in designing hypercubes is, therefore, to achieve a high ratio of computation time to communication time. The dissertation addresses primarily ways to enhance system performance by minimizing the communication time among processors. The need for improving the performance of hypercube networks is clearly explained. Three novel topologies related to hypercubes with improved performance are proposed and analyzed. Firstly, the Bridged Hypercube (BHC) is introduced. It is shown that this design is remarkably more efficient and cost-effective than the standard hypercube due to its low diameter. Basic routing algorithms such as one to one and broadcasting are developed for the BHC and proven optimal. Shortcomings of the BHC such as its asymmetry and limited application are clearly discussed. The Folded Hypercube (FHC), a symmetric network with low diameter and low degree of the node, is introduced. This new topology is shown to support highly efficient communications among the processors. For the FHC, optimal routing algorithms are developed and proven to be remarkably more efficient than those of the conventional hypercube. For both BHC and FHC, network parameters such as average distance, message traffic density, and communication delay are derived and comparatively analyzed. Lastly, to enhance the fault tolerance of the hypercube, a new design called Fault Tolerant Hypercube (FTH) is proposed. The FTH is shown to exhibit a graceful degradation in performance with the existence of faults. Probabilistic models based on Markov chain are employed to characterize the fault tolerance of the FTH. The results are verified by Monte Carlo simulation. The most attractive feature of all new topologies is the asymptotically zero overhead associated with them. The designs are simple and implementable. These designs can lead themselves to many parallel processing applications requiring high degree of performance

Modeling and simulation of adaptive multimodal optical sensors for target tracking in the visible to near infrared

This work investigates an integrated aerial remote sensor design approach to address moving target detection and tracking problems within highly cluttered, dynamic ground-based scenes. Sophisticated simulation methodologies and scene phenomenology validations have resulted in advancements in artificial multimodal truth video synthesis. Complex modeling of novel micro-opto-electro-mechanical systems (MOEMS) devices, optical systems, and detector arrays has resulted in a proof of concept for a state-of-the-art imaging spectropolarimeter sensor model that does not suffer from typical multimodal image registration problems. Test methodology developed for this work provides the ability to quantify performance of a target tracking application with varying ground scenery, flight characteristics, or sensor specifications. The culmination of this research is an end-to-end simulated demonstration of multimodal aerial remote sensing and target tracking. Deeply hidden target recognition is shown to be enhanced through the fusing of panchromatic, hyperspectral, and polarimetric image modalities. The Digital Imaging and Remote Sensing Image Generation model was leveraged to synthesize truth spectropolarimetric sensor-reaching radiance image cubes comprised of coregistered Stokes vector bands in the visible to near-infrared. An intricate synthetic urban scene containing numerous moving vehicular targets was imaged from a virtual sensor aboard an aerial platform encircling a stare point. An adaptive sensor model was designed with a superpixel array of MOEMS devices fabricated atop a division of focal plane detector. Degree of linear polarization (DoLP) imagery is acquired by combining three adjacent micropolarizer outputs within each 2x2 superpixel whose respective transmissions vary with wavelength, relative angle of polarization, and wire-grid spacing. A novel micromirror within each superpixel adaptively relays light between a panchromatic imaging channel and a hyperspectral spectrometer channel. All optical and detector sensor effects were radiometrically modeled using MATLAB and optical lens design software. Orthorectification of all sensor outputs yields multimodal pseudonadir observation video at a fixed ground sampled distance across an area of responsibility. A proprietary MATLAB-based target tracker accomplishes change detection between sequential panchromatic or DoLP observation frames, and queries the sensor for hyperspectral pixels to aid in track initialization and maintenance. Image quality, spectral quality, and tracking performance metrics are reported for varying scenario parameters including target occlusions within the scene, declination angle and jitter of the aerial platform, micropolarizer diattenuation, and spectral/spatial resolution of the adaptive sensor outputs. DoLP observations were found to track moving vehicles better than panchromatic observations at high oblique angles when facing the sensor generally toward the sun. Vehicular occlusions due to tree canopies and parallax effects of tall buildings significantly reduced tracking performance as expected. Smaller MOEMS pixel sizes drastically improved track performance, but also generated a significant number of false tracks. Atmospheric haze from urban aerosols eliminated the tracking utility of DoLP observations, while aerial platform jitter without image stabilization eliminated tracking utility in both modalities. Wire-grid micropolarizers with very low VNIR diattenuation were found to still extinguish enough cross-polarized light to successfully distinguish and track moving vehicles from their urban background. Thus, state-of-the-art lithographic techniques to create finer wire-grid spacings that exhibit high VNIR diattenuation may not be required

Performance analysis of wormhole routing in multicomputer interconnection networks

Perhaps the most critical component in determining the ultimate performance potential of a multicomputer is its interconnection network, the hardware fabric supporting communication among individual processors. The message latency and throughput of such a network are affected by many factors of which topology, switching method, routing algorithm and traffic load are the most significant. In this context, the present study focuses on a performance analysis of k-ary n-cube networks employing wormhole switching, virtual channels and adaptive routing, a scenario of especial interest to current research. This project aims to build upon earlier work in two main ways: constructing new analytical models for k-ary n-cubes, and comparing the performance merits of cubes of different dimensionality. To this end, some important topological properties of k-ary n-cubes are explored initially; in particular, expressions are derived to calculate the number of nodes at/within a given distance from a chosen centre. These results are important in their own right but their primary significance here is to assist in the construction of new and more realistic analytical models of wormhole-routed k-ary n-cubes. An accurate analytical model for wormhole-routed k-ary n-cubes with adaptive routing and uniform traffic is then developed, incorporating the use of virtual channels and the effect of locality in the traffic pattern. New models are constructed for wormhole k-ary n-cubes, with the ability to simulate behaviour under adaptive routing and non-uniform communication workloads, such as hotspot traffic, matrix-transpose and digit-reversal permutation patterns. The models are equally applicable to unidirectional and bidirectional k-ary n-cubes and are significantly more realistic than any in use up to now. With this level of accuracy, the effect of each important network parameter on the overall network performance can be investigated in a more comprehensive manner than before. Finally, k-ary n-cubes of different dimensionality are compared using the new models. The comparison takes account of various traffic patterns and implementation costs, using both pin-out and bisection bandwidth as metrics. Networks with both normal and pipelined channels are considered. While previous similar studies have only taken account of network channel costs, our model incorporates router costs as well thus generating more realistic results. In fact the results of this work differ markedly from those yielded by earlier studies which assumed deterministic routing and uniform traffic, illustrating the importance of using accurate models to conduct such analyses

Results on geometric networks and data structures

This thesis discusses four problems in computational geometry. In traditional colored range-searching problems, one wants to store a set of n objects with m distinct colors for the following queries: report all colors such that there is at least one object of that color intersecting the query range. Such an object, however, could be an `outlier' in its color class. We consider a variant of this problem where one has to report only those colors such that at least a fraction t of the objects of that color intersects the query range, for some parameter t. Our main results are on an approximate version of this problem, where we are also allowed to report those colors for which a fraction (1-epsilon)t intersects the query range, for some fixed epsilon > 0. We present efficient data structures for such queries with orthogonal query ranges in sets of colored points, and for point stabbing queries in sets of colored rectangles. A box-tree is a bounding-volume hierarchy that uses axis-aligned boxes as bounding volumes. R-trees are box-trees with nodes of high degree. The query complexity of a box-tree with respect to a given type of query is the maximum number of nodes visited when answering such a query. We describe several new algorithms for constructing box-trees with small worst-case query complexity with respect to queries with axis-parallel boxes and with points. We also prove lower bounds on the worst-case query complexity for box-trees, which show that our results are optimal or close to optimal. The geometric minimum-diameter spanning tree (MDST) of a set of n points is a tree that spans the set and minimizes the Euclidian length of the longest path in the tree. So far, the MDST can only be found in slightly subcubic time. We give two fast approximation schemes for the MDST, i.e. factor-(1+epsilon) approximation algorithms. One algorithm uses a grid and takes time O*(1/epsilon^(5 2/3) + n), where the O*-notation hides terms of type O(log^O(1) 1/epsilon). The other uses the well-separated pair decomposition and takes O(1/epsilon^3 n + (1/epsilon) n log n) time. A combination of the two approaches runs in O*(1/epsilon^5 + n) time. The dilation of a geometric graph is the maximum, over all pairs of points in the graph, of the ratio of the Euclidean length of the shortest path between them in the graph and their Euclidean distance. We consider a generalized version of this notion, where the nodes of the graph are not points but axis-parallel rectangles in the plane. The arcs in the graph are horizontal or vertical segments connecting a pair of rectangles, and the distance measure we use is the L1-distance. We study the following problem: given n non-intersecting rectangles and a graph describing which pairs of rectangles are to be connected, we wish to place the connecting segments such that the dilation is minimized. We obtain the following results: for arbitrary graphs, the problem is NP-hard; for trees, we can solve the problem by linear programming on O(n^2) variables and constraints; for paths, we can solve the problem in time O(n^3 log n); for rectangles sorted vertically along a path, the problem can be solved in O(n^2) time

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Collection of abstracts of the 24th European Workshop on Computational Geometry

International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum