Exploiting a prioritized MAC protocol to efficiently compute min and max in multihop networks

Consider a wireless sensor network (WSN) where a broadcast from a sensor node does not reach all sensor nodes in the network; such networks are often called multihop networks. Sensor nodes take sensor readings but individual sensor readings are not very important. It is important however to compute aggregated quantities of these sensor readings. The minimum and maximum of all sensor readings at an instant are often interesting because they indicate abnormal behavior, for example if the maximum temperature is very high then it may be that a fire has broken out. We propose an algorithm for computing the min or max of sensor reading in a multihop network. This algorithm has the particularly interesting property of having a time complexity that does not depend on the number of sensor nodes; only the network diameter and the range of the value domain of sensor readings matter.

A two-competitive approximate schedulability analysis of CAN

Consider the problem of deciding whether a set of n sporadic message streams meet deadlines on a Controller Area Network (CAN) bus for a specified priority assignment. It is assumed that message streams have implicit deadlines and no release jitter. An algorithm to solve this problem is well known but unfortunately it time complexity is non-polynomial. We present an algorithm with polynomial time-complexity for computing an upper bound on the response times. Clearly, if the upper bound on the response time does not exceed the deadline then all deadlines are met. The pessimism of our approach is proven: if the upper bound of the response time exceeds the deadline then the response time exceeds the deadline as well for a CAN network with half the speed.

Highly scalable aggregate computations in cyber-physical systems: physical environment meets communication protocols

In this paper, we focus on large-scale and dense Cyber- Physical Systems, and discuss methods that tightly integrate communication and computing with the underlying physical environment. We present Physical Dynamic Priority Dominance ((PD)2) protocol that exemplifies a key mechanism to devise low time-complexity communication protocols for large-scale networked sensor systems. We show that using this mechanism, one can compute aggregate quantities such as the maximum or minimum of sensor readings in a time-complexity that is equivalent to essentially one message exchange. We also illustrate the use of this mechanism in a more complex task of computing the interpolation of smooth as well as non-smooth sensor data in very low timecomplexity.

Localizing objects in large-scale cyber- physical systems

We use the term Cyber-Physical Systems to refer to large-scale distributed sensor systems. Locating the geographic coordinates of objects of interest is an important problemin such systems. We present a new distributed approach to localize objects and events of interest in time complexity independent of number of nodes.

Using a prioritized MAC protocol to efficiently compute aggregated quantities

Consider a distributed computer system such that every computer node can perform a wireless broadcast and when it does so, all other nodes receive this message. The computer nodes take sensor readings but individual sensor readings are not very important. It is important however to compute the aggregated quantities of these sensor readings. We show that a prioritized medium access control (MAC) protocol for wireless broadcast can compute simple aggregated quantities in a single transaction, and more complex quantities with many (but still a small number of) transactions. This leads to significant improvements in the time-complexity and as a consequence also similar reduction in energy “consumption”.

Task assignment algorithms for two-type heterogeneous multiprocessors

Consider the problem of assigning implicit-deadline sporadic tasks on a heterogeneous multiprocessor platform comprising two different types of processors—such a platform is referred to as two-type platform. We present two low degree polynomial time-complexity algorithms, SA and SA-P, each providing the following guarantee. For a given two-type platform and a task set, if there exists a task assignment such that tasks can be scheduled to meet deadlines by allowing them to migrate only between processors of the same type (intra-migrative), then (i) using SA, it is guaranteed to find such an assignment where the same restriction on task migration applies but given a platform in which processors are 1+α/2 times faster and (ii) SA-P succeeds in finding a task assignment where tasks are not allowed to migrate between processors (non-migrative) but given a platform in which processors are 1+α times faster. The parameter 0<α≤1 is a property of the task set; it is the maximum of all the task utilizations that are no greater than 1. We evaluate average-case performance of both the algorithms by generating task sets randomly and measuring how much faster processors the algorithms need (which is upper bounded by 1+α/2 for SA and 1+α for SA-P) in order to output a feasible task assignment (intra-migrative for SA and non-migrative for SA-P). In our evaluations, for the vast majority of task sets, these algorithms require significantly smaller processor speedup than indicated by their theoretical bounds. Finally, we consider a special case where no task utilization in the given task set can exceed one and for this case, we (re-)prove the performance guarantees of SA and SA-P. We show, for both of the algorithms, that changing the adversary from intra-migrative to a more powerful one, namely fully-migrative, in which tasks can migrate between processors of any type, does not deteriorate the performance guarantees. For this special case, we compare the average-case performance of SA-P and a state-of-the-art algorithm by generating task sets randomly. In our evaluations, SA-P outperforms the state-of-the-art by requiring much smaller processor speedup and by running orders of magnitude faster.

A survey of distributed data aggregation algorithms

Distributed data aggregation is an important task, allowing the de- centralized determination of meaningful global properties, that can then be used to direct the execution of other applications. The resulting val- ues result from the distributed computation of functions like count, sum and average. Some application examples can found to determine the network size, total storage capacity, average load, majorities and many others. In the last decade, many di erent approaches have been pro- posed, with di erent trade-o s in terms of accuracy, reliability, message and time complexity. Due to the considerable amount and variety of ag- gregation algorithms, it can be di cult and time consuming to determine which techniques will be more appropriate to use in speci c settings, jus- tifying the existence of a survey to aid in this task. This work reviews the state of the art on distributed data aggregation algorithms, providing three main contributions. First, it formally de nes the concept of aggrega- tion, characterizing the di erent types of aggregation functions. Second, it succinctly describes the main aggregation techniques, organizing them in a taxonomy. Finally, it provides some guidelines toward the selection and use of the most relevant techniques, summarizing their principal characteristics.

Geometry-based demosaicking

Demosaicking is a particular case of interpolation problems where, from a scalar image in which each pixel has either the red, the green or the blue component, we want to interpolate the full-color image. State-of-the-art demosaicking algorithms perform interpolation along edges, but these edges are estimated locally. We propose a level-set-based geometric method to estimate image edges, inspired by the image in-painting literature. This method has a time complexity of O(S) , where S is the number of pixels in the image, and compares favorably with the state-of-the-art algorithms both visually and in most relevant image quality measures.

To select or to weigh: a comparative study of linear combination schemes for superparent-one-dependence estimators

We conduct a large-scale comparative study on linearly combining superparent-one-dependence estimators (SPODEs), a popular family of seminaive Bayesian classifiers. Altogether, 16 model selection and weighing schemes, 58 benchmark data sets, and various statistical tests are employed. This paper's main contributions are threefold. First, it formally presents each scheme's definition, rationale, and time complexity and hence can serve as a comprehensive reference for researchers interested in ensemble learning. Second, it offers bias-variance analysis for each scheme's classification error performance. Third, it identifies effective schemes that meet various needs in practice. This leads to accurate and fast classification algorithms which have an immediate and significant impact on real-world applications. Another important feature of our study is using a variety of statistical tests to evaluate multiple learning methods across multiple data sets.

Populaation monimuotoisuuden mittaaminen liukulukukoodatuissa evoluutioalgoritmeissa

Diplomityössä esitetään menetelmä populaation monimuotoisuuden mittaamiseen liukulukukoodatuissa evoluutioalgoritmeissa, ja tarkastellaan kokeellisesti sen toimintaa. Evoluutioalgoritmit ovat populaatiopohjaisia menetelmiä, joilla pyritään ratkaisemaan optimointiongelmia. Evoluutioalgoritmeissa populaation monimuotoisuuden hallinta on välttämätöntä, jotta suoritettu haku olisi riittävän luotettavaa ja toisaalta riittävän nopeaa. Monimuotoisuuden mittaaminen on erityisen tarpeellista tutkittaessa evoluutioalgoritmien dynaamista käyttäytymistä. Työssä tarkastellaan haku- ja tavoitefunktioavaruuden monimuotoisuuden mittaamista. Toistaiseksi ei ole ollut olemassa täysin tyydyttäviä monimuotoisuuden mittareita, ja työn tavoitteena on kehittää yleiskäyttöinen menetelmä liukulukukoodattujen evoluutioalgoritmien suhteellisen ja absoluuttisen monimuotoisuuden mittaamiseen hakuavaruudessa. Kehitettyjen mittareiden toimintaa ja käyttökelpoisuutta tarkastellaan kokeellisesti ratkaisemalla optimointiongelmia differentiaalievoluutioalgoritmilla. Toteutettujen mittareiden toiminta perustuu keskihajontojen laskemiseen populaatiosta. Keskihajonnoille suoritetaan skaalaus, joko alkupopulaation tai nykyisen populaation suhteen, riippuen lasketaanko absoluuttista vai suhteellista monimuotoisuutta. Kokeellisessa tarkastelussa havaittiin kehitetyt mittarit toimiviksi ja käyttökelpoisiksi. Tavoitefunktion venyttäminen koordinaattiakseleiden suunnassa ei vaikuta mittarin toimintaan. Myöskään tavoitefunktion kiertäminen koordinaatistossa ei vaikuta mittareiden tuloksiin. Esitetyn menetelmän aikakompleksisuus riippuu lineaarisesti populaation koosta, ja mittarin toiminta on siten nopeaa suuriakin populaatioita käytettäessä. Suhteellinen monimuotoisuus antaa vertailukelpoisia tuloksia riippumatta parametrien lukumäärästä tai populaation koosta.

New Distance Transforms for Gray Level Image Compression

This thesis deals with distance transforms which are a fundamental issue in image processing and computer vision. In this thesis, two new distance transforms for gray level images are presented. As a new application for distance transforms, they are applied to gray level image compression. The new distance transforms are both new extensions of the well known distance transform algorithm developed by Rosenfeld, Pfaltz and Lay. With some modification their algorithm which calculates a distance transform on binary images with a chosen kernel has been made to calculate a chessboard like distance transform with integer numbers (DTOCS) and a real value distance transform (EDTOCS) on gray level images. Both distance transforms, the DTOCS and EDTOCS, require only two passes over the graylevel image and are extremely simple to implement. Only two image buffers are needed: The original gray level image and the binary image which defines the region(s) of calculation. No other image buffers are needed even if more than one iteration round is performed. For large neighborhoods and complicated images the two pass distance algorithm has to be applied to the image more than once, typically 3 10 times. Different types of kernels can be adopted. It is important to notice that no other existing transform calculates the same kind of distance map as the DTOCS. All the other gray weighted distance function, GRAYMAT etc. algorithms find the minimum path joining two points by the smallest sum of gray levels or weighting the distance values directly by the gray levels in some manner. The DTOCS does not weight them that way. The DTOCS gives a weighted version of the chessboard distance map. The weights are not constant, but gray value differences of the original image. The difference between the DTOCS map and other distance transforms for gray level images is shown. The difference between the DTOCS and EDTOCS is that the EDTOCS calculates these gray level differences in a different way. It propagates local Euclidean distances inside a kernel. Analytical derivations of some results concerning the DTOCS and the EDTOCS are presented. Commonly distance transforms are used for feature extraction in pattern recognition and learning. Their use in image compression is very rare. This thesis introduces a new application area for distance transforms. Three new image compression algorithms based on the DTOCS and one based on the EDTOCS are presented. Control points, i.e. points that are considered fundamental for the reconstruction of the image, are selected from the gray level image using the DTOCS and the EDTOCS. The first group of methods select the maximas of the distance image to new control points and the second group of methods compare the DTOCS distance to binary image chessboard distance. The effect of applying threshold masks of different sizes along the threshold boundaries is studied. The time complexity of the compression algorithms is analyzed both analytically and experimentally. It is shown that the time complexity of the algorithms is independent of the number of control points, i.e. the compression ratio. Also a new morphological image decompression scheme is presented, the 8 kernels' method. Several decompressed images are presented. The best results are obtained using the Delaunay triangulation. The obtained image quality equals that of the DCT images with a 4 x 4

Scalable algorithms for height field illumination

Global illumination algorithms are at the center of realistic image synthesis and account for non-trivial light transport and occlusion within scenes, such as indirect illumination, ambient occlusion, and environment lighting. Their computationally most difficult part is determining light source visibility at each visible scene point. Height fields, on the other hand, constitute an important special case of geometry and are mainly used to describe certain types of objects such as terrains and to map detailed geometry onto object surfaces. The geometry of an entire scene can also be approximated by treating the distance values of its camera projection as a screen-space height field. In order to shadow height fields from environment lights a horizon map is usually used to occlude incident light. We reduce the per-receiver time complexity of generating the horizon map on N N height fields from O(N) of the previous work to O(1) by using an algorithm that incrementally traverses the height field and reuses the information already gathered along the path of traversal. We also propose an accurate method to integrate the incident light within the limits given by the horizon map. Indirect illumination in height fields requires information about which other points are visible to each height field point. We present an algorithm to determine this intervisibility in a time complexity that matches the space complexity of the produced visibility information, which is in contrast to previous methods which scale in the height field size. As a result the amount of computation is reduced by two orders of magnitude in common use cases. Screen-space ambient obscurance methods approximate ambient obscurance from the depth bu er geometry and have been widely adopted by contemporary real-time applications. They work by sampling the screen-space geometry around each receiver point but have been previously limited to near- field effects because sampling a large radius quickly exceeds the render time budget. We present an algorithm that reduces the quadratic per-pixel complexity of previous methods to a linear complexity by line sweeping over the depth bu er and maintaining an internal representation of the processed geometry from which occluders can be efficiently queried. Another algorithm is presented to determine ambient obscurance from the entire depth bu er at each screen pixel. The algorithm scans the depth bu er in a quick pre-pass and locates important features in it, which are then used to evaluate the ambient obscurance integral accurately. We also propose an evaluation of the integral such that results within a few percent of the ray traced screen-space reference are obtained at real-time render times.

Defining Contexts in Context-Free Grammars

This thesis introduces an extension of Chomsky’s context-free grammars equipped with operators for referring to left and right contexts of strings.The new model is called grammar with contexts. The semantics of these grammars are given in two equivalent ways — by language equations and by logical deduction, where a grammar is understood as a logic for the recursive definition of syntax. The motivation for grammars with contexts comes from an extensive example that completely defines the syntax and static semantics of a simple typed programming language. Grammars with contexts maintain most important practical properties of context-free grammars, including a variant of the Chomsky normal form. For grammars with one-sided contexts (that is, either left or right), there is a cubic-time tabular parsing algorithm, applicable to an arbitrary grammar. The time complexity of this algorithm can be improved to quadratic,provided that the grammar is unambiguous, that is, it only allows one parsefor every string it defines. A tabular parsing algorithm for grammars withtwo-sided contexts has fourth power time complexity. For these grammarsthere is a recognition algorithm that uses a linear amount of space. For certain subclasses of grammars with contexts there are low-degree polynomial parsing algorithms. One of them is an extension of the classical recursive descent for context-free grammars; the version for grammars with contexts still works in linear time like its prototype. Another algorithm, with time complexity varying from linear to cubic depending on the particular grammar, adapts deterministic LR parsing to the new model. If all context operators in a grammar define regular languages, then such a grammar can be transformed to an equivalent grammar without context operators at all. This allows one to represent the syntax of languages in a more succinct way by utilizing context specifications. Linear grammars with contexts turned out to be non-trivial already over a one-letter alphabet. This fact leads to some undecidability results for this family of grammars

Strongly distance-balanced graphs and graph products

A graph G is strongly distance-balanced if for every edge uv of G and every i 0 the number of vertices x with d.x; u/ D d.x; v/ 1 D i equals the number of vertices y with d.y; v/ D d.y; u/ 1 D i. It is proved that the strong product of graphs is strongly distance-balanced if and only if both factors are strongly distance-balanced. It is also proved that connected components of the direct product of two bipartite graphs are strongly distancebalanced if and only if both factors are strongly distance-balanced. Additionally, a new characterization of distance-balanced graphs and an algorithm of time complexity O.mn/ for their recognition, wheremis the number of edges and n the number of vertices of the graph in question, are given

Synthesis of a systolic array genetic algorithm

The paper presents a design for a hardware genetic algorithm which uses a pipeline of systolic arrays. These arrays have been designed using systolic synthesis techniques which involve expressing the algorithm as a set of uniform recurrence relations. The final design divorces the fitness function evaluation from the hardware and can process chromosomes of different lengths, giving the design a generic quality. The paper demonstrates the design methodology by progressively re-writing a simple genetic algorithm, expressed in C code, into a form from which systolic structures can be deduced. This paper extends previous work by introducing a simplification to a previous systolic design for the genetic algorithm. The simplification results in the removal of 2N 2 + 4N cells and reduces the time complexity by 3N + 1 cycles.