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Description
A central concept of combinatorics is partitioning structures with given constraints. Partitions of on-line posets and on-line graphs, which are dynamic versions of the more familiar static structures posets and graphs, are examined. In the on-line setting, vertices are continually added to a poset or graph while a chain partition

A central concept of combinatorics is partitioning structures with given constraints. Partitions of on-line posets and on-line graphs, which are dynamic versions of the more familiar static structures posets and graphs, are examined. In the on-line setting, vertices are continually added to a poset or graph while a chain partition or coloring (respectively) is maintained. %The optima of the static cases cannot be achieved in the on-line setting. Both upper and lower bounds for the optimum of the number of chains needed to partition a width $w$ on-line poset exist. Kierstead's upper bound of $\frac{5^w-1}{4}$ was improved to $w^{14 \lg w}$ by Bosek and Krawczyk. This is improved to $w^{3+6.5 \lg w}$ by employing the First-Fit algorithm on a family of restricted posets (expanding on the work of Bosek and Krawczyk) . Namely, the family of ladder-free posets where the $m$-ladder is the transitive closure of the union of two incomparable chains $x_1\le\dots\le x_m$, $y_1\le\dots\le y_m$ and the set of comparabilities $\{x_1\le y_1,\dots, x_m\le y_m\}$. No upper bound on the number of colors needed to color a general on-line graph exists. To lay this fact plain, the performance of on-line coloring of trees is shown to be particularly problematic. There are trees that require $n$ colors to color on-line for any positive integer $n$. Furthermore, there are trees that usually require many colors to color on-line even if they are presented without any particular strategy. For restricted families of graphs, upper and lower bounds for the optimum number of colors needed to maintain an on-line coloring exist. In particular, circular arc graphs can be colored on-line using less than 8 times the optimum number from the static case. This follows from the work of Pemmaraju, Raman, and Varadarajan in on-line coloring of interval graphs.
ContributorsSmith, Matthew Earl (Author) / Kierstead, Henry A (Thesis advisor) / Colbourn, Charles (Committee member) / Czygrinow, Andrzej (Committee member) / Fishel, Susanna (Committee member) / Hurlbert, Glenn (Committee member) / Arizona State University (Publisher)
Created2012
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Description
This research describes software based remote attestation schemes for obtaining the integrity of an executing user application and the Operating System (OS) text section of an untrusted client platform. A trusted external entity issues a challenge to the client platform. The challenge is executable code which the client must execute,

This research describes software based remote attestation schemes for obtaining the integrity of an executing user application and the Operating System (OS) text section of an untrusted client platform. A trusted external entity issues a challenge to the client platform. The challenge is executable code which the client must execute, and the code generates results which are sent to the external entity. These results provide the external entity an assurance as to whether the client application and the OS are in pristine condition. This work also presents a technique where it can be verified that the application which was attested, did not get replaced by a different application after completion of the attestation. The implementation of these three techniques was achieved entirely in software and is backward compatible with legacy machines on the Intel x86 architecture. This research also presents two approaches to incorporating software based "root of trust" using Virtual Machine Monitors (VMMs). The first approach determines the integrity of an executing Guest OS from the Host OS using Linux Kernel-based Virtual Machine (KVM) and qemu emulation software. The second approach implements a small VMM called MIvmm that can be utilized as a trusted codebase to build security applications such as those implemented in this research. MIvmm was conceptualized and implemented without using any existing codebase; its minimal size allows it to be trustworthy. Both the VMM approaches leverage processor support for virtualization in the Intel x86 architecture.
ContributorsSrinivasan, Raghunathan (Author) / Dasgupta, Partha (Thesis advisor) / Colbourn, Charles (Committee member) / Shrivastava, Aviral (Committee member) / Huang, Dijiang (Committee member) / Dewan, Prashant (Committee member) / Arizona State University (Publisher)
Created2011
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Description
Finding the optimal solution to a problem with an enormous search space can be challenging. Unless a combinatorial construction technique is found that also guarantees the optimality of the resulting solution, this could be an infeasible task. If such a technique is unavailable, different heuristic methods are generally used to

Finding the optimal solution to a problem with an enormous search space can be challenging. Unless a combinatorial construction technique is found that also guarantees the optimality of the resulting solution, this could be an infeasible task. If such a technique is unavailable, different heuristic methods are generally used to improve the upper bound on the size of the optimal solution. This dissertation presents an alternative method which can be used to improve a solution to a problem rather than construct a solution from scratch. Necessity analysis, which is the key to this approach, is the process of analyzing the necessity of each element in a solution. The post-optimization algorithm presented here utilizes the result of the necessity analysis to improve the quality of the solution by eliminating unnecessary objects from the solution. While this technique could potentially be applied to different domains, this dissertation focuses on k-restriction problems, where a solution to the problem can be presented as an array. A scalable post-optimization algorithm for covering arrays is described, which starts from a valid solution and performs necessity analysis to iteratively improve the quality of the solution. It is shown that not only can this technique improve upon the previously best known results, it can also be added as a refinement step to any construction technique and in most cases further improvements are expected. The post-optimization algorithm is then modified to accommodate every k-restriction problem; and this generic algorithm can be used as a starting point to create a reasonable sized solution for any such problem. This generic algorithm is then further refined for hash family problems, by adding a conflict graph analysis to the necessity analysis phase. By recoloring the conflict graphs a new degree of flexibility is explored, which can further improve the quality of the solution.
ContributorsNayeri, Peyman (Author) / Colbourn, Charles (Thesis advisor) / Konjevod, Goran (Thesis advisor) / Sen, Arunabha (Committee member) / Stanzione Jr, Daniel (Committee member) / Arizona State University (Publisher)
Created2011
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Description
Thanks to continuous technology scaling, intelligent, fast and smaller digital systems are now available at affordable costs. As a result, digital systems have found use in a wide range of application areas that were not even imagined before, including medical (e.g., MRI, remote or post-operative monitoring devices, etc.), automotive (e.g.,

Thanks to continuous technology scaling, intelligent, fast and smaller digital systems are now available at affordable costs. As a result, digital systems have found use in a wide range of application areas that were not even imagined before, including medical (e.g., MRI, remote or post-operative monitoring devices, etc.), automotive (e.g., adaptive cruise control, anti-lock brakes, etc.), security systems (e.g., residential security gateways, surveillance devices, etc.), and in- and out-of-body sensing (e.g., capsule swallowed by patients measuring digestive system pH, heart monitors, etc.). Such computing systems, which are completely embedded within the application, are called embedded systems, as opposed to general purpose computing systems. In the design of such embedded systems, power consumption and reliability are indispensable system requirements. In battery operated portable devices, the battery is the single largest factor contributing to device cost, weight, recharging time, frequency and ultimately its usability. For example, in the Apple iPhone 4 smart-phone, the battery is $40\%$ of the device weight, occupies $36\%$ of its volume and allows only $7$ hours (over 3G) of talk time. As embedded systems find use in a range of sensitive applications, from bio-medical applications to safety and security systems, the reliability of the computations performed becomes a crucial factor. At our current technology-node, portable embedded systems are prone to expect failures due to soft errors at the rate of once-per-year; but with aggressive technology scaling, the rate is predicted to increase exponentially to once-per-hour. Over the years, researchers have been successful in developing techniques, implemented at different layers of the design-spectrum, to improve system power efficiency and reliability. Among the layers of design abstraction, I observe that the interface between the compiler and processor micro-architecture possesses a unique potential for efficient design optimizations. A compiler designer is able to observe and analyze the application software at a finer granularity; while the processor architect analyzes the system output (power, performance, etc.) for each executed instruction. At the compiler micro-architecture interface, if the system knowledge at the two design layers can be integrated, design optimizations at the two layers can be modified to efficiently utilize available resources and thereby achieve appreciable system-level benefits. To this effect, the thesis statement is that, ``by merging system design information at the compiler and micro-architecture design layers, smart compilers can be developed, that achieve reliable and power-efficient embedded computing through: i) Pure compiler techniques, ii) Hybrid compiler micro-architecture techniques, and iii) Compiler-aware architectures''. In this dissertation demonstrates, through contributions in each of the three compiler-based techniques, the effectiveness of smart compilers in achieving power-efficiency and reliability in embedded systems.
ContributorsJeyapaul, Reiley (Author) / Shrivastava, Aviral (Thesis advisor) / Vrudhula, Sarma (Committee member) / Clark, Lawrence (Committee member) / Colbourn, Charles (Committee member) / Arizona State University (Publisher)
Created2012
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Description
Gray codes are perhaps the best known structures for listing sequences of combinatorial objects, such as binary strings. Simply defined as a minimal change listing, Gray codes vary greatly both in structure and in the types of objects that they list. More specific types of Gray codes are universal cycles

Gray codes are perhaps the best known structures for listing sequences of combinatorial objects, such as binary strings. Simply defined as a minimal change listing, Gray codes vary greatly both in structure and in the types of objects that they list. More specific types of Gray codes are universal cycles and overlap sequences. Universal cycles are Gray codes on a set of strings of length n in which the first n-1 letters of one object are the same as the last n-1 letters of its predecessor in the listing. Overlap sequences allow this overlap to vary between 1 and n-1. Some of our main contributions to the areas of Gray codes and universal cycles include a new Gray code algorithm for fixed weight m-ary words, and results on the existence of universal cycles for weak orders on [n]. Overlap cycles are a relatively new structure with very few published results. We prove the existence of s-overlap cycles for k-permutations of [n], which has been an open research problem for several years, as well as constructing 1- overlap cycles for Steiner triple and quadruple systems of every order. Also included are various other results of a similar nature covering other structures such as binary strings, m-ary strings, subsets, permutations, weak orders, partitions, and designs. These listing structures lend themselves readily to some classes of combinatorial objects, such as binary n-tuples and m-ary n-tuples. Others require more work to find an appropriate structure, such as k-subsets of an n-set, weak orders, and designs. Still more require a modification in the representation of the objects to fit these structures, such as partitions. Determining when and how we can fit these sets of objects into our three listing structures is the focus of this dissertation.
ContributorsHoran, Victoria E (Author) / Hurlbert, Glenn H. (Thesis advisor) / Czygrinow, Andrzej (Committee member) / Fishel, Susanna (Committee member) / Colbourn, Charles (Committee member) / Sen, Arunabha (Committee member) / Arizona State University (Publisher)
Created2012