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Communication networks, both wired and wireless, are expected to have a certain level of fault-tolerance capability.These networks are also expected to ensure a graceful degradation in performance when some of the network components fail. Traditional studies on fault tolerance in communication networks, for the most part, make no assumptions regarding the location of node/link faults, i.e., the faulty nodes and links may be close to each other or far from each other. However, in many real life scenarios, there exists a strong spatial correlation among the faulty nodes and links. Such failures are often encountered in disaster situations, e.g., natural calamities or enemy attacks. In presence of such region-based faults, many of traditional network analysis and fault-tolerant metrics, that are valid under non-spatially correlated faults, are no longer applicable. To this effect, the main thrust of this research is design and analysis of robust networks in presence of such region-based faults. One important finding of this research is that if some prior knowledge is available on the maximum size of the region that might be affected due to a region-based fault, this piece of knowledge can be effectively utilized for resource efficient design of networks. It has been shown in this dissertation that in some scenarios, effective utilization of this knowledge may result in substantial saving is transmission power in wireless networks. In this dissertation, the impact of region-based faults on the connectivity of wireless networks has been studied and a new metric, region-based connectivity, is proposed to measure the fault-tolerance capability of a network. In addition, novel metrics, such as the region-based component decomposition number(RBCDN) and region-based largest component size(RBLCS) have been proposed to capture the network state, when a region-based fault disconnects the network. Finally, this dissertation presents efficient resource allocation techniques that ensure tolerance against region-based faults, in distributed file storage networks and data center networks.
ContributorsBanerjee, Sujogya (Author) / Sen, Arunabha (Thesis advisor) / Xue, Guoliang (Committee member) / Richa, Andrea (Committee member) / Hurlbert, Glenn (Committee member) / Arizona State University (Publisher)
Created2013
Description
The construction of many families of combinatorial objects remains a challenging problem. A t-restriction is an array where a predicate is satisfied for every t columns; an example is a perfect hash family (PHF). The composition of a PHF and any t-restriction satisfying predicate P yields another t-restriction also satisfying P with more columns than the original t-restriction had. This thesis concerns three approaches in determining the smallest size of PHFs.
Firstly, hash families in which the associated property is satisfied at least some number lambda times are considered, called higher-index, which guarantees redundancy when constructing t-restrictions. Some direct and optimal constructions of hash families of higher index are given. A new recursive construction is established that generalizes previous results and generates higher-index PHFs with more columns. Probabilistic methods are employed to obtain an upper bound on the optimal size of higher-index PHFs when the number of columns is large. A new deterministic algorithm is developed that generates such PHFs meeting this bound, and computational results are reported.
Secondly, a restriction on the structure of PHFs is introduced, called fractal, a method from Blackburn. His method is extended in several ways; from homogeneous hash families (every row has the same number of symbols) to heterogeneous ones; and to distributing hash families, a relaxation of the predicate for PHFs. Recursive constructions with fractal hash families as ingredients are given, and improve upon on the best-known sizes of many PHFs.
Thirdly, a method of Colbourn and Lanus is extended in which they horizontally copied a given hash family and greedily applied transformations to each copy. Transformations of existential t-restrictions are introduced, which allow for the method to be applicable to any t-restriction having structure like those of hash families. A genetic algorithm is employed for finding the "best" such transformations. Computational results of the GA are reported using PHFs, as the number of transformations permitted is large compared to the number of symbols. Finally, an analysis is given of what trade-offs exist between computation time and the number of t-sets left not satisfying the predicate.
Firstly, hash families in which the associated property is satisfied at least some number lambda times are considered, called higher-index, which guarantees redundancy when constructing t-restrictions. Some direct and optimal constructions of hash families of higher index are given. A new recursive construction is established that generalizes previous results and generates higher-index PHFs with more columns. Probabilistic methods are employed to obtain an upper bound on the optimal size of higher-index PHFs when the number of columns is large. A new deterministic algorithm is developed that generates such PHFs meeting this bound, and computational results are reported.
Secondly, a restriction on the structure of PHFs is introduced, called fractal, a method from Blackburn. His method is extended in several ways; from homogeneous hash families (every row has the same number of symbols) to heterogeneous ones; and to distributing hash families, a relaxation of the predicate for PHFs. Recursive constructions with fractal hash families as ingredients are given, and improve upon on the best-known sizes of many PHFs.
Thirdly, a method of Colbourn and Lanus is extended in which they horizontally copied a given hash family and greedily applied transformations to each copy. Transformations of existential t-restrictions are introduced, which allow for the method to be applicable to any t-restriction having structure like those of hash families. A genetic algorithm is employed for finding the "best" such transformations. Computational results of the GA are reported using PHFs, as the number of transformations permitted is large compared to the number of symbols. Finally, an analysis is given of what trade-offs exist between computation time and the number of t-sets left not satisfying the predicate.
ContributorsDougherty, Ryan Edward (Author) / Colbourn, Charles J (Thesis advisor) / Czygrinow, Andrzej (Committee member) / Forrest, Stephanie (Committee member) / Richa, Andrea (Committee member) / Arizona State University (Publisher)
Created2019