Novel Solutions and Applications of the Object Partitioning Problem

Abstract

This thesis considers the fundamental problem of "partitioning" which is allpervasive in computer science. It has applications in "Big Data" because the vast amounts of data encountered in "Big Data" applications cannot be processed in a single block, but are better analyzed when it is partitioned in various monolithic units. It also has direct applications in numerous areas including databases, process scheduling, mapping and image retrieval. In this research we consider a specific instantiation of the Object Partitioning Problem, namely the Equi-Partitioning Problem (EPP), in which the partitions are equi-sized. In particular we concentrate on the various Learning Automata (LA)-based solutions. In this regard, the Object Migration Automata (OMA), and its variants have been the benchmark solutions. The thesis thoroughly investigates the structural aspects of the OMA such as its internal grouping-based transitions, structure, initialization methods, convergence criteria and its recorded deficiencies. Rather than solely consider how the transitions can be designed, we specifically investigate how the well-known Pursuit paradigm, that has been recently invoked to enhance the field of LA, can be used to optimize the OMA. To do this, we propose two models for the Environment when it is noisy and noiseless, and show that the LA's convergence can be improved if we can discern the so-called "divergent" queries, namely, those which cause the LA to be sluggish. We have thus devised a technique that recognizes the "divergent" pairs and excludes them from the learning cycle, and to thus effectively pursue the optimal solution. This has resulted in the Pursuit OMA (POMA), whose performance is sometimes nearly two times faster than the original OMA. Other researchers have observed and corrected the deadlock phenomenon in the original OMA, and have thus designed the so-called Enhanced OMA (EOMA). In this thesis, we have shown how the Pursuit phenomenon can be incorporated into the EOMA to yield the Pursuit EOMA (PEOMA), which, in some cases, is more than forty times faster that the traditional OMA. Thereafter, we have observed that all the previous versions of the OMA were not able to include the property of transitivity. To include this phenomenon, we have also extracted the relations among the objects by utilizing the information in the iii Pursuit matrix. The newly-proposed method that incorporates Transitivity, the socalled Transitive PEOMA (TPEOMA) outperforms the PEOMA by a factor of two, and is sometimes about ninety times faster than the OMA. To finally demonstrate the power of the OMA-based paradigm in a real-life application, we have also incorporated it to resolve the outlier detection problem in Noisy Sensors Networks (NSNs). iv ACKNOWLEDGEMENTS I will, first and foremost, thank God, my Creator, for giving me the strength and patience to see this work through to its fruitful conclusion. This has been no small endeavor, which has encountered numerous obstacles, highs and lows. He has helped me all along. I am also g...

On Designing Adaptive Data Structures with Adaptive Data "Sub"-Structures

“…else if ξ j mod N = 0 then O j is at internal state 8: end if 15: end Source: Excerpt from [55] where O is the set of abstract objects.…”

“…These two metrics are vital in reporting the convergence and performance capabilities of the OMA for various Environments. Table 2.1 below shows the empirical convergence results for the OMA (as reported in [55]) for different sizes of W and R, with p = 0.7, 0.8 and 0.9. Note that p = 0.7 is the most difficult of these Environments.…”

“…end loop 24: end Source: Excerpt from [55] In the BAM, the queried elements are processed as a pair. Every abstract object, O i , for a particular query element is designated by a real number X i .…”

“…Decide on the final partitions based on the states {ξ i } 12: end Source: Excerpt from [55] Performance Analysis…”

“…end if 8: end Source: Excerpt from [55] objects to be partitioned increased the convergence rate of the OMA was an order of magnitude superior to the BAM. Although the convergence rates for Tsetlin's and Krinsky's automata are better than the OMA, it has the advantage of being computationally feasible to partition large enough object sets into classes.…”