Burrows-Wheeler compression is a three stage process in which the data is transformed with the Burrows-Wheeler Transform, then transformed with Move-To-Front, and finally encoded with an entropy coder. Move-To-Front, Transpose, and Frequency Count are some of the many algorithms used on the List Update problem. In 1985, Competitive Analysis first showed the superiority of Move-To-Front over Transpose and Frequency Count for the List Update problem with arbitrary data. Earlier studies due to Bitner assumed independent identically distributed data, and showed that while Move-To-Front adapts to a distribution faster, incurring less overwork, the asymptotic costs of Frequency Count and Transpose are less. The improvements to Burrows-Wheeler compression this work covers are increases in the amount, not speed, of compression. Best x of 2x-1 is a new family of algorithms created to improve on Move-To-Front's processing of the output of the Burrows-Wheeler Transform which is like piecewise independent identically distributed data. Other algorithms for both the middle stage of Burrows-Wheeler compression and the List Update problem for which overwork, asymptotic cost, and competitive ratios are also analyzed are several variations of Move One From Front and part of the randomized algorithm Timestamp. The Best x of 2x - 1 family includes Move-To-Front, the part of Timestamp of interest, and Frequency Count. Lastly, a greedy choosing scheme, Snake, switches back and forth as the amount of compression that two List Update algorithms achieves fluctuates, to increase overall compression. The Burrows-Wheeler Transform is based on sorting of contexts. The other improvements are better sorting orders, such as “aeioubcdf...” instead of standard alphabetical “abcdefghi...” on English text data, and an algorithm for computing orders for any data, and Gray code sorting instead of standard sorting. Both techniques lessen the overwork incurred by whatever List Update algorithms are used by reducing the difference between adjacent sorted …
Many activities are comprised of temporally dependent events that must be executed in a specific chronological order. Supportive software applications must preserve these temporal dependencies. Whenever the processing of this type of an application includes transactions submitted to a database that is shared with other such applications, the transaction concurrency control mechanisms within the database must also preserve the temporal dependencies. A basis for preserving temporal dependencies is established by using (within the applications and databases) real-time timestamps to identify and order events and transactions. The use of optimistic approaches to transaction concurrency control can be undesirable in such situations, as they allow incorrect results for database read operations. Although the incorrectness is detected prior to transaction committal and the corresponding transaction(s) restarted, the impact on the application or entity that submitted the transaction can be too costly. Three transaction concurrency control algorithms are proposed in this dissertation. These algorithms are based on timestamp ordering, and are designed to preserve temporal dependencies existing among data-dependent transactions. The algorithms produce execution schedules that are equivalent to temporally ordered serial schedules, where the temporal order is established by the transactions' start times. The algorithms provide this equivalence while supporting currency to the extent out-of-order commits and reads. With respect to the stated concern with optimistic approaches, two of the proposed algorithms are risk-free and return to read operations only committed data-item values. Risk with the third algorithm is greatly reduced by its conservative bias. All three algorithms avoid deadlock while providing risk-free or reduced-risk operation. The performance of the algorithms is determined analytically and with experimentation. Experiments are performed using functional database management system models that implement the proposed algorithms and the well-known Conservative Multiversion Timestamp Ordering algorithm.
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