On this page I'll try to summarize my research concepts and ideas on the theory of Sequence Indexing.
The theory of Sequence Indexing deals with the notion of structured Enumeration, the mathematical concept of counting objects. It tries to answer one simple question: Given a collection of objects - how to create, access and identify various groups of objects drawn from that collection?
Few frequently used sequences that are well known are: Range Sequences, Permutation Sequences and Combination Sequences. For an implemenation of constant-time access to the elements of these sequences, refer to: http://www.geocities.com/krishnapg/SequenceIndexing.html (By constant-time we mean any element of the sequence can be accessed in constant amount of time indepdent of the sequence length (that is, we do not need to go through the entire list of elements in the sequence)).
What I would like to share here, instead, is a way of modeling Multi-Dimensional databases using Sequences.
Sequence Modeling for MultiDimensional Databases
Database is a collection facts. The mechanism used for the representation of facts highly affects the performance of the fact access and modification procedures. One of the major drawbacks of existing fact representation mechanisms is that their access time is dependent on the number of records present in the database. In other words, the database size affects the data access complexity. Sequence Modeling presents an innovative mechanism for representing the facts that offer constant access and modification time disregard to the size of the database. This technique uses the functionality of Sequences to model the multi-dimensional databases, the light weight nature of which opens whole new set of facilities such as in-memory, or on-chip databases for storing and accessing complex fact tables for effective and efficient processing.
Find the Mathematical theory in the attachments.
A practical discussion on how to render this mathematical theory into a more practical storage mechanism would follow soon in forthcoming posts.