Omnidimensional Formulas Four Families and Upgrading Data Structure and Algorithm Omnidimensional Big Oh Time and Space Complexities
From Raw Data to Formula-Compressed Computing: OMNIBAL, OmniFit, HORN and the Search for O(1) Algorithms Modern computing usually treats data as individual elements. If a system contains one million values, we commonly store one million values. If we need their total, we may scan them, preprocess them, index them, or maintain an additional data structure. But what happens when those million values are not truly independent? What if they follow a mathematical structure? This question leads to an interesting direction in OMNIBAL and Omnidimensional Formula research: Instead of storing every element, can we store the mathematical rule that generates the elements? And if we can identify that rule, can some operations that traditionally depend on N become independent of N? That is the idea behind combining: OmniFit + OmniSegment + OMNIBAL + HORN into a formula-oriented data-structures-and-algorithms architecture. 1. The Four Omnidimensional Formula Families The mathematical foundation begin...