Why Encubation?

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Rohan Baingolkar, The University of Texas at El PasoFollow
Swapnil S. Chauhan, The University of Texas at El PasoFollow
Ishtjot S. Kamboj, The University of Texas at El PasoFollow

Publication Date

3-2018

Comments

Technical Report: UTEP-CS-18-29

Published in International Journal of Computing and Optimization, 2018, Vol. 5, No. 1, pp. 5-8.

Abstract

It is known that some algorithms are feasible, and some take too long to be practical/ For example, if the running time of an algorithm is 2ⁿ, where n = len(x) is the bit size of the input x, then already for n = 500, the computation time exceeds the lifetime of the Universe. In computer science, it is usually assumed that an algorithm A is feasible if and only if it is polynomial-time, i.e., if its number of computational steps t_A(x) on any input x is bounded by a polynomial P(n) of the input length n = len}(x).

An interesting encubation phenomenon is that once we succeed in finding a polynomial-time algorithm for solving a problem, eventually it turns out to be possible to further decrease its computation time until we either reach the cubic time t_A(x) ~ n³ or reach some even faster time n^α for α < 3.

In this paper, we provide a possible physics-based explanation for the encubation phenomenon.