Publication Date



Technical Report: UTEP-CS-18-29

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


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 tA(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 tA(x) ~ n3 or reach some even faster time nα for α < 3.

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