Improving multivariate Homer schemes with Monte Carlo tree search
Optimizing the cost of evaluating a polynomial is a classic problem in comp. titer science. For polynomials in one variable, Homer's method provides a scheme for producing a computationally efficient form. For multivariate polynomials it is possible to generalize Horner's method, but this leaves freedom in the order of the variables. Traditionally, greedy schemes like most-occurring variable first are used. This simple textbook algorithm has given remarkably efficient results. Finding better algorithms has proved difficult. In trying to improve upon the greedy scheme we have implemented Monte Carlo tree search, a recent search method from the field of artificial intelligence. This results in better Homer schemes and reduces the cost of evaluating polynomials, sometimes by factors up to two. (C) 2013 Elsevier ay. All rights reserved.
computational techniques