Polynomial Time Summary Statistics for Two general Classes of Functions

In previous work we showed, by Walsh analysis, that summary statistics such as mean, variance, skew, and higher order statistics can be computed in polynomial time for embedded landscapes. We then used these statistics to study the epistatic structure of MAXSAT problems. These results were dependent on two facts: these functions have a polynomial number of nonzero Walsh coe cients and the coe cients can be computed in polynomial time. It has since been shown that for any arbitrary function in which the number of epistatically interacting bits is bounded above by k the nonzero Walsh coe cients are also polynomial in number and can be computed in polynomial time. This extends the applicability of our earlier results. In this paper, I extend these results further to include hyperplane statistics. These statistics can help us understand the hyperplane structure of sparsely epistatic functions as well as functions of bounded epistasis.

• Type: Conference
• Year: 2000
• Where: GECCO
• Authors: Robert B. Heckendorn
• Keywords: GECCO 2000, Nonzero Walsh Coe, Optimization, Polynomial Time, Walsh Coe Cients