Linkage Identification by Non-monotonicity Detection for Overlapping Functions

Abstract

This paper presents the linkage identification by non-monotonicity detection (LIMD) procedure and its extension for overlapping functions by introducing the tightness detection (TD) procedure. The LIMD identifies linkage groups directly by performing order-2 simultaneous perturbations on a pair of loci to detect monotonicity/non-monotonicity of fitness changes. The LIMD can identify linkage groups with at most order of k when it is applied to O(2k) strings. The TD procedure calculates tightness of linkage between a pair of loci based on the linkage groups obtained by the LIMD. By removing loci with weak tightness from linkage groups, correct linkage groups are obtained for overlapping functions, which were considered difficult for linkage identification procedures

Efficient Linkage Discovery by Limited Probing

“…Strictly speaking, these results do not apply to the LINC algorithm of [MG99b] since the above analysis assumes that the backgrounds of probes are chosen independently, and this is not the case for the LINC algorithm. However, our empirical results show that these formulas are quite accurate when the backgrounds are chosen from a population.…”

“…The order-2 version of this algorithm is similar to the LINC algorithm of [MG99b]. However, they start with a population of strings.…”

“…(See Section 8.) In fact, it is much more accurate than the population sizing formula given by [MG99b].…”

“…In fact, MAX3SAT problems are equivalent to problems of low epistasis in which all epistatic interactions are known and they are provably NP-complete [Hec99]. Still, knowing the location of epistatically interacting blocks of bits may be used to guide a search for the optimum or the formulation of a representation [MG99b,MG99a,KP01]. If the function is separable, each component can be solved separately.…”

“…Munetomo and Goldberg showed a simple direct perturbational approach to generalized linkage discovery over a binary alphabet in [MG99b] [MG99a]. These papers also summarize some other approaches to the problem.…”