Some novel locality results for the blob code spanning tree representation

The Blob Code is a bijective tree code that represents each tree on n labelled vertices as a string of n − 2 vertex labels. In recent years, several researchers have deployed the Blob Code as a GA representation, and have reported promising results across a range of tree-based optimization problems. In this paper, we exploit a recently discovered linear-time decoding algorithm for the Blob Code to develop some novel locality results, extending previous work by Julstrom. Let Δ be the random variable representing the number of tree edges that are changed by a random single-element string mutation. Under the Blob Code, we demonstrate that pessimal mutations (i.e., mutations for which Δ = n−1) can arise for any n > 4. However, as n grows, the probability of perfect mutation P(Δ = 1) approaches one, following a power-law relationship, and E(Δ) approaches two. These results show that the locality of the Blob Code is high, but not as high as that of Dandelion-like codes. We also s...

• Type: Conference
• Year: 2007
• Where: GECCO
• Authors: Tim Paulden, David K. Smith
• Keywords: Blob Code, Discrete Mathematics, GECCO 2007, Tree Edges