A better length function for Artin's braid groups

Having a good length function on a group is the main ingredient in a recent combined memory/length approach to solving random equations in that group. Currently, the groups of greatest interest in this respect are Artin’s braid groups. We demonstrate, by a series of experiments, that a length function based on the Birman-Ko-Lee presentation of the braid group is substantially better than the corresponding function based on the Artin presentation.