Ordinal algorithms for packing with target center of gravity

The problem of arranging N unit length weights on a line segment of length N, given a target center of gravity on this line segment, is examined under the assumption that the only information we have about the weights is their order, i.e., a₁ a₂ ... a_N. Lower bounds on worst case performance of algorithms for this problem are developed, and algorithms (permutations) which come close to achieving these bounds are provided.This work was partially supported under Natural Sciences and Engineering Research Council (NSERC) of Canada research grant number OGP0002507.