 
Summary: 5 Upper bounds for c(0+)
This is written (November 2006) in the format of an Appendix to the paper
Percolating paths through random points by David Aldous and Maxim
Krikun, published as ALEA 1 (2006) 89109. The purpose is to show some
simulations and record (for the constant c(0+) in dimension 2)
· a heuristic upper bound of 0.52
· an upper bound of 0.607 which is rigorous up to sampling error in a
fixedsize Monte Carlo simulation.
These are based on a certain "crude algorithm" (described later) for finding
paths with small average edgelength. This algorithm is not claimed to
be close to optimal (developing nearoptimal heuristic algorithms for the
problems considered in this paper remains an open problem) but is easy to
implement.
5.1 A heuristic upper bound
q
q q
q
q
q q
q qq
