  Using Monte Carlo simulations we examine the diffusive properties of the
greedy algorithm in the d-dimensional traveling salesman problem. Our results
show that for d=3 and 4 the average squared distance from the origin <r^2> is
proportional to the number of steps t. In the d=2 case such a scaling is
modified with some logarithmic corrections, which might suggest that d=2 is the
critical dimension of the problem. The distribution of lengths also shows
marked differences between d=2 and d>2 versions. A simple strategy adopted by
the salesman might resemble strategies chosen by some foraging and hunting
animals, for which anomalous diffusive behavior has recently been reported and
interpreted in terms of Levy flights. Our results suggest that broad and
Levy-like distributions in such systems might appear due to dimension-dependent
properties of a search space.
