Assuming that we know the distance to the target for multiple (2) agent
search it is easy enough to concoct the formula for the distance
traveled according to each search strategy employed. If the distance
is known to be d, the sensor radius r, then number of rendezvous
attempts made will have to be 
for strategy
, where 
is the integer ceiling
operator, the smallest integer not less than the operand. Then the distance
traveled by each strategy, 
is given by
and the resulting curve is plotted, for example d=10, in figure 3.
Figure 3: A plot of distances walked by the different strategies for a target at distance, d=10. Here r=1 WLOG. Note: the curve is monotonically increasing to the right after 
Of course the competitive ratio that we are examining here is in comparison to the distance traveled by an omniscient agent that simply walks to the target and back to the rendezvous location, for distance of 2d.
