Searching in The Plane
Ricardo A. Baeza-Yates, Joseph C. Culberson and Gregory J. E. Rawlins
Information and Computation, vol 106(2), 234-252, 1993
Abstract
In this paper we initiate a new area of study dealing with the
best way to search a possibly unbounded region for an object.
The model for our search algorithms is that we must pay costs
proportional to the distance of the next probe position relative
to our current position.
This model is meant to give a realistic
cost measure for a robot moving in the plane.
We also examine the effect of decreasing the amount of
a priori information given to search problems.
Problems of this type are very simple analogues of non-trivial problems
on searching an unbounded region,
processing digitized images, and robot navigation.
We show that for some simple search problems, the relative
information of knowing the general direction of the goal is much
higher than knowing the distance to the goal.
Here are some of the results presented in this paper that suggest that
the relative information of knowing the general direction
of a goal is much higher than knowing just the distance to the goal.
Knowledge
Problem Direction Distance Nothing
Point on a line n 3n 9n
Point on m-rays n (2m-1)n (1+2(m^m)/(m-1)^(m-1))n
Point in Lattice n in [2n^2+4n-1,2n^2+5n+2]
" " with Parity n <= 2n^2+4n+(n mod 2)
The Advantage of Knowing Where Things Are
Ricardo Baeza-Yates rbaeza@dcc.uchile.cl
Gregory J. E. Rawlins rawlins@cs.indiana.edu
Joseph Culberson joe@cs.ualberta.ca