Expected asymptotically optimal planar point location

Given a fixed distribution of point location queries among the triangles in a triangulation of the plane, a data structure is presented that achieves, within constant multiplicative factors, the entropy bound on the expected point location query time. The data structure is a simple variation of Kirkpatrick's classic planar point location structure [D.G. Kirkpatrick, SIAM J. Comput. 12 (1) (1983) 28-35], and has linear construction costs and space requirements. (C) 2004 Elsevier B.V. All rights reserved.