By J.-R. Sack and J. Urrutia (Eds.)
ISBN-10: 0444825371
ISBN-13: 9780444825377
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Monma and S. Suri, Transitions in geometric minimum spanning trees. Discrete Comput. Geom. 8 (1992), 265-293. M. Mount, The number of shortest paths on the surface of a polyhedron, SIAM J. Comput. 19 (1990), 593-611. [112] R. MuUin and R. Stanton, A map-theoretic approach to Davenport-Schinzel sequences. Pacific J. Math. 40 (1972), 167-172. [113] K. Mulmuley, Hidden surface removal with respect to a moving point, Proc. 23rd Annu. ACM Sympos. Theory Comput. (1991), 512-522. [114] K. Mulmuley, On levels in arrangements and Voronoi diagrams.
A shortest path on the surface of a convex poly tope can be represented by the sequence of edges that it crosses, and we refer to such a sequence of edges as a shortestpath edge sequence. It is known that there are 6)(n'*) shortest path edge-sequences [111, 133]. Agarwal et al. [4] have shown that the exact set of all shortest-path edge sequences can be computed in time 0{n^Xs (n) \ogn), for some constant ^ > 0, improving a previous algorithm by Schevon and O'Rourke [134]. Baltsan and Sharir [28] considered the special case where O consists of two disjoint convex poly topes (and p and q lie anywhere in the free space).
34] J. H. Reif, New lower bound techniques for robot motion planning problems, Proc. 28th Annu. IEEE Sympos. Found. Comput. Sci. (1987), 49-60. [35] B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir and J. Snoeyink, Computing a face in an arrangement of line segments and related problems, SIAM J. Comput. 22 (1993), 1286-1302. [36] B. J. Guibas, Fractional cascading: I. A data structuring technique, Algorithmica 1 (1986), 133-162. [37] B. T. Lee, On a circle placement problem. Computing 36 (1986), 1-16.
Handbook of Computational Geometry by J.-R. Sack and J. Urrutia (Eds.)
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