A NEW STRING MATCHING ALGORITHM

In this paper a new exact string-matching algorithm with sub-linear average case complexity has been presented. Unlike other sub-linear string-matching algorithms it never performs more than n text character comparisons while working on a text of length n. It requires only O(m þ s) extra pre-processing time and space, where m is the length of the pattern and s is the size of the alphabet

On the number of shortest descending paths on the surface of a convex terrain

The shortest paths on the surface of a convex polyhedron can be grouped into equivalence classes according to the sequences of edges, consisting of n-triangular faces, that they cross. Mount (1990) [7] proved that the total number of such equivalence classes is Θ(n4). In this paper, we consider descending paths on the surface of a 3D terrain. A path in a terrain is called a descending path if the z-coordinate of a point p never increases, if we move p along the path from the source to the target. More precisely, a descending path from a point s to another point t is a path Π such that for every pair of points p=(x(p),y(p),z(p)) and q=(x(q),y(q),z(q)) on Π, if dist(s,p)<dist(s,q) then z(p)≥z(q). Here dist(s,p) denotes the distance of p from s along Π. We show that the number of equivalence classes of the shortest descending paths on the surface of a convex terrain is Θ(n4). We also discuss the difficulty of finding the number of equivalence classes on a convex polyhedron

Approximation algorithms for shortest descending paths in terrains

A path from s to t on a polyhedral terrain is descending if the height of a point p never increases while we move p along the path from s to t. No efficient algorithm is known to find a shortest descending path (SDP) from s to t in a polyhedral terrain. We present two approximation algorithms that solve the SDP problem on general terrains. We also introduce a generalization of the shortest descending path problem, called the shortest gently descending path (SGDP) problem, where a path descends, but not too steeply. The additional constraint to disallow a very steep descent makes the paths more realistic in practice. We present two approximation algorithms to solve the SGDP problem on general terrains. All of our algorithms are simple, robust and easy to implement