Search

Let be a graph, be a source node and be a target node. The sequence of adjacent nodes (graph walk) visited by a routing algorithm is a -competitive route if its length in is at most times the length of the shortest path from to in . We present a -competitive online routing algorithm on the Delaunay triangulation of an arbitrary given set of points in the plane. This improves the competitive ratio on Delaunay triangulations from the previous best of . We also present a -competitive online routing algorithm for Delaunay triangulations of point sets in convex position. [ABSTRACT FROM AUTHOR]

(I) We exhibit a set of 23 points in the plane that has dilation at least , improving the previous best lower bound of for the worst-case dilation of plane spanners. (II) For every , there exists an -element point set such that the degree dilation of equals in the domain of plane geometric spanners. In the same domain, we show that for every , there exists a an -element point set such that the degree dilation of equals The previous best lower bound of holds for any degree. (III) For every , there exists an -element point set such that the stretch factor of the greedy triangulation of is at least . [ABSTRACT FROM AUTHOR]