Constrained routing between non-visible vertices

In this paper we study local routing strategies on geometric graphs. Such use properties of the graph like coordinates current and target nodes to route. Specifically, in presence constraints which are obstacles that edges not allowed cross. Let P be a set n points plane let S line segments whose endpoints P, with no two intersecting properly. We present first deterministic 1-local O(1)-memory algorithm is guaranteed find path between vertices visibility respect S. The strategy never looks beyond direct neighbors node does store more than O(1)-information reach target. then turn our attention finding competitive strategies. show when any triangulation T such S⊆T, o(n)-competitive exists restricts its triangles intersected by segment from source (a technique commonly used unconstrained setting). Finally, provide an O(n)-competitive T, optimal worst case, given lower bound.