Computing homotopic shortest paths efficiently

Geometric shortest paths are a major topic in computational geometry; see the survey paper by Mitchell [12]. A shortest path between two points in a simple polygon can be found in linear time using the "funnel" algorithm of Chazelle [3] and Lee and Preparata [10]. A more general problem is to find a shortest path between two points in a polygonal domain. In this case the "rubber band" solution is not unique, or, to put it another way, different paths may have different homotopy types. When the homotopy type of the solution is not specified, there are two main approaches, the visibility graph approach, and the continuous Dijkstra (or shortest path map) approach [12]. In this paper, we address the problem of finding a shortest path when the homotopy type is specified. Colloquially, we have a "sketch" of how the path should wind its way among the obstacles, and we want to pull the path tight to shorten it. Homotopic shortest paths are used in VLSI routing [4...

• Type: Journal
• Year: 2006
• Where: COMGEO
• Authors: Alon Efrat, Stephen G. Kobourov, Anna Lubiw
• Keywords: Applied Computing, COMGEO 2006, Homotopic Shortest Path, Homotopy Type, Shortest Path