Shortest Circular Paths on Planar Graphs

The shortest circular-path problem is similar to the ordinary shortest path problem, but instead of specifying a distinguished starting and end node, the path has to form a closed loop. This problem has several applications in optimization problems as they occur in image segmentation or shape matching. We propose a new algorithm to compute shortest circular paths on planar graphs that has a typical computation time of O(|V | log |V |) and a worst case complexity of O(|V | log |V |). The fastest previously known algorithm for this problem has an average computation time of O(|V | log |V |) and a worst case performance of O(|V |2 log |V |).