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The subpath planning problem is a branch of the path planning problem, whichhas widespread applications in automated manufacturing process as well asvehicle and robot navigation. This problem is to find the shortest path or toursubject for travelling a set of given subpaths. The current approaches fordealing with the subpath planning problem are all based on meta-heuristicapproaches. It is well-known that meta-heuristic based approaches have severaldeficiencies. To address them, we propose a novel approximation algorithm inthe O(n^3) time complexity class, which guarantees to solve any subpathplanning problem instance with the fixed ratio bound of 2. Also, the formalproofs of the claims, our empirical evaluation shows that our approximationmethod acts much better than a state-of-the-art method, both in result andexecution time.

An Approximation Approach for Solving the Subpath Planning Problem