Definition: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Input: The subpath planning problem is a branch of the path planning problem, which has widespread applications in automated manufacturing process as well as vehicle and robot navigation. This problem is to find the shortest path or tour subject for travelling a set of given subpaths. The current approaches for dealing with the subpath planning problem are all based on meta-heuristic approaches. It is well-known that meta-heuristic based approaches have several deficiencies. To address them, we propose a novel approximation algorithm in the O(n3) time complexity class, which guarantees to solve any subpath planning problem instance with the fixed ratio bound of 2. Beside the formal proofs of the claims, our empirical evaluation shows that our approximation method acts much better than a state-of-the-art method, both in result and execution time. Note to Practitioners—In some real world applications such as robot and vehicle navigation in structured and industrial environments as well as some of the manufacturing processes such as electronic printing and polishing, it is required for the agent to travel a set of predefined paths. Automating this process includes three steps: 1) capturing the environment of the actual problem and formulating it as a subpath planning problem; 2) solving subpath planning problem to find the near optimal path or tour; 3) command the robot to follow the output. The most challenging phase is the second one that this paper tries to tackle it. To design an effective automation for the aforementioned applications, it is essential to make use of methods with low computational cost but near optimal outputs in the second phase. According to the fact that the length of the final output has a direct effect on the cost of performing the task, it is desirable to incorporate methods with low complexity that can guarantee a bound for the difference between length of the optimal path and 1 ar X iv :1 60 3. 06 21 7v 1 [ cs .R O ] 2 0 M ar 2 01 6 the output. Current approaches for solving subpath planning problem are all meta-heuristic based. These methods do not provide such a bound. And plus, they are usually very time consuming. They may find promising results for some instances of problems, but there is no guarantee that they always exhibit such a good behaviour. In this paper, in order to avoid the issues of metaheuristics methods, we present an approximation algorithm, which provides an appropriate bound for the optimality of its solution. To gauge the performance of proposed methods, we conducted a set of experiments the results of which show that our proposed method finds shorter paths in less time in comparison with a state-of-the-art method.

An Approximation Approach for Solving the Subpath Planning Problem