{"type":"ScholarlyArticle","title":"An Improved Approximation Algorithm for the Subpath Planning Problem and Its Generalization","authors":[{"name":"Hanna Sumita","slug":"hanna-sumita","given":"Hanna","family":"Sumita","affiliation":"† National Institute of Informatics"},{"name":"Yuma Yonebayashi","slug":"yuma-yonebayashi","given":"Yuma","family":"Yonebayashi","affiliation":"‡ University of Tokyo §"},{"name":"Naonori Kakimura","slug":"naonori-kakimura","given":"Naonori","family":"Kakimura","affiliation":"Keio University"},{"name":"Ken-ichi Kawarabayashi","slug":"ken-ichi-kawarabayashi","given":"Ken-ichi","family":"Kawarabayashi","affiliation":"† National Institute of Informatics"}],"abstract":"This paper focuses on a generalization of the traveling salesman problem (TSP), called the subpath planning problem (SPP). Given 2n vertices and n independent edges on a metric space, we aim to find a shortest tour that contains all the edges. SPP is one of the fundamental problems in both artificial intelligence and robotics. Our main result is to design a 1.5-approximation algorithm that runs in polynomial time, improving the currently best approximation algorithm. The idea is direct use of techniques developed for TSP. In addition, we propose a generalization of SPP called the subgroup planning problem (SGPP). In this problem, we are given a set of disjoint groups of vertices, and we aim to find a shortest tour such that all the vertices in each group are traversed sequentially. We propose a 3-approximation algorithm for SGPP. We also conduct numerical experiments. Compared with previous algorithms, our algorithms improve the solution quality by more than 10% for large instances with more than 10,000 vertices.","doi":"10.24963/ijcai.2017/616","url":"https://ijcai.org/proceedings/2017/616","pdf":"https://ijcai.org/proceedings/2017/0616.pdf","markdown":"https://ijcai.org/proceedings/2017/616.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/616","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Planning and Scheduling","track":"Main track","number":616,"pages":{"first":4412,"last":4418},"keywords":["Planning and Scheduling: Theoretical Foundations of Planning","Combinatorial & Heuristic Search: Combinatorial search/optimisation"],"videos":[],"references":[{"position":1,"raw":"[Arora, 1998] S. 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