Author:
Kobayashi Koji M.,Li Ying
Abstract
AbstractThe online graph exploration problem, which was proposed by Kalyanasundaram and Pruhs (Theor Comput Sci 130(1):125–138, 1994), is defined as follows: Given an edge-weighted undirected connected graph and a specified vertex (called the origin), the task of an algorithm is to compute a path from the origin to the origin which contains all the vertices of the given graph. The goal of the problem is to find such a path of minimum weight. At each time, an online algorithm knows only the weights of edges each of which consists of visited vertices or vertices adjacent to visited vertices. Fritsch (Inform Process Lett 168:1006096, 2021) showed that the competitive ratio of an online algorithm is at most three for any unicyclic graph. On the other hand, Brandt et al. (Theor Comput Sci 839:176–185, 2020) showed a lower bound of two on the competitive ratio for any unicyclic graph. In this paper, we showed the competitive ratio of an online algorithm is at most 5/2 for any unicyclic graph.
Publisher
Springer Science and Business Media LLC
Reference19 articles.
1. Asahiro Y, Miyano E, Miyazaki S, Yoshimuta T (2010) Weighted nearest neighbor algorithms for the graph exploration problem on cycles. Inf Process Lett 110(3):93–98
2. Baligács J, Disser Y, Heinrich I, Schweitzer P (2023) Exploration of graphs with excluded minors. In: Proceeding of the 31st Annual European Symposium on Algorithms, pp 11:1–11:15
3. Birx A, Disser Y, Hopp AV, Karousatou C (2021) An improved lower bound for competitive graph exploration. Theor Comput Sci 868:65–86
4. Böckenhauer H.-J, Fuchs J, Unger W (2018) Exploring sparse graphs with advice (extended abstract). In: Proceeding of of the 16th international workshop on approximation and online algorithms, pp 102–117
5. Böckenhauer H.-J Fuchs J, Unger W (2022) Exploring sparse graphs with advice. Inform Comput 289, Part A:104950