Exploration of Dynamic Ring Networks by a Single Agent with the H-hops and S-time Steps View

Abstract

The researches about a mobile entity (called agent) on dynamic networks have attracted a lot of attention in recent years. Exploration which requires an agent to visit all the nodes in the network is one of the most fundamental problems. While the exploration with complete information or with no information about network changes is proposed, despite its practical scenario and applicability, an agent with partial information about the network changes has not been considered yet. In this paper, we consider the exploration of 1-interval connected rings by a single agent with the H-hops and S-time steps view such that the agent can see not all but a part of network changes, i.e., the network changes of links within H-hops for the next S-time steps. In the setting, we show that $H+S \ge n$ and $S \ge \lceil n/2 \rceil$ (n is the size of networks) is necessary and sufficient condition to explore 1-interval connected rings by a single agent. Moreover, we investigate the upper-bounds and the lower-bounds of the exploration time. It is proven that the exploration time is $O(n^2)$ for $S < n-1$, $O(n^2/H + n \log H)$ for $S \ge n-1$, and $\varOmega (n^2/H)$ for any S.

This work was supported by JSPS KAKENHI Grant Numbers 17K19977, 18K11167, 18K18000 and 19H04085 and JST SICORP Grant Numbers JPMJSC1606 and JPMJSC1806.