eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-02-15
11:1
11:18
10.4230/LIPIcs.OPODIS.2022.11
article
Computational Power of a Single Oblivious Mobile Agent in Two-Edge-Connected Graphs
Inoue, Taichi
1
Kitamura, Naoki
1
Izumi, Taisuke
1
Masuzawa, Toshimitsu
1
Osaka University, Japan
We investigated the computational power of a single mobile agent in an n-node graph with storage (i.e., node memory). Generally, a system with one-bit agent memory and O(1)-bit storage is as powerful as that with O(n)-bit agent memory and O(1)-bit storage. Thus, we focus on the difference between one-bit memory and oblivious (i.e., zero-bit memory) agents. Although their computational powers are not equivalent, all the known results exhibiting such a difference rely on the fact that oblivious agents cannot transfer any information from one side to the other across the bridge edge. Hence, our main question is as follows: Are the computational powers of one-bit memory and oblivious agents equivalent in 2-edge-connected graphs or not? The main contribution of this study is to answer this question under the relaxed assumption that each node has O(logΔ)-bit storage (where Δ is the maximum degree of the graph). We present an algorithm for simulating any algorithm for a single one-bit memory agent using an oblivious agent with O(n²)-time overhead per round. Our results imply that the topological structure of graphs differentiating the computational powers of oblivious and non-oblivious agents is completely characterized by the existence of bridge edges.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol253-opodis2022/LIPIcs.OPODIS.2022.11/LIPIcs.OPODIS.2022.11.pdf
mobile agent
depth-first search
space complexity