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.
@InProceedings{inoue_et_al:LIPIcs.OPODIS.2022.11, author = {Inoue, Taichi and Kitamura, Naoki and Izumi, Taisuke and Masuzawa, Toshimitsu}, title = {{Computational Power of a Single Oblivious Mobile Agent in Two-Edge-Connected Graphs}}, booktitle = {26th International Conference on Principles of Distributed Systems (OPODIS 2022)}, pages = {11:1--11:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-265-5}, ISSN = {1868-8969}, year = {2023}, volume = {253}, editor = {Hillel, Eshcar and Palmieri, Roberto and Rivi\`{e}re, Etienne}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2022.11}, URN = {urn:nbn:de:0030-drops-176311}, doi = {10.4230/LIPIcs.OPODIS.2022.11}, annote = {Keywords: mobile agent, depth-first search, space complexity} }
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