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In the graph exploration problem, a team of mobile computational entities, called agents, arbitrarily positioned at some nodes of a graph, must cooperate so that each node is eventually visited by at least one agent. In the literature, the…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-05-21 Giuseppe Antonio Di Luna , Stefan Dobrev , Paola Flocchini , Nicola Santoro

We consider the problem of exploration of an anonymous, port-labeled, undirected graph with $n$ nodes and $m$ edges and diameter $D$, by a single mobile agent. Initially the agent does not know the graph topology nor any of the global…

Data Structures and Algorithms · Computer Science 2015-12-01 Artur Menc , Dominik Pająk , Przemysław Uznański

A mobile agent, starting from a node $s$ of a simple undirected connected graph $G=(V,E)$, has to explore all nodes and edges of $G$ using the minimum number of edge traversals. To do so, the agent uses a deterministic algorithm that allows…

Data Structures and Algorithms · Computer Science 2024-10-18 Stéphane Devismes , Yoann Dieudonné , Arnaud Labourel

We consider the fundamental task of network exploration. A network is modeled as a simple connected undirected n-node graph with unlabeled nodes, and all ports at any node of degree d are arbitrarily numbered 0,.....,d-1. Each of two…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-01-25 Subhash Bhagat , Andrzej Pelc

This paper considers gossiping among mobile agents in graphs: agents move on the graph and have to disseminate their initial information to every other agent. We focus on self-stabilizing solutions for the gossip problem, where agents may…

Distributed, Parallel, and Cluster Computing · Computer Science 2008-12-18 Toshimitsu Masuzawa , Sébastien Tixeuil

We study the problem of deterministically exploring an undirected and initially unknown graph with $n$ vertices either by a single agent equipped with a set of pebbles, or by a set of collaborating agents. The vertices of the graph are…

Data Structures and Algorithms · Computer Science 2018-05-10 Yann Disser , Jan Hackfeld , Max Klimm

We study the fundamental problem of graph exploration in dynamic graphs using mobile agents. We consider $1$-interval connected dynamic graphs, where the topology may change arbitrarily from round to round as long as the graph remains…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-05-15 Ashish Saxena , Anisur Rahaman Molla , Kaushik Mondal , Gokarna Sharma

Self-stabilization is a versatile technique to withstand any transient fault in a distributed system. Mobile robots (or agents) are one of the emerging trends in distributed computing as they mimic autonomous biologic entities. The…

Data Structures and Algorithms · Computer Science 2009-09-29 Lélia Blin , Maria Gradinariu Potop-Butucaru , Sébastien Tixeuil

We investigate the computational power of the deterministic single-agent model where the agent and each node are equipped with a limited amount of persistent memory. Tasks are formalized as decision problems on properties of input graphs,…

Data Structures and Algorithms · Computer Science 2022-09-07 Taisuke Izumi , Kazuki Kakizawa , Yuya Kawabata , Naoki Kitamura , Toshimitsu Masuzawa

Moving an autonomous agent through an unknown environment is one of the crucial problems for robotics and network analysis. Therefore, it received a lot of attention in the last decades and was analyzed in many different settings. The graph…

Computational Complexity · Computer Science 2018-04-23 Hans-Joachim Böckenhauer , Janosch Fuchs , Walter Unger

We consider the problem of collective exploration of a known $n$-node edge-weighted graph by $k$ mobile agents that have limited energy but are capable of energy transfers. The agents are initially placed at an arbitrary subset of nodes in…

Discrete Mathematics · Computer Science 2021-02-26 J. Czyzowicz , S. Dobrev , R. Killick , E. Kranakis , D. Krizanc , L. Narayanan , J. Opatrny , D. Pankratov , S. Shende

We study the self-stabilizing leader election problem in anonymous $n$-nodes networks. Achieving self-stabilization with low space memory complexity is particularly challenging, and designing space-optimal leader election algorithms remains…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-02-20 Lelia Blin , Sylvain Gay , Isabella Ziccardi

We consider the problem of periodic graph exploration in which a mobile entity with constant memory, an agent, has to visit all n nodes of an arbitrary undirected graph G in a periodic manner. Graphs are supposed to be anonymous, that is,…

Discrete Mathematics · Computer Science 2009-05-13 J. Czyzowicz , S. Dobrev , L. Gasieniec , D. Ilcinkas , J. Jansson , R. Klasing , I. Lignos , R. Martin , K. Sadakane , W. -K. Sung

We investigate two fundamental problems in mobile computing: exploration and rendezvous, with two distinct mobile agents in an unknown graph. The agents may communicate by reading and writing information on whiteboards that are located at…

Multiagent Systems · Computer Science 2024-07-08 Romain Cosson

We study deterministic exploration by a single agent in $T$-interval-connected graphs, a standard model of dynamic networks in which, for every time window of length $T$, the intersection of the graphs within the window is connected. The…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-04-07 Yuichi Sudo , Naoki Kitamura , Masahiro Shibata , Junya Nakamura , Sébastien Tixeuil , Toshimitsu Masuzawa , Koichi Wada

In the distributed backup-placement problem each node of a network has to select one neighbor, such that the maximum number of nodes that make the same selection is minimized. This is a natural relaxation of the perfect matching problem, in…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-08-19 Leonid Barenboim , Gal Oren

We study the dispersion problem in anonymous port-labeled graphs: $k \leq n$ mobile agents, each with a unique ID and initially located arbitrarily on the nodes of an $n$-node graph with maximum degree $\Delta$, must autonomously relocate…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-07-03 Debasish Pattanayak , Ajay D. Kshemkalyani , Manish Kumar , Anisur Rahaman Molla , Gokarna Sharma

A communication network is said to be "anonymous" if its agents are indistinguishable from each other; it is "dynamic" if its communication links may appear or disappear unpredictably over time. Assuming that each of the $n$ agents of an…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-08-26 Giuseppe A. Di Luna , Giovanni Viglietta

We consider the task of graph exploration. An $n$-node graph has unlabeled nodes, and all ports at any node of degree $d$ are arbitrarily numbered $0,\dots, d-1$. A mobile agent has to visit all nodes and stop. The exploration time is the…

Data Structures and Algorithms · Computer Science 2016-11-17 Barun Gorain , Andrzej Pelc

Temporal graphs are graphs where the edge set can change in each time step, and the vertex set stays the same. Exploration of temporal graphs whose snapshot in each time step is a connected graph, called connected temporal graphs, has been…

Data Structures and Algorithms · Computer Science 2024-07-19 Konstantinos Dogeas , Thomas Erlebach , Frank Kammer , Johannes Meintrup , William K. Moses
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