# Exploration of Constantly Connected Dynamic Graphs Based on Cactuses

@inproceedings{Ilcinkas2014ExplorationOC, title={Exploration of Constantly Connected Dynamic Graphs Based on Cactuses}, author={David Ilcinkas and Ralf Klasing and Ahmed Mouhamadou Wade}, booktitle={SIROCCO}, year={2014} }

We study the problem of exploration by a mobile entity (agent) of a class of dynamic networks, namely constantly connected dynamic graphs. This problem has already been studied in the case where the agent knows the dynamics of the graph and the underlying graph is a ring of n vertices [5]. In this paper, we consider the same problem and we suppose that the underlying graph is a cactus graph (a connected graph in which any two simple cycles have at most one vertex in common). We propose an…

## 37 Citations

Exploration of the T-Interval-Connected Dynamic Graphs: the Case of the Ring

- MathematicsTheory of Computing Systems
- 2017

This paper studies the T-interval-connected dynamic graphs from the point of view of the time necessary and sufficient for their exploration by a mobile entity (agent) and shows that the worst-case time complexity for the exploration problem is 2n − T − Θ(1) time units if the agent knows the dynamics of the graph.

Exploration of Dynamic Cactuses with Sub-logarithmic Overhead

- Computer ScienceTheory of Computing Systems
- 2020

This paper proposes an algorithm that allows the agent to explore these dynamic graphs in at most O(nlognloglogn)2 and shows that the lower bound of the algorithm is Ω (nlogn(logl Cogn)2).

Distributed exploration of dynamic rings

- MathematicsDistributed Computing
- 2018

The main focus is on the impact that the level of synchrony as well as other factors such as anonymity, knowledge of the size of the ring, and chirality have on the solvability of the problem, focusing on the minimum number of agents necessary.

Tight Bounds on Distributed Exploration of Temporal Graphs

- Mathematics, Computer ScienceOPODIS
- 2019

This paper considers for the first time the problem of exploring temporal graphs of arbitrary unknown topology, and studies the feasibility of exploration, under both the Fsync and Ssync schedulers, focusing on the number of agents necessary and sufficient to explore such graphs.

Patrolling on Dynamic Ring Networks

- Computer ScienceSOFSEM
- 2019

This paper provides the first known results for collaborative patrolling on dynamic graphs on 1-interval-connected ring networks and shows a clear separation in terms of idle time, for agents that have prior knowledge of the dynamic networks compared to agents that do not have such knowledge.

Exploration of dynamic networks: Tight bounds on the number of agents

- Mathematics, Computer ScienceJ. Comput. Syst. Sci.
- 2021

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

- Computer ScienceSSS
- 2019

This paper considers the exploration of 1-interval connected rings by a single agent with the H-hop 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.

Group Exploration of Dynamic Tori

- Computer Science2018 IEEE 38th International Conference on Distributed Computing Systems (ICDCS)
- 2018

It is proved for exploration of the n × m dynamic torus that, without the link presence detection, n+1 agents are necessary and sufficient, and, with the link Presence detection, ⌈n/2⌉ + 1 agents are required and sufficient.

Live Exploration of Dynamic Rings

- Mathematics2016 IEEE 36th International Conference on Distributed Computing Systems (ICDCS)
- 2016

This paper starts the study of the decentralized exploration of dynamic graphs, i.e. when the agents operate in the graph unaware of the location and timing of the changes, and investigates the feasibility of their exploration, in both the fully synchronous and semi-synchronous cases.

Broadcasting with Mobile Agents in Dynamic Networks

- Computer ScienceOPODIS
- 2020

How many agents are necessary and sufficient to solve the broadcast problem in dynamic networks modelled as an evolving graph is determined and lower bounds on the number of agents are shown.

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