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… 
Exploration of the T-Interval-Connected Dynamic Graphs: the Case of the Ring
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
Exploration of Dynamic Ring Networks by a Single Agent with the H-hops and S-time Steps View
TLDR
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
TLDR
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
TLDR
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
TLDR
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.
...
...

References

SHOWING 1-10 OF 13 REFERENCES
Distributed computation in dynamic networks
TLDR
A worst-case model in which the communication links for each round are chosen by an adversary, and nodes do not know who their neighbors for the current round are before they broadcast their messages is considered.
The Cover Times of Random Walks on Hypergraphs
TLDR
An expression for C(H) is given which is tractable for many classes of hypergraphs, and C (H) and I(H ) are calculated exactly for random r-regular, s-uniform hyper graphs.
Building a Reference Combinatorial Modelfor Dynamic Networks:Initial Results in Evolving Graphs
TLDR
It is shown how the modeling of time-changes unsettles old questions and allows for new insights into central problems in networking, like routing metrics, connectivity, and spanning trees.
Dynamic networks: models and algorithms
TLDR
This column surveys some recent work on dynamic network algorithms, focusing on the effect that model parameters such as the type of adversary, the network diameter, and the graph expansion can have on the performance of algorithms.
Information Spreading in Dynamic Networks
TLDR
An $\Omega(nk/\log n)$ lower bound on the number of rounds needed for any deterministic token-forwarding algorithm to solve gossip, a step towards understanding the power and limitation of token- forwarding algorithms in dynamic networks.
Information dissemination in highly dynamic graphs
TLDR
This work investigates to what extent flooding and routing is possible if the graph is allowed to change unpredictably at each time step, and looks at algorithmic constraints such as limited storage, no knowledge of an upper bound on the number of nodes, and no usage of identifiers.
Approximating Graphic TSP by Matchings
  • Tobias Mömke, O. Svensson
  • Computer Science, Mathematics
    2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
  • 2011
TLDR
A framework for approximating the metric TSP based on a novel use of matchings that allows for generalizations in a natural way and also leads to a 1.586-approximation algorithm for the traveling salesman path problem on graphic metrics where the start and end vertices are prespecified.
Shorter tours by nicer ears: 7/5-Approximation for the graph-TSP, 3/2 for the path version, and 4/3 for two-edge-connected subgraphs
TLDR
The key new ingredient of all algorithms is a special kind of ear-decomposition optimized using forest representations of hypergraphs that provides the lower bounds that are used to deduce the approximation ratios.
13/9-approximation for Graphic TSP
TLDR
This paper provides an improved analysis of the approach used by Momke and Svensson, yielding a bound of 13/9 on the approximation factor, as well as a Bound of 19/12+epsilon for any epsilon>0 for a more general Travelling Salesman Path Problem in graphic metrics.
A linear algorithm for the pos/neg-weighted 1-median problem on a cactus
TLDR
The 1-median problem on a network asks for a vertex minimizing the sum of the weighted shortest path distances from itself to all other vertices, each associated with a certain positive weight, and an exact algorithm for the resulting ‘pos/neg-weighted’ problem defined on a cactus is devised.
...
...