Exploration of Constantly Connected Dynamic Graphs Based on Cactuses

Ilcinkas, David; Klasing, Ralf; Wade, Ahmed Mouhamadou

doi:10.1007/978-3-319-09620-9_20

Cited by 33 publications

(23 citation statements)

References 11 publications

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“…In the centralised setting (when agents know the dynamic of the graph apriori) the problem of exploring a graph in the fastest possible way has been studied in several papers [1,18,31]. The task is NP-hard on general graphs and it becomes polynomial on special topologies [2,22]. Notably, in the case of interval connected ring the exploration can be done in O(n) rounds [24].…”

Section: Related Workmentioning

confidence: 99%

Patrolling on Dynamic Ring Networks

Das

Luna

Gąsieniec

2019

SOFSEM 2019: Theory and Practice of Computer Science

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We study the problem of patrolling the nodes of a network collaboratively by a team of mobile agents, such that each node of the network is visited by at least one agent once in every I(n) time units, with the objective of minimizing the idle time I(n). While patrolling has been studied previously for static networks, we investigate the problem on dynamic networks with a fixed set of nodes, but dynamic edges. In particular, we consider 1-interval-connected ring networks and provide various patrolling algorithms for such networks, for k = 2 or k > 2 agents. We also show almost matching lower bounds that hold even for the best starting configurations. Thus, our algorithms achieve close to optimal idle time. Further, we show 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. This paper provides the first known results for collaborative patrolling on dynamic graphs.

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Section: Related Workmentioning

confidence: 99%

Patrolling on Dynamic Ring Networks

Das

Luna

Gąsieniec

2019

SOFSEM 2019: Theory and Practice of Computer Science

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“…The notion of 1-interval connectivity dynamism was introduced in [27] for complete graphs and requires an adversary to connect the nodes of the graph such that in every round there must exist a connected spanning subgraph of the nodes. This model was studied by [27], [22], and [21] for complete graphs, rings and cactuses respectively. [10] studied the model where for a given ring of nodes, in each round an adversary chooses at most one edge of the ring and removes it for that round.…”

Section: Related Workmentioning

confidence: 99%

“…The notion of 1-interval connectivity dynamism was introduced in [27] for complete graphs and requires an adversary to connect the nodes of the graph such that in every round there must exist a connected spanning subgraph of the nodes. [27] studied it for complete graphs, [22] studied it for the case of rings, and [21] looked into it for cactuses. Note that the connections between nodes need not remain from round to round.…”

Section: Nature Of Dynamismmentioning

confidence: 99%

Deterministic Dispersion of Mobile Robots in Dynamic Rings

Agarwalla

Augustine

Moses

et al. 2018

Proceedings of the 19th International Conference on Distributed Computing and Networking

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In this work, we study the problem of dispersion of mobile robots on dynamic rings. The problem of dispersion of n robots on an n node graph, introduced by Augustine and Moses Jr. [1], requires robots to coordinate with each other and reach a configuration where exactly one robot is present on each node. This problem has real world applications and applies whenever we want to minimize the total cost of n agents sharing n resources, located at various places, subject to the constraint that the cost of an agent moving to a different resource is comparatively much smaller than the cost of multiple agents sharing a resource (e.g. smart electric cars sharing recharge stations). The study of this problem also provides indirect benefits to the study of scattering on graphs, the study of exploration by mobile robots, and the study of load balancing on graphs.We solve the problem of dispersion in the presence of two types of dynamism in the underlying graph: (i) vertex permutation and (ii) 1-interval connectivity. We introduce the notion of vertex permutation dynamism and have it mean that for a given set of nodes, in every round, the adversary ensures a ring structure is maintained, but the connections between the nodes may change. We use the idea of 1-interval connectivity from Di Luna et al. [10], where for a given ring, in each round, the adversary chooses at most one edge to remove.We assume robots have full visibility and present asymptotically time optimal algorithms to achieve dispersion in the presence of both types of dynamism when robots have chirality. When robots do not have chirality, we present asymptotically time optimal algorithms to achieve dispersion subject to certain constraints. Finally, we provide impossibility results for dispersion when robots have no visibility.

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“…On the other hand, few algorithms have been designed for robots evolving in dynamic graphs. The majority of them deals with the problem of exploration [3,4,11,13,18] (robots must visit each node of the graph at least once or infinitely often depending on the variant of the problem). In the most related work to ours [19], Di Luna et al study the gathering problem in dynamic rings.…”

Section: Introductionmentioning

confidence: 99%

Gracefully Degrading Gathering in Dynamic Rings

Bournat¹,

Dubois²,

Petit³

2018

Lecture Notes in Computer Science

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Gracefully degrading algorithms [Biely et al., TCS 2018] are designed to circumvent impossibility results in dynamic systems by adapting themselves to the dynamics. Indeed, such an algorithm solves a given problem under some dynamics and, moreover, guarantees that a weaker (but related) problem is solved under a higher dynamics under which the original problem is impossible to solve. The underlying intuition is to solve the problem whenever possible but to provide some kind of quality of service if the dynamics become (unpredictably) higher.In this paper, we apply for the first time this approach to robot networks. We focus on the fundamental problem of gathering a squad of autonomous robots on an unknown location of a dynamic ring. In this goal, we introduce a set of weaker variants of this problem. Motivated by a set of impossibility results related to the dynamics of the ring, we propose a gracefully degrading gathering algorithm. arXiv:1805.05137v2 [cs.DC] 2 Aug 2018 Rules for Phase K K 1 :: AllButT woW aitingW alker() −→ InitiateWalk() K 2 :: W aitingW alker() −→ StopMoving() K 3 :: ∃r ∈ N odeM ate(), P otentialM inOrSearcherW ithM inW aiting(r ) −→ BecomeWaitingWalker(r') K 4 :: ∃r ∈ N odeM ate(), RighterW ithM inW aiting(r ) ∧ ExistsEdge(right, current) −→ BecomeAwareSearcher(r') Rules for Phase M M 1 :: P otentialM inOrRighter() ∧ M inDiscovery() −→ BecomeMinWaitingWalker(r) M 2 :: ∃r ∈ N odeM ate(), N otW alkerW ithHeadW alker(r ) ∧ ExistsEdge(right, current) −→ BecomeAwareSearcher(r') M 3 :: ∃r ∈ N odeM ate(), N otW alkerW ithHeadW alker(r ) −→ BecomeAwareSearcher(r'); StopMoving() M 4 :: ∃r ∈ N odeM ate(), N otW alkerW ithT ailW alker(r ) −→ BecomeTailWalker(r'); Walk() M 5 :: ∃r ∈ N odeM ate(), P otentialM inW ithAwareSearcher(r ) −→ BecomeAwareSearcher(r'); Search() M 6 :: AllButOneRighter() −→ InitiateSearch() M 7 :: ∃r ∈ N odeM ate(), RighterW ithSearcher(r ) −→ BecomeAwareSearcher(r'); Search() M 8 :: P otentialM inOrRighter() −→ MoveRight() M 9 :: DumbSearcherM inRevelation() −→ BecomeAwareSearcher(r); Search() M 10 :: ∃r ∈ N odeM ate(), DumbSearcherW ithAwareSearcher(r ) −→ BecomeAwareSearcher(r'); Search() M 11 :: Searcher() −→ Search()

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Exploration of Constantly Connected Dynamic Graphs Based on Cactuses

Cited by 33 publications

References 11 publications

Patrolling on Dynamic Ring Networks

Patrolling on Dynamic Ring Networks

Deterministic Dispersion of Mobile Robots in Dynamic Rings

Gracefully Degrading Gathering in Dynamic Rings

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