Smart Robot Teams Exploring Sparse Trees

Dynia, Miroslaw; Kutyłowski, Jarosław; Heide, Friedhelm Meyer auf der; Schindelhauer, Christian

doi:10.1007/11821069_29

Cited by 20 publications

(13 citation statements)

References 17 publications

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“…We look at the case of larger groups of agents, for which D is the dominant factor in this lower bound. This complements previous research on the topic for trees [6,8] and grids [17], which usually focused on the case of small groups of agents (when n/k is dominant).…”

Section: Introductionsupporting

confidence: 68%

“…In [13] authors show that the competitive ratio of the strategy presented in [8] is precisely k/ log k. Another DFS-based algorithm, given in [2], has an exploration time of O(n/k+D k−1 ) time steps, which provides an improvement only for graphs of small diameter and small teams of agents, k = O(log D n). For a special subclass of trees called sparse trees, [6] introduces online strategies with a competitive ratio of O(D 1−1/p ), where p is the density of the tree as defined in that work. The best currently known lower bound is much lower: in [7], it is shown that any deterministic exploration strategy with k < √ n has a competitive ratio of Ω(log k/ log log k), even in the global communication model.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Fast collaborative graph exploration

Dereniowski

Disser

Kosowski

et al. 2015

Information and Computation

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We study the following scenario of online graph exploration. A team of k agents is initially located at a distinguished vertex r of an undirected graph. At every time step, each agent can traverse an edge of the graph. All vertices have unique identifiers, and upon entering a vertex, an agent obtains the list of identifiers of all its neighbors. We ask how many time steps are required to complete exploration, i.e., to make sure that every vertex has been visited by some agent.We consider two communication models: one in which all agents have global knowledge of the state of the exploration, and one in which agents may only exchange information when simultaneously located at the same vertex. As our main result, we provide the first strategy which performs exploration of a graph with n vertices at a distance of at most D from r in time O(D), using a team of agents of polynomial size k = Dn 1+ < n 2+ , for any > 0. Our strategy works in the local communication model, without knowledge of global parameters such as n or D.We also obtain almost-tight bounds on the asymptotic relation between exploration time and team size, for large k.

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Section: Introductionsupporting

confidence: 68%

Section: Related Workmentioning

confidence: 99%

Fast collaborative graph exploration

Dereniowski

Disser

Kosowski

et al. 2015

Information and Computation

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“…For a given graph with n nodes, n robot collaborative exploration [12,19,13,5,6,20,11] asks that these robots coordinate amongst each other and collectively visit every node of the graph at least once. Notice that any solution to dispersion immediately applies to n robot collaborative exploration for the same assumptions and model parameters.…”

Section: Background and Motivationmentioning

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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“…In particular, on trees the problem of exploring all vertices is equivalent to exploring all edges. Apart from the aforementioned previous work on our problem in planar graphs [23] and cycles [2,25], it has been studied on un-weighted trees also for multiple synchronously moving searchers [13,14,17].…”

Section: Introductionmentioning

confidence: 99%

Online Graph Exploration: New Results on Old and New Algorithms

Megow¹,

Mehlhorn²,

Schweitzer³

2011

Automata, Languages and Programming

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Abstract. We study the problem of exploring an unknown undirected connected graph. Beginning in some start vertex, a searcher must visit each node of the graph by traversing edges. Upon visiting a vertex for the first time, the searcher learns all incident edges and their respective traversal costs. The goal is to find a tour of minimum total cost. Kalyanasundaram and Pruhs [23] proposed a sophisticated generalization of a Depth First Search that is 16-competitive on planar graphs. While the algorithm is feasible on arbitrary graphs, the question whether it has constant competitive ratio in general has remained open. Our main result is an involved lower bound construction that answers this question negatively. On the positive side, we prove that the algorithm has constant competitive ratio on any class of graphs with bounded genus. Furthermore, we provide a constant competitive algorithm for general graphs with a bounded number of distinct weights.

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Smart Robot Teams Exploring Sparse Trees

Cited by 20 publications

References 17 publications

Fast collaborative graph exploration

Fast collaborative graph exploration

Deterministic Dispersion of Mobile Robots in Dynamic Rings

Online Graph Exploration: New Results on Old and New Algorithms

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