A General Lower Bound for Collaborative Tree Exploration

Disser, Yann; Mousset, Frank; Noever, Andreas; Škorić, Nemanja; Steger, Angelika

doi:10.1007/978-3-319-72050-0_8

Cited by 11 publications

(22 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are many results for this problem. Several works assume specific topologies such as trees [1], [10], [12], [14]. For general graphs, the results depend on the different system models and assumptions such as the following.…”

Section: Related Workmentioning

confidence: 99%

“…(lines 6, 7): if a robot is docked and the node has been visited before, robot i backtracks. [8][9][10][11][12][13][14]: if robot j is docked at the node but the node has not been visited before, robot i marks visited[j] as true and increments port entered in a modulo fashion (mod degree of node). If the new value of port entered equals its old value, i changes state to backtrack and moves through port entered; else the old value of port entered is pushed onto the stack and i moves through port entered to continue the forward exploration of the graph.…”

Section: Independent Dispersion In the Asynchronous Modelmentioning

confidence: 99%

See 1 more Smart Citation

Efficient dispersion of mobile robots on graphs

Kshemkalyani

Ali

2019

Proceedings of the 20th International Conference on Distributed Computing and Networking

View full text Add to dashboard Cite

The dispersion problem on graphs requires k robots placed arbitrarily at the n nodes of an anonymous graph, where k ≤ n, to coordinate with each other to reach a final configuration in which each robot is at a distinct node of the graph. The dispersion problem is important due to its relationship to graph exploration by mobile robots, scattering on a graph, and load balancing on a graph. In addition, an intrinsic application of dispersion has been shown to be the relocation of self-driven electric cars (robots) to recharge stations (nodes). We propose three efficient algorithms to solve dispersion on graphs. Our algorithms require O(k log ∆) bits at each robot, and O(m) steps running time, where m is the number of edges and ∆ is the degree of the graph. The algorithms differ in whether they address the synchronous or the asynchronous system model, and in what, where, and how data structures are maintained.

show abstract

Section: Related Workmentioning

confidence: 99%

Section: Independent Dispersion In the Asynchronous Modelmentioning

confidence: 99%

Efficient dispersion of mobile robots on graphs

Kshemkalyani

Ali

2019

Proceedings of the 20th International Conference on Distributed Computing and Networking

View full text Add to dashboard Cite

show abstract

“…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%

“…When k robots all start at a given node and coordinate to explore a graph, it is referred to as k robot collaborative graph exploration [12,19,13,5,6,20,11]. When k = n, any solution to dispersion also acts as a solution to k robot exploration under the same conditions.…”

Section: Related Workmentioning

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

View full text Add to dashboard Cite

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.

show abstract

“…As for the edge-exploration of general graphs (where apart from vertices also every edge has to be explored) see [3,11]. The competitive ratio of exploration arbitrary graphs for teams of size bigger than √ n was studied in [6,7]. As for different graph classes, grids [15] and rings [13] were investigated.…”

mentioning

confidence: 99%

Minimizing the Cost of Team Exploration

Osula

2019

SOFSEM 2019: Theory and Practice of Computer Science

View full text Add to dashboard Cite

A group of mobile agents is given a task to explore an edge-weighted graph G, i.e., every vertex of G has to be visited by at least one agent. There is no centralized unit to coordinate their actions, but they can freely communicate with each other. The goal is to construct a deterministic strategy which allows agents to complete their task optimally. In this paper we are interested in a cost-optimal strategy, where the cost is understood as the total distance traversed by agents coupled with the cost of invoking them. Two graph classes are analyzed, rings and trees, in the off-line and on-line setting, i.e., when a structure of a graph is known and not known to agents in advance. We present algorithms that compute the optimal solutions for a given ring and tree of order n, in O(n) time units. For rings in the on-line setting, we give the 2-competitive algorithm and prove the lower bound of 3/2 for the competitive ratio for any on-line strategy. For every strategy for trees in the on-line setting, we prove the competitive ratio to be no less than 2, which can be achieved by the DF S algorithm.

show abstract

A General Lower Bound for Collaborative Tree Exploration

Cited by 11 publications

References 31 publications

Efficient dispersion of mobile robots on graphs

Efficient dispersion of mobile robots on graphs

Deterministic Dispersion of Mobile Robots in Dynamic Rings

Minimizing the Cost of Team Exploration

Contact Info

Product

Resources

About