Space Lower Bounds for Graph Exploration via Reduced Automata

Fraigniaud, Pierre; Ilcinkas, David; Rajsbaum, Sergio; Tixeuil, Sébastien

doi:10.1007/11429647_13

Cited by 14 publications

(18 citation statements)

References 8 publications

(25 reference statements)

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“…As already indicated, graph exploration is the process by which each vertex of a graph is visited by some entity. A great research effort on graph exploration by robots has been on the minimal assumptions (in terms of robots/network requirements) required to explore a graph (e.g., [4,9]). Some works focus on robots endowed with a finite persistent storage and direct communication with other robots (e.g., [2]).…”

Section: Related Workmentioning

confidence: 99%

“…Graph exploration is mainly divided into perpetual graph exploration (e.g., [6]) where the robots have to travel the graph infinitely often, and graph exploration with stop (e.g., [9]) where each robot has to eventually stop after having explored the graph. Some papers focus on the exploration of the graph by a single robot (e.g., [1,2,8]).…”

Section: Related Workmentioning

confidence: 99%

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Anonymous graph exploration without collision by mobile robots

Baldoni

Bonnet

Milani

et al. 2008

Information Processing Letters

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Considering autonomous mobile robots moving on a finite anonymous graph, this paper focuses oil the Constrained Perpetual Graph Exploration problem (CPGE). That problem requires each robot to perpetually visit all the vertices of the graph, in such a way that no vertex hosts more than one robot at a time, and each edge is traversed by at most one robot at a time. The paper states an tipper bound k oil the number of robots that can be placed in the graph while keeping CPGE solvability. To make the impossibility result as strong as possible (no more than k robots can be initially placed in the graph), this upper bound is established under a strong assumption, namely, there is an omniscient daemon that is able to coordinate the robots movements at each round of the synchronous system. Interestingly, this upper bound is related to the topology of the graph. More precisely, the paper associates with each graph a labeled tree that captures the paths that have to be traversed by a single robot at a time (as if they were a simple edge). The length of the longest of these labeled paths reveals to be the key parameter to determine the upper bound k oil the number of robots. (C) 2008 Elsevier B.V. All rights reserved

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Anonymous graph exploration without collision by mobile robots

Baldoni

Bonnet

Milani

et al. 2008

Information Processing Letters

View full text Add to dashboard Cite

show abstract

“…A great research effort on graph exploration by robots has been done on the minimal assumptions (in terms of robots/network requirements) required to explore a graph (e.g., [4,9]). Some works focus on robots endowed with a finite persistent storage and direct communication with other robots (e.g., [2]).…”

Section: Related Workmentioning

confidence: 99%

“…On the type of graph exploration Graph exploration is mainly divided into perpetual graph exploration (e.g., [6]) where the robots have to travel the graph infinitely often, and graph exploration with stop (e.g., [9]) where each robot has to eventually stop after having explored the graph. Some papers focus on the exploration of the graph by a single robot (e.g., [1,2,8]).…”

Section: Related Workmentioning

confidence: 99%

“…To complete the proof an algorithm A that solves the CP GE problem when f (p, q) = p − q has to be designed. for x from 1 to number of robots do % move the robot x along the cycle C % ( 6) Determine the vertex v where the robot x currently is; ( 7) Compute the rank i of the first occurrence of v in the cycle C; ( 8) while (x has not reached the i − 1 vertex of C) do ( 9) Compute the next edge e of C that the robot x has to traverse; (10) if e belongs to a cycle (11) then Compute a canonical directed elementary cycle Ce that includes e; (12) All robots of Ce moves one step ahead on Ce; (13) else Move robots to obtain an empty vertex at the end of e; (14) Move the robot x along e (15) end if (16) end while (17) end for (18) end while Figure 6: An algorithm that f -solves the CP GE problem for ρ = ∞ An algorithm that f -solves the CP GE problem when ρ = ∞ The algorithm is described in Figure 6. Its underlying principles are the following ones.…”

Section: Theoremmentioning

confidence: 99%

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