Graph Exploration by a Finite Automaton

Fraigniaud, Pierre; Ilcinkas, David; Peer, Guy; Pełc, Andrzej; Peleg, David

doi:10.1007/978-3-540-28629-5_34

Cited by 54 publications

(63 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [12,13,4,14,15,16,17], the explored graph is undirected and the agent can traverse edges in both directions. Also, two alternative e ciency measures are adopted in most papers devoted to graph exploration, namely, the time of completing the task [7,12,8,9,13,10,14], or the number of memory bits (states in the automaton) available to the agent.…”

Section: Related Workmentioning

confidence: 99%

More Efficient Periodic Traversal in Anonymous Undirected Graphs

Czyzowicz

Dobrev

Gąsieniec

et al. 2010

Structural Information and Communication Complexity

Self Cite

View full text Add to dashboard Cite

Abstract. We consider the problem of periodic graph exploration in which a mobile entity with (at most) constant memory, an agent, has to visit all n nodes of an arbitrary undirected graph G in a periodic manner. Graphs are supposed to be anonymous, that is, nodes are unlabeled. However, while visiting a node, the robot has to distinguish between edges incident to it. For each node v the endpoints of the edges incident to v are uniquely identi ed by di erent integer labels called port numbers. We are interested in the minimisation of the length of the exploration period. This problem is unsolvable if the local port numbers are set arbitrarily, see [1]. However, surprisingly small periods can be achieved when assigning carefully the local port numbers. Dobrev et al. [2] described an algorithm for assigning port numbers, and an oblivious agent (i.e., an agent with no persistent memory) using it, such that the agent explores all graphs of size n within period 10n. Providing the agent with a constant number of memory bits, the optimal length of the period was proved in [3] to be no more than 3.75n (using a di erent assignment of the port numbers). In this paper, we improve both these bounds. More precisely, we show a period of length at most 4 1 3 n for oblivious agents, and a period of length at most 3.5n for agents with constant memory. Finally, we give the rst non-trivial lower bound, 2.8n, on the period length for the oblivious case.

show abstract

Section: Related Workmentioning

confidence: 99%

More Efficient Periodic Traversal in Anonymous Undirected Graphs

Czyzowicz

Dobrev

Gąsieniec

et al. 2010

Structural Information and Communication Complexity

Self Cite

View full text Add to dashboard Cite

show abstract

“…They concern the total duration needed to complete a visit of the nodes (e.g. [6,11,13]), or the size of the memory of the robot necessary to explore a graph (e.g., it is proved in [8] that a robot needs O(D log d) bits of local memory in order to explore any graph of diameter D and maximum degree d). Impossibility results for one or more robots with bounded memory (computationally speaking, a robot is then a finite state automaton) to explore all graphs have been stated in [5,15].…”

Section: On the Solvability Of Anonymous Partial Grids Exploration Bymentioning

confidence: 99%

“…Some papers focus on the exploration of the graph by a single robot (e.g., [1,2,8]). Cooperative graph exploration by a team of mobile robots has also received attention (e.g., [4,7,12]).…”

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%

“…Try deterministically all possible moves composed of k cs-moves memorizing all the states; ( 4) if (the graph can be entirely deduced) ( 5) then Compute the parameters p and q of the graph; ( 6) Compute kmax ( 7) end if; ( 8) k ← k + 1 ( 9) end while Sequences composed of two cs-moves. During these sequences, A does not increase its knowledge of the map.…”

Section: Every Robot Learns the Map Of The Gridmentioning

confidence: 99%

See 2 more Smart Citations

On the Solvability of Anonymous Partial Grids Exploration by Mobile Robots

Baldoni

Bonnet

Milani

et al. 2008

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Cooperating Mobile Agents

Ghosh

Dasgupta

2012

Mobile Agents in Networking and Distributed Computing

View full text Add to dashboard Cite

This article discusses four different applications where mobile agents cooperate with one another to accomplish a task in a network of processes. These applications range from topology discovery and distributed data structure implementation to fault diagnosis and system stabilization. IntroductionA mobile agent is a piece of code that migrates from one machine to another. The code (often called the script), which is an executable program, executes at the host machine where it lands. In addition to the code, agents carry data values or procedure arguments or results that need to be transported across machines. Compared to messages that are passive, agents are active, and can be viewed as messengers.Mobile agents are convenient tools in distributed systems, both at the applications layer and as well as at the middleware level. The promise of mobile agents in bandwidth conservation or disconnected modes of operation is now well accepted. Deploying multiple mobile agents cooperating with one another can add a new dimension to distributed applications. While parallelism is the obvious advantage, the issues of load balancing, agent rendezvous, and fault tolerance play major roles. Among numerous possible applications, we highlight the following four problems, each with a different flavor of cooperation.Mapping of an unknown network. Network mapping is also known as the topology discovery problem. Making such a discovery using a single mobile agent is equivalent to developing an efficient algorithm for graph traversal. With multiple agents, the challenge is to develop an efficient cooperation mechanism so that the discovery is complete in the fewest number of hops and redundant traversals are avoided.Concurrent reading and writing. A distributed data structure has different components mapped to host machines at different geographic locations. As multiple agents concurrently access such a distributed data structure, the reading agent the writing agent need to be properly synchronize their operations so that the semantics of data sharing are preserved. Black hole search.A black hole is a node that can potentially capture a visiting agent and thus, disrupt an application. Although it implies a malicious intent on the part of the host, a black hole can be as simple as a crashed node. If black holes can be located, then traversal paths can be rerouted without incurring further loss of mobile agents.Stabilization. Transient failures occasionally corrupt the global state of a distributed system, and stabilization is an important technique for restoring normal operation. To stabilize a network, a mobile agent patrols the network, and plays the role of traveling repairperson. Multiple agents can expedite the process of stabilization, but in doing so, some synchronization issues need to be resolved. We will address how multiple agents can be deployed for maximum speedup of a stabilizing application.This article has seven sections. Section 2 describes the model and the notations. Sections 3 through 6 address the four problems high...

show abstract

Graph Exploration by a Finite Automaton

Cited by 54 publications

References 21 publications

More Efficient Periodic Traversal in Anonymous Undirected Graphs

More Efficient Periodic Traversal in Anonymous Undirected Graphs

On the Solvability of Anonymous Partial Grids Exploration by Mobile Robots

Cooperating Mobile Agents

Contact Info

Product

Resources

About