Tree exploration with little memory

Diks, Krzysztof; Fraigniaud, Pierre; Kranakis, Evangelos; Pełc, Andrzej

doi:10.1016/j.jalgor.2003.10.002

Cited by 115 publications

(104 citation statements)

References 15 publications

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“…An exception is when the graph is acyclic, meaning the graph is a tree [14,30]. Different models for marking the nodes have been used to solve the exploration problem.…”

Section: Backgrounds and Related Workmentioning

confidence: 99%

A Review of Computation Solutions by Mobile Agents in an Unsafe Environment

Zarrad¹,

Daadaa²

2013

IJACSA

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Abstract-Exploration in an unsafe environment is one of the major problems that can be seen as a basic block for many distributed mobile protocols. In such environment we consider that either the nodes (hosts) or the agents can pose some danger to the network. Two cases are considered. In the first case, the dangerous node is a called black hole, a node where incoming agents are trapped, and the problem is for the agents to locate it. In the second case, the dangerous agent is a virus; an agent moving between nodes infecting them, and the problem is for the "good" agents to capture it, and decontaminate the network.In this paper, we present several solutions for a black-hole and network decontamination problems. Then, we analyze their efficiency. Efficiency is evaluated based on the complexity, and the effort is in the minimization of the number of simultaneous decontaminating elements active in the system while performing the decontamination techniques.

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“…An exception is when the graph is acyclic, meaning the graph is a tree [14,30]. Different models for marking the nodes have been used to solve the exploration problem.…”

Section: Backgrounds and Related Workmentioning

confidence: 99%

A Review of Computation Solutions by Mobile Agents in an Unsafe Environment

Zarrad¹,

Daadaa²

2013

IJACSA

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“…In particular, a central question is to determine what minimal hypotheses allow a given problem P to be solved. Examples of this type of investigations are the studies on topology-reconstruction (e.g., see [3,4]), graph-exploration [6,16], wake-up [2,9], rendez-vous [1,19], etc.…”

Section: Related Workmentioning

confidence: 99%

Mobile Search for a Black Hole in an Anonymous Ring

et al. 2007

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In this paper we address the problem of mobile agents searching for a highly harmful item (called black hole) in a ring network. The black hole is a stationary process that destroys visiting agents upon their arrival without leaving any observable trace of such a destruction. The task is to have at least one surviving agent able to unambiguously report the location of the black hole.We consider different scenarios and in each situation we answer some computational as well as complexity questions. We first consider agents that start from the same homebase (co-located). We prove that two such agents are necessary and sufficient to locate the black hole; in our algorithm the agents perform O(nlogn) moves (where n is the size of the ring) and we show that such a bound is optimal. We also consider time complexity and we show how to achieve the optimal bound of 2n − 4 units of time using n − 1 agents. We generalize our technique to establish a trade-off between time and number of agents. We then consider the case of agents that start from different homebases (dispersed) and we show that, if the ring is oriented, two dispersed agents * A preliminary version of this paper appeared in the Proceedings of the 15th International Symposium on Distributed Computing [8].† University of Ottawa, email:sdobrev@site.uottawa.ca ‡ University of Ottawa, email:flocchin@site.uottawa.ca § contact author: Università di Pisa, Dipartimento di Informatica, Via Buonarroti, 2 -56100, Pisa, tel.+39 050 2213148, fax. +39 050 2212726, email:prencipe@di.unipi.it ¶ Carleton University, email: santoro@scs.carleton.ca 1 are still necessary and sufficient. Also in this case our algorithm is optimal in terms of number of moves (Θ(nlogn)). We finally show that, if the ring is unoriented, three agents are necessary and sufficient; an optimal algorithm follows from the oriented case.

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“…The investigations on exploration with multiple agents are a generalization of the extensive earlier work on exploration by a single agent (e.g., [1,5,9,15,17,19,28,38,41,47]); they focus on different aspects of the problem, each result giving us some knowledge on the impact that factors such as memory size, computation capabilities, and a priori knowledge have on the solvability and complexity of the problem. For example, the earlier investigations, by Blum and Kozen [12] and Kozen [35], considered a team of agents that were finite-automata.…”

Section: Related Workmentioning

confidence: 99%

Searching for a black hole in arbitrary networks: optimal mobile agents protocols

et al. 2006

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Consider a networked environment, supporting mobile agents, where there is a black hole: a harmful host that disposes of visiting agents upon their arrival, leaving no observable trace of such a destruction. The black hole search problem is the one of assembling a team of asynchronous mobile agents, executing the same protocol and communicating by means of whiteboards, to successfully identify the location of the black hole; we are concerned with solutions that are generic (i.e., topology-independent). We establish tight bounds on the size of the team (i.e., the number of agents), and the cost (i.e., the number of moves) of a size-optimal solution protocol. These bounds depend on the a priori knowledge the agents have about the network, and on the consistency of the local labellings. In particular, we prove that: with topological ignorance ∆ + 1 agents are needed and suffice, and the cost is Θ(n 2 ), where ∆ is the maximal degree of a node and n is the number of nodes in the network; with topological ignorance but in presence of sense of direction only two agents suffice and the cost is Θ(n 2 ); and with complete topological knowledge only two agents suffice and the cost is Θ(n log n). All the upper-bound proofs are constructive.

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Tree exploration with little memory

Cited by 115 publications

References 15 publications

A Review of Computation Solutions by Mobile Agents in an Unsafe Environment

A Review of Computation Solutions by Mobile Agents in an Unsafe Environment

Mobile Search for a Black Hole in an Anonymous Ring

Searching for a black hole in arbitrary networks: optimal mobile agents protocols

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