Connected Treewidth and Connected Graph Searching

Fraigniaud, Pierre; Nisse, Nicolas

doi:10.1007/11682462_45

Cited by 34 publications

(36 citation statements)

References 12 publications

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“…A clean site becomes contaminated if at least one of its neighbors is contaminated. External decontamination has been studied in the context of intruder capture to design algorithms to neutralize a virus in a network, or in graph search (e.g., [3,31,25,6,4]). The main goal of decontamination in these settings is usually to design a strategy that employs the minimum possible size of the team of cleaning agents.…”

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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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 the problem of connected graph searching [1,2,11,12,18], the clear part must remain connected during all steps of the search strategy. This property is very useful as soon as we want to ensure secure communications between the searchers.…”

Section: Related Workmentioning

confidence: 99%

The cost of monotonicity in distributed graph searching

2009

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Blin et al. [5] (TCS 2008) proposed a distributed protocol enabling the smallest possible number of searchers to clear any unknown graph in a decentralized manner. However, the strategy that is actually performed lacks of an important property, namely the monotonicity. This paper deals with the smallest number of searchers that are necessary and sufficient to monotonously clear any unknown graph in a decentralized manner. The clearing of the graph is required to be connected, i.e., the clear part of the graph must remain permanently connected, and monotone, i.e., the clear part of the graph only grows. We prove that a distributed protocol clearing any unknown n-node graph in a monotone connected way, in a decentralized setting, can achieve but cannot beat competitive ratio of Θ ( n log n ), compared with the centralized minimum number of searchers. Moreover, our lower bound holds even in a synchronous setting, while our constructive upper bound holds even in an asynchronous setting.

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“…In particular, research has looked at variations of the decontamination problem in which the agents are allowed to "jump" from one node to any other node. The focus has often been on determining the minimum number of agents able to perform decontamination because this number is closely related to standard graph parameters such as pathwidth and treewidth (e.g., see [10,11,26,28,29]). …”

Section: The Problemmentioning

confidence: 99%

“…More precisely, it is known that csn(G)/sn(G) ≤ log n + 1 (see [11]), and, for a tree T , csn(T )/sn(T ) ≤ 2 (see [3]). Monotonicity also plays an important role in connected graph searches.…”

Section: Related Workmentioning

confidence: 99%

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Decontamination of hypercubes by mobile agents

2008

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In this paper we consider the decontamination problem in a hypercube network of size n. The nodes of the network are assumed to be contaminated and they have to be decontaminated by a sufficient number of agents. An agent is a mobile entity that asynchronously moves along the network links and decontaminates all the nodes it touches. A decontaminated node that is not occupied by an agent is re-contaminated if it has a contaminated neighbour.We consider some variations of the model based on the capabilities of mobile agents: locality, where the agents can only access local information; visibility, where they can "see" the state of their neighbours;and cloning, where they can create copies of themselves. We also consider synchronicity as an alternative system requirement.For each model, we design a decontamination strategy and we make several observations. For agents with locality, our strategy is based on the use of a coordinator that leads the other agents. Our strategy results in an optimal number of agents, Θ( n √ log n ), and requires O(n log n) moves and O(n log n) time steps. For agents with visibility, we assume that the agents can move autonomously. In this setting, our decontamination strategy achieves an optimal time complexity (log n time steps), but the number of agents increases to n 2 . Finally, we show that when the agents have the capability to clone combined with either visibility or synchronicity, we can reduce the move complexity-which becomes optimal-at the expense of an increase in the number of agents.

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Connected Treewidth and Connected Graph Searching

Cited by 34 publications

References 12 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

The cost of monotonicity in distributed graph searching

Decontamination of hypercubes by mobile agents

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