Bootstrapping a Hop-Optimal Network in the Weak Sensor Model

a b s t r a c tGossiping is a well-studied problem in Radio Networks. However, due to the strong resource limitations of sensor nodes, previous solutions are frequently not feasible in Sensor Networks. In this paper, we study the Gossiping problem in the restrictive context of Sensor Networks. We present a distributed algorithm that completes Gossiping with high probability in a Sensor Network of unknown topology and adversarial start-up. This algorithm exploits the geometry of sensor node distributions to achieve an optimal running time of Θ(D + ∆), where D is the diameter and ∆ the maximum degree of the network.Given that any algorithm for Gossiping also solves the Broadcast problem, this result shows that the classical Broadcast lower bound of Kushilevitz and Mansour does not hold if nodes are allowed to do preprocessing. The proposed algorithm requires that a linear number of messages be stored and transmitted per unit time. We also show an optimal distributed algorithm that solves the problem in linear time for the case where only a constant number of messages can be stored.

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“…We use a relaxed version of the Weak Sensor Model described in [27] including the following assumptions.…”

Section: Node Capabilities Modelmentioning

confidence: 99%

Optimal memory-aware Sensor Network Gossiping (or how to break the Broadcast lower bound)

Farach-Colton

Anta

Mosteiro

2013

Theoretical Computer Science

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“…In view of its practical importance, it is not surprising that there has recently been a lot of effort in designing efficient algorithms for setting up initial structures, i.e., [4,8,13,18,19,30]. The unstructured radio network model was first proposed in [14] and subsequently improved and generalized in [13].…”

Section: Related Workmentioning

confidence: 99%

“…The paper [21] goes one step further by giving an algorithm for computing a maximal independent set in the unstructured radio network model in time O(log 2 n). Finally, the authors of [4] present an algorithm that, based on [21], computes a constant degree subgraph with low stretch.…”

Section: Related Workmentioning

confidence: 99%

“…As in our work, the algorithms in [2] are capable of coping with asynchronous wake-up they assume that nodes are given an upper bound on the number of nodes and the maximum degree in the network. When appropriately restricting the techniques developed in [2] to the one-hop coloring scenario, their randomized algorithm achieves an O(∆)-coloring in time O(∆ 3 log n), whereas the algorithm in this paper requires time O(κ 4 2 ∆ log n). Notice that κ 2 is typically a small constant; particularly in dense networks, it is significantly smaller than ∆.…”

Section: Related Workmentioning

confidence: 99%

“…Furthermore, with probability at least 1 − 4n −1 every node irrevocably decides on its color O(κ 4 2 ∆ log n) time slots after its wake-up.…”

Section: Theoremmentioning

confidence: 99%

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Coloring unstructured radio networks

Moscibroda

Wattenhofer

2008

Distrib. Comput.

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During and immediately after their deployment, ad hoc and sensor networks lack an efficient communication scheme rendering even the most basic network coordination problems difficult. Before any reasonable communication can take place, nodes must come up with an initial structure that can serve as a foundation for more sophisticated algorithms. In this paper, we consider the problem of obtaining a vertex coloring as such an initial structure. We propose an algorithm that works in the unstructured radio network model. This model captures the characteristics of newly deployed ad hoc and sensor networks, i.e. asynchronous wake-up, no collision-detection, and scarce knowledge about the network topology. When modeling the network as a graph with bounded independence, our algorithm produces a correct coloring with O(∆) colors in time O(∆ log n) with high probability, where n and ∆ are the number of nodes in the network and the maximum degree, respectively. Also, the number of locally used colors depends only on the local node density. Graphs with bounded independence generalize unit disk graphs as well as many other well-known models for A preliminary version of this work has been published in [20] as Coloring Unstructured Radio Networks, In

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