Optimal Nearest Neighbor Queries in Sensor Networks

Sharma, Gokarna; Busch, Costas

doi:10.1007/978-3-642-45346-5_19

Cited by 5 publications

(4 citation statements)

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“…This competitive ratio of O(log 2 n · log D) obtained above in general networks becomes O(log 3 n) when D < n O (1) . Nevertheless, from a fine-tuned analysis similar to the one given in Section 4.2.2, we can prove that the update competitive ratio in general networks is indeed O(log 3 n) even when D > n O (1) .…”

Section: Extensions To General Networkmentioning

confidence: 83%

“…For the constant-doubling networks where D < n O (1) , the competitive ratio given in Lemma 4.7 is already small. We now argue that the competitive ratio of O(log n) holds even when D > n O (1) .…”

Section: O(log N) Analysismentioning

confidence: 93%

“…Nevertheless, from a fine-tuned analysis similar to the one given in Section 4.2.2, we can prove that the update competitive ratio in general networks is indeed O(log 3 n) even when D > n O (1) . Therefore, combining these two different competitive ratio results, we obtain that the update competitive ratio of Algorithm 1 is O(min{log 3 n, log 2 n · log D}) in general networks.…”

Section: Extensions To General Networkmentioning

confidence: 95%

“…We now argue that the competitive ratio of O(log n) holds even when D > n O (1) . This analysis is more involved in the sense that we need to separate the operations into ranges according to the distance between the source and destination proxies.…”

Section: O(log N) Analysismentioning

confidence: 97%

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Optimal nearest neighbor queries in sensor networks

Sharma

Busch

2015

Theoretical Computer Science

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Given a set of m mobile objects in a sensor network, we consider the problem of finding the nearest object among them from any node in the network at any time. These mobile objects are tracked by nearby sensors called proxy nodes. This problem requires an object tracking mechanism which typically relies on two basic operations: query and update. A query is invoked by a node each time when there is a need to find the closest object from it in the network. Updates of an object's location are initiated when the object moves from one location (proxy node) to another. We present a scalable distributed algorithm for tracking these mobile objects such that both the query cost and the update cost are small. The main idea in our algorithm is to maintain a virtual tree of downward paths pointing to the objects. Our algorithm guarantees an asymptotically optimal O(1) approximation for query cost and an O(min{log n, log D}) approximation for update cost in the constantdoubling graph model, where n and D, respectively, are the number of nodes and the diameter of the network. We also give polylogarithmic approximations for both query and update cost in the general graph model. Our algorithm requires only polylogarithmic bits of memory per node. To the best of our knowledge, this is the first algorithm that is asymptotically optimal in handling nearest neighbor queries with low update cost in a distributed setting.

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Section: Extensions To General Networkmentioning

confidence: 83%

Section: O(log N) Analysismentioning

confidence: 93%

Section: Extensions To General Networkmentioning

confidence: 95%

Section: O(log N) Analysismentioning

confidence: 97%

See 2 more Smart Citations