Time-Optimal Proximity Graph Computations on Enhanced Meshes

Olariu, Stephan; Zomaya, Albert Y.

doi:10.1006/jpdc.1997.1421

Cited by 3 publications

(3 citation statements)

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“…It can be stated as follows: given a set S of n planar points, determine, for every point in S, a point that is closest to it. In [12], Olariu and Stojmenovic proposed a time-optimal algorithm to solve the ANN problem.…”

Section: The Model Of Computationmentioning

confidence: 99%

“…To find the closest pair among n bases stations, we will use the ANN algorithm presented by Olariu and Stojmenovic [12] as described in Proposition 2.4. It takes O(logn) time on a mesh with broadcasting of size n x n. Once the closest neighbor for each point is found, it takes another O(logn) time to find the closest pair among those n points by Proposition 2.1.…”

Section: Parallel Algorithm and Its Complexitymentioning

confidence: 99%

“…Because two base stations must keep at least |S| apart, there are a constant number of base stations that are within a distance of 2 |S| from each base station. To find all pairs of base stations at distance less than 2 |S|, we can adopt the algorithm for finding all nearest neighbors presented in [12]. During merging, instead of keeping a list of candidate nearest points for each point, we keep the base stations that are within a distance of 2 |S| from each base station.…”

Section: Parallel Algorithm and Its Complexitymentioning

confidence: 99%

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Time-optimal parallel algorithms for constructing optimal virtual cellular networks

Zhang

Vrbsky

Fan

Ninth International Conference on Parallel and Distributed Systems, 2002. Proceedings.

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In a cellular network, the base stations are not necessarily uniformly distributed, and their corresponding cell sizes are not necessarily the same. For example, a cell in a well-populated city cell is usually smaller than a cell in a rural area. To study a cellular network with non-uniform cell sizes, one approach is to use a virtual cellular network with a uniform cell size such that each virtual cell contains at most one base station. This paper has proposed parallel algorithms for meshes with multiple broadcasting to construct virtual mesh and honeycomb cellular networks for non-uniformly distributed base stations. The constructed virtual cellular networks are optimal in the sense that their corresponding uniform cell sizes reach the largest possible. The algorithms run in O(logn) time on a mesh with multiple broadcasting of size nxn to construct optimal virtual mesh and honeycomb cellular networks for n non-uniformly distributed base stations. Furthermore, those algorithms are time-optimal.

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Section: The Model Of Computationmentioning

confidence: 99%

Section: Parallel Algorithm and Its Complexitymentioning

confidence: 99%

Section: Parallel Algorithm and Its Complexitymentioning

confidence: 99%

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