An average case analysis of the minimum spanning tree heuristic for the power assignment problem

Maurits  de Graaf; Richard Boucherie; Johann L. Hurink; Jan C.W. van Ommeren

doi:10.1002/rsa.20831

An average case analysis of the minimum spanning tree heuristic for the power assignment problem

Maurits de Graaf (Corresponding Author), Richard Boucherie, Johann L. Hurink, Jan C.W. van Ommeren

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Abstract

We present an average case analysis of the minimum spanning tree heuristic for the power assignment problem. The worst-case approximation ratio of this heuristic is 2.We show that in Euclidean d-dimensional space, when the vertex set consists of a set of i.i.d. uniform random independent, identically distributed random variables in [0,1]d , and the distance power gradient equals the dimension d, the minimum spanning tree-based power assignment converges completely to a constant depending only on d.

Original language	English
Article number	RSA20831
Pages (from-to)	89-103
Number of pages	15
Journal	Random Structures and Algorithms
Volume	55
Issue number	1
Early online date	6 Dec 2018
DOIs	https://doi.org/10.1002/rsa.20831
Publication status	Published - Aug 2019

Keywords

UT-Hybrid-D
Analysis of algorithms
Approximation algorithms
Average case analysis
Point processes
Power assignment
Range assignment
Ad-hoc networks

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10.1002/rsa.20831Licence: CC BY-NC-ND

Graaf2018averageFinal published version, 390 KBLicence: CC BY-NC-ND

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title = "An average case analysis of the minimum spanning tree heuristic for the power assignment problem",

abstract = "We present an average case analysis of the minimum spanning tree heuristic for the power assignment problem. The worst-case approximation ratio of this heuristic is 2.We show that in Euclidean d-dimensional space, when the vertex set consists of a set of i.i.d. uniform random independent, identically distributed random variables in [0,1]d , and the distance power gradient equals the dimension d, the minimum spanning tree-based power assignment converges completely to a constant depending only on d.",

keywords = "UT-Hybrid-D, Analysis of algorithms, Approximation algorithms, Average case analysis, Point processes, Power assignment, Range assignment, Ad-hoc networks",

author = "{de Graaf}, Maurits and Richard Boucherie and Hurink, {Johann L.} and {van Ommeren}, {Jan C.W.}",

note = "Wiley deal This research was supported by the Nederlands Organisation for Scientific Research (N.W.O.).",

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AU - de Graaf, Maurits

AU - Boucherie, Richard

AU - Hurink, Johann L.

AU - van Ommeren, Jan C.W.

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N2 - We present an average case analysis of the minimum spanning tree heuristic for the power assignment problem. The worst-case approximation ratio of this heuristic is 2.We show that in Euclidean d-dimensional space, when the vertex set consists of a set of i.i.d. uniform random independent, identically distributed random variables in [0,1]d , and the distance power gradient equals the dimension d, the minimum spanning tree-based power assignment converges completely to a constant depending only on d.

AB - We present an average case analysis of the minimum spanning tree heuristic for the power assignment problem. The worst-case approximation ratio of this heuristic is 2.We show that in Euclidean d-dimensional space, when the vertex set consists of a set of i.i.d. uniform random independent, identically distributed random variables in [0,1]d , and the distance power gradient equals the dimension d, the minimum spanning tree-based power assignment converges completely to a constant depending only on d.

KW - UT-Hybrid-D

KW - Analysis of algorithms

KW - Approximation algorithms

KW - Average case analysis

KW - Point processes

KW - Power assignment

KW - Range assignment

KW - Ad-hoc networks

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SN - 1042-9832

IS - 1

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ER -

An average case analysis of the minimum spanning tree heuristic for the power assignment problem

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