On the Bounded-Hop Range Assignment Problem

Carmi, Paz; Chaitman-Yerushalmi, Lilach; Trabelsi, Ohad

doi:10.1007/978-3-319-21840-3_12

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…We refer to a spanning trees satisfying this condition as a k-hop spanning tree. This problem has applications in network design [7,8,9], distributed system design [15], and wireless networks [11].…”

Section: Introductionmentioning

confidence: 99%

A PTAS for $k$-hop MST on the Euclidean plane: Improving Dependency on $k$

Fakcharoenphol¹,

Wongwattanakij²

2021

Preprint

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For any> 0, Laue and Matijević [CCCG'07, IPL'08] give a PTAS for finding a (1 + )approximate solution to the k-hop MST problem in the Euclidean plane that runs in time (n/ ) O(k/ ) . In this paper, we present an algorithm that runs in time (n/ ) O(log k•(1/ ) 2 •log 2 (1/ )) . This gives an improvement on the dependency on k on the exponent, while having a worse dependency on . As in Laue and Matijević, we follow the framework introduced by Arora for Euclidean TSP. Our key ingredients include exponential distance scaling and compression of dynamic programming state tables.

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Section: Introductionmentioning

confidence: 99%

A PTAS for $k$-hop MST on the Euclidean plane: Improving Dependency on $k$

Fakcharoenphol¹,

Wongwattanakij²

2021

Preprint

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“…The bi-criteria approximation algorithm for the general case (not necessarily Euclidian) with guaranteed upper bounds has been proposed in [15]. The authors of [16] propose improved constant factor approximation for the planar Euclidian case of the problem.…”

Section: Introductionmentioning

confidence: 99%

Constructive Heuristics for Min-Power Bounded-Hops Symmetric Connectivity Problem

Plotnikov

Erzin

2019

Mathematical Optimization Theory and Operations Research

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We consider a Min-Power Bounded-Hops Symmetric Connectivity problem that consists in the construction of communication spanning tree on a given graph, where the total energy consumption spent for the data transmission is minimized and the maximum number of hops between two nodes is bounded by some predefined constant. We focus on the planar Euclidian case of this problem where the nodes are placed at the random uniformly spread points on a square and the power cost necessary for the communication between two network elements is proportional to the squared distance between them. Since this is an NP-hard problem, we propose different polynomial heuristic algorithms for the approximation solution to this problem. We perform a posteriori comparative analysis of the proposed algorithms and present the obtained results in this paper.Due to the prevalence of wireless sensor networks (WSNs) in human life, the different optimization problems aimed to increase their efficiency remain actual. Since usually WSN consists of elements with the non-renewable power supply with restricted capacity, one of the most important issues related to the design of WSN is prolongation its lifetime by minimizing energy consumption of its elements per time unit. A significant part of sensor energy is spent on the communication with other network elements. Therefore, the modern sensors often have an ability to adjust their transmission ranges changing the transmitter power. Herewith, usually, the energy consumption of a network's element is assumed to be proportional to d s , where s ≥ 2 and d is the transmission range [1].The problem of search of the optimal power assignment in WSN is wellstudied. The most general Range Assignment Problem, where the goal is to ⋆ The research is supported by the Russian Science Foundation (project 18-71-00084).

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“…The bi-criteria approximation algorithm for the general case (not necessarily Euclidian) with guaranteed upper bounds has been proposed in [15]. The authors of [16] propose an improved constant factor approximation for the planar Euclidian case of the problem.…”

mentioning

confidence: 99%

Metaheuristics for Min-Power Bounded-Hops Symmetric Connectivity Problem

Plotnikov

Erzin

2020

Lecture Notes in Computer Science

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The article is submitted to the special session: Synergy of machine learning, combinatorial optimization, and computational geometry: problems, algorithms, bounds, and applications.Abstract. We consider a Min-Power Bounded-Hops Symmetric Connectivity problem that consists of the construction of communication spanning tree on a given graph, where the total energy consumption spent for the data transmission is minimized and the maximum number of edges between two nodes is bounded by some predefined constant. We focus on the planar Euclidian case of this problem where the nodes are placed at the random uniformly spread points on a square and the power cost necessary for the communication between two network elements is proportional to the squared distance between them. Since this is an NP-hard problem, we propose different heuristics based on the following metaheuristics: genetic local search, variable neighborhood search, and ant colony optimization. We perform a posteriori comparative analysis of the proposed algorithms and present the obtained results in this paper.

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On the Bounded-Hop Range Assignment Problem

Cited by 4 publications

References 15 publications

A PTAS for $k$-hop MST on the Euclidean plane: Improving Dependency on $k$

A PTAS for $k$-hop MST on the Euclidean plane: Improving Dependency on $k$

Constructive Heuristics for Min-Power Bounded-Hops Symmetric Connectivity Problem

Metaheuristics for Min-Power Bounded-Hops Symmetric Connectivity Problem

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