## Optimizing Wireless Networks for Heterogeneous Spatial Loads

Citations: | 1 - 0 self |

### BibTeX

@MISC{Rengarajan_optimizingwireless,

author = {Balaji Rengarajan and Gustavo De Veciana},

title = {Optimizing Wireless Networks for Heterogeneous Spatial Loads},

year = {}

}

### OpenURL

### Abstract

Abstract—Large-scale wireless networks must be designed such that there are no gaps in coverage. It is also desirable to minimize the number of access points used in order to minimize the cost of equipment, installation and maintenance. In this paper, we propose a grid-based approximation algorithm to compute the placement of access points. The algorithm minimizes the number of access points required while ensuring that the received SNR at each location is sufficient to meet the offered load at that location. The algorithm can be used when the offered load is spatially non-homogenous or when access points can be operated in different modes. The proposed algorithm is guaranteed to find a solution with at most O(copt log copt) access points, if there exists a solution to the access point placement problem using copt access points. Index Terms—wireless networks, network optimization, network provisioning, minimum set cover I.

### Citations

949 |
On the uniform convergence of relative frequencies of events to their probabilities. Theory Probab
- Vapnik, Chervonenkis
- 1971
(Show Context)
Citation Context ...d by R on Y , denoted by R |Y . We say Y is shattered by R if |R |Y | = 2 Y . (X, R) is said to have VCdimension d, if d is the smallest integer such that no d + 1 point subset Y ⊆ X can be shattered =-=[11]-=-. If a subset N ⊆ X has a non-empty intersection with each set R ∈ R of size greater than ǫ|X|, it is called an ǫ-net [12]. This definition can be generalized by putting an additive weight function w ... |

259 | Epsilon-nets and simplex range queries
- Haussler, Welzl
- 1986
(Show Context)
Citation Context ...s the smallest integer such that no d + 1 point subset Y ⊆ X can be shattered [11]. If a subset N ⊆ X has a non-empty intersection with each set R ∈ R of size greater than ǫ|X|, it is called an ǫ-net =-=[12]-=-. This definition can be generalized by putting an additive weight function w on the power set of X. The additive weight function is defined as follows. A positive weight, w(x) is associated with each... |

161 | Almost optimal set covers in finite VC-dimension
- Brönnimann, Goodrich
- 1995
(Show Context)
Citation Context ...d by an access point placed at l. V. RELEVANT DEFINITIONS We first review some basic definitions and results from computational geometry. We will use, for the most part, the terminology introduced in =-=[10]-=-. A set system (X, R) consists of a set X along with a collection R of subsets of X. R is called the range space. A set cover is a subcollection T ⊆ R such that ⋃ T ∈T T = X. The size of the cover is ... |

117 |
Wireless Communications: Principles and Practice. Upper Saddle
- Rappaport
- 1996
(Show Context)
Citation Context ... as to achieve coverage while minimizing the number of access points required. Similar to [3], we assume a CAD tool is available to model and/or simulate the environment’s propagation characteristics =-=[4]-=-. Another aspect that should be taken into consideration in the deployment of a wireless network is the characteristics of the spatial load that will be supported. Typically, it is assumed that the sp... |

107 | A deterministic view of random sampling and its use in geometry
- Chazelle, Friedman
- 1990
(Show Context)
Citation Context ...ble. TABLE II THE ALGORITHM provides a bound on the VC-dimension of the set system under consideration. Algorithms to find ǫ-nets for set systems of finite VCdimension are described in [12], [14] and =-=[15]-=-. It is proved in [12] that, for a set system of VC-dimension d, choosing a random sample of size O(dclog c) according to the distribution induced by the weights, results in an 1 c -net with high prob... |

48 |
WiSE design of indoor wireless systems: Practical computation and optimization
- Fortune, Gay, et al.
- 1995
(Show Context)
Citation Context ...n [1], [2]. In this paper, we present an approximation algorithm to automate the placement of access points so as to achieve coverage while minimizing the number of access points required. Similar to =-=[3]-=-, we assume a CAD tool is available to model and/or simulate the environment’s propagation characteristics [4]. Another aspect that should be taken into consideration in the deployment of a wireless n... |

46 | Product range spaces, sensitive sampling, and derandomization
- Brönnimann, Chazelle, et al.
- 1999
(Show Context)
Citation Context ... is possible. TABLE II THE ALGORITHM provides a bound on the VC-dimension of the set system under consideration. Algorithms to find ǫ-nets for set systems of finite VCdimension are described in [12], =-=[14]-=- and [15]. It is proved in [12] that, for a set system of VC-dimension d, choosing a random sample of size O(dclog c) according to the distribution induced by the weights, results in an 1 c -net with ... |

43 |
Large-Scale Wireless Lan Design
- Hills
- 2001
(Show Context)
Citation Context ... educated guess by the person installing the access points followed by manual site surveys to ensure adequate coverage. A description of a typical wireless LAN deployment process can be found in [1], =-=[2]-=-. In this paper, we present an approximation algorithm to automate the placement of access points so as to achieve coverage while minimizing the number of access points required. Similar to [3], we as... |

33 |
Optimal location of transmitters for microcellular radio communication system design
- Sherali, Pendyala, et al.
- 1996
(Show Context)
Citation Context ...mation algorithm based on simulated annealing. [6] and [7] propose two approximation algorithms based on genetic algorithms, while an algorithm based on the gradient descent technique is presented in =-=[8]-=-. The convergence properties of these algorithms depends strongly on the choice of the initial solution and the simulation parameters. Since a good initial solution and simulation parameters are not a... |

20 |
Coverage planning for outdoor wireless LAN systems,” presented at Int
- Kamenetsky, Unbehaun
- 2002
(Show Context)
Citation Context ...nverge at all. So, no bound can be provided on the number of iterations required to reach the final solution. Also, no bound is provided on how far the final solution is from the optimal solution. In =-=[9]-=-, a simple heuristic algorithm based on pruning and neighborhood search is proposed. The proposed algorithm, however, only finds a local optimum. To find a solution close to the global optimum, this s... |

18 | Optimizing microcell base station locations using simulated annealing techniques - Anderson, McGeehan - 1994 |

16 |
Radio coverage optimization with genetic algorithms
- Lieska, Laitinen, et al.
- 1998
(Show Context)
Citation Context ...wireless networks. III. BACKGROUND The problem of determining ’optimal’ access point locations is a hard one in general. Hence [5] presented an approx-imation algorithm based on simulated annealing. =-=[6]-=- and [7] propose two approximation algorithms based on genetic algorithms, while an algorithm based on the gradient descent technique is presented in [8]. The convergence properties of these algorithm... |

3 | Deployment Issues in Enterprise Wireless Lans
- Raniwala, Chiueh
- 2003
(Show Context)
Citation Context ...on an educated guess by the person installing the access points followed by manual site surveys to ensure adequate coverage. A description of a typical wireless LAN deployment process can be found in =-=[1]-=-, [2]. In this paper, we present an approximation algorithm to automate the placement of access points so as to achieve coverage while minimizing the number of access points required. Similar to [3], ... |

1 |
Optimizing indoor base station locations
- Nagy, Farkas, et al.
- 2000
(Show Context)
Citation Context ... networks. III. BACKGROUND The problem of determining ’optimal’ access point locations is a hard one in general. Hence [5] presented an approx-imation algorithm based on simulated annealing. [6] and =-=[7]-=- propose two approximation algorithms based on genetic algorithms, while an algorithm based on the gradient descent technique is presented in [8]. The convergence properties of these algorithms depend... |

1 |
Densité et dimension,” Ann. Institut Fourier
- Assouad
- 1983
(Show Context)
Citation Context ... |Y is at most n, thus if |Y | > log 2(n), Y cannot be shattered by R. Also, the VC-dimension of the dual set system (R,X ∗ ) is less than 2 d+1 , where d is the VC-dimension of the primal set system =-=[13]-=-. VII. THE ALGORITHM The algorithm is based on using an ǫ-net finder and a verifier. The net-finder and the verifier are discussed in detail in the sequel. The algorithm starts with a very low estimat... |