R. Mathar and T. Niessen, "Optimum positioning of base stations for cellular radio networks," Wireless Networks, vol. 6, no. 6, pp. 421--428, 2000.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and with respect to power range assignment (see [3] However, the problem of positioning base stations in an optimal way has not been considered in depth from a complexitytheoretic point of view. While simulation and planning tools (see [16] and solutions based on linear programming (see, e.g. [12]) are known, not much has been proven about (non )solvability and (non )approximability of arising combinatorial problems. In [4] optimum non approximability results for planning problems for telecommunication networks, where antennas are placed in balloons at a certain height, were given. In ....

R. Mathar and T. Niessen. Optimum positioning of base stations for cellular radio networks. In Wireless Networks, 1999.

....simulation and planning tools [TLT97] but also to have precise results about (non ) solvability and (non ) approximability of combinatorial problems that arise in this model. In the present paper we consider the following optimization problems: Maximize number of totally supplied nodes (MTSN) MN99] Given is a set N of demand nodes (DN) a set B of potential locations for base stations (BS) Part of this work has been supported by NORTEL External Research. 1 a budget k 2 N (i.e. a maximum of k base stations is allowed to be built) and an interference factor 2 Q with 1. ....

....GSM systems as well as in the IS 95 system or in future UMTS networks that rely on the CDMA technology. It is known that the above problems are (as decision problems) NP complete. We rst show that their optimization versions are even hard to approximate (improving a result for MTSN given in [MN99] Our hardness result builds on the recent characterization of the class NP by so called probabilistically checkable proofs (PCP) leading to strong non approximability theorems for the CLIQUE problem (see [AL97] We show how CLIQUE reduces to our problems in such a way that the approximation ....

[Article contains additional citation context not shown here]

R. Mathar and T. Niessen. Optimum positioning of base stations for cellular radio networks. In Wireless Networks, 1999.

....to strong non approximability theorems for the CLIQUE problem (see [2] We show how CLIQUE reduces to our problems in such a way that the approximation ratio is preserved. This shows that to compute approximate solutions for MTSN and MBS is infeasible. Our result improves a hardness result from [9], where, using a reduction from the dominating set problem, only a weaker non approximability statement was given. In order to be able to construct efficient algorithms for practical applications, we have to restrict the model in an appropriate way. In this paper, we consider the Euclidean ....

MATHAR, R., AND NIESSEN, T. Optimum positioning of base stations for cellular radio networks. In Wireless Networks (1999).

....is the maximal cost of the CLIQUEinstance G. In addition we obtain: Cost CLIQUE (G; g(f(G) B) Cost MTSN (f(G) B) 2 The class ZPP is de ned as ZPP df =R coR. Thus P is a subclass of ZPP. Furthermore ZPP is considered as a complexity class near to P. 3 There is a similar result in [MN98] The author received that paper during the completion of this article. In [MN98] the problem MDS (minimum dominating set) is reduced to MBS. 12 Therefore, the following holds: Cost CLIQUE (G; B 0 ) Cost MTSN (f(G) B) b h(jf(G)j) b h(jGj) The last equality follows from the ....

....(G; g(f(G) B) Cost MTSN (f(G) B) 2 The class ZPP is de ned as ZPP df =R coR. Thus P is a subclass of ZPP. Furthermore ZPP is considered as a complexity class near to P. 3 There is a similar result in [MN98] The author received that paper during the completion of this article. In [MN98] the problem MDS (minimum dominating set) is reduced to MBS. 12 Therefore, the following holds: Cost CLIQUE (G; B 0 ) Cost MTSN (f(G) B) b h(jf(G)j) b h(jGj) The last equality follows from the fact that f preserves the size of an instance, i.e. the size of the ....

R. Mathar, T. Niessen. Optimum Positioning of Base Stations for Cellular Radio Networks. 1998.

....simulation and planning tools [TLT97] but also to have precise results about (non ) solvability and (non ) approximability of combinatorial problems that arise in this model. In the present paper we consider the following optimization problems: Maximize number of totally supplied nodes (MTSN) MN99] Given is a set N of demand nodes (DN) a set B of potential locations for base stations (BS) Part of this work has been supported by NORTEL External Research. 1 a budget k 2 N and an interference factor 2 Q with 1. Furthermore, for every i 2 B and j 2 N , variables u i;j 2 Q and ....

....GSM systems as well as in the IS 95 system or in future UMTS networks that rely on the CDMA technology. It is known that the above problems are (as decision problems) NP complete. We rst show that their optimization versions are even hard to approximate (improving a result for MTSN given in [MN99] Our hardness result builds on the recent characterization of the class NP by so called probabilistically checkable proofs (PCP) leading to strong non approximability theorems for the CLIQUE problem (see [AL97] We show how CLIQUE reduces to our problems in such a way that the approximation ....

[Article contains additional citation context not shown here]

R. Mathar and T. Niessen. Optimum positioning of base stations for cellular radio networks. In Wireless Networks, 1999.

....respect to power range assignment (see [CPS00] However, the problem of positioning base stations in an optimal way has not been considered in depth from a complexity theoretic point of view. While simulation and planning tools (see [TLT97] and solutions based on linear programming (see, e.g. MN99] are known, not much has been proven about (non )solvability and (non )approximability of arising combinatorial problems. In [ESW98] optimum non approximability results for planning problems for telecommunication networks, where antennas are placed in balloons at a certain height, were given. ....

R. Mathar and T. Niessen. Optimum positioning of base stations for cellular radio networks. In Wireless Networks, 1999.

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R. Mathar and T. Niessen, "Optimum positioning of base stations for cellular radio networks," Wireless Networks, vol. 6, no. 6, pp. 421--428, 2000.

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R. Mathar and T. Niessen; "Optimum positioning of base stations for cellular radio networks"; Wireless Networks, pages 421-428, 2000.

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