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Recent developments, especially in wireless and mobile networks, have enabled the use of location based services in many application areas. Accurate location discovery, however, is still an open problem. A widely used and practical localization method is trilateration. However, trilateration works best when exact range measurements are available, which is not apparently the case in real-world due to device errors or environmental noise. In this paper, localization through trilateration when the distance measurements are imprecise, is shown to be NP-complete. Moreover, the authors also prove that no matter how small the ranging errors get, the problem is still intractable.
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