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This paper proposes a decentralized state-estimation approach that relies on an elaborated instance of the Lagrangian relaxation decomposition technique. The proposed algorithm does not require a central coordinator but just to moderate interchanges of information among neighboring regions, and exploits the structure of the problem to achieve a fast and accurate convergence. Additionally, a decentralized bad measurement identification procedure is developed, which is efficient and robust in terms of identifying bad measurements within regions and in border tie-lines. The accuracy and efficiency of the proposed procedures are assessed by a large number of simulations, which allows drawing statistically sound conclusions. [ABSTRACT FROM PUBLISHER]

Abstract: For a set of n points in the plane, we consider the axis-aligned -Box Covering problem: Find p axis-aligned, pairwise-disjoint boxes that together contain at least points. In this paper, we consider the boxes to be either squares or rectangles, and we want to minimize the area of the largest box. For general p we show that the problem is NP-hard for both squares and rectangles. For a small, fixed number p, we give algorithms that find the solution in the following running times: For squares we have time for , and time for . For rectangles we get for and time for . In all cases, our algorithms use space. [ABSTRACT FROM AUTHOR]