Tag Archives: Discrete Mathematics

Cross-identification of stellar catalogs with multiple stars: Complexity and Resolution [CL]

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http://arxiv.org/abs/1710.09417


In this work, I present an optimization problem which consists of assigning entries of a stellar catalog to multiple entries of another stellar catalog such that the probability of such assignment is maximum. I prove that the problem is NP-Hard and show a way of modeling this problem as a maximum weighted stable set problem. A real application is solved in this way through integer programming.

Read this paper on arXiv…

D. Severin
Fri, 27 Oct 17
27/60

Comments: N/A

Integer-ambiguity resolution in astronomy and geodesy [CL]

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http://arxiv.org/abs/1312.4920


Recent theoretical developments in astronomical aperture synthesis have revealed the existence of integer-ambiguity problems. Those problems, which appear in the self-calibration procedures of radio imaging, have been shown to be similar to the nearest-lattice point (NLP) problems encountered in high-precision geodetic positioning, and in global navigation satellite systems. In this paper, we analyse the theoretical aspects of the matter and propose new methods for solving those NLP problems. The related optimization aspects concern both the preconditioning stage, and the discrete-search stage in which the integer ambiguities are finally fixed. Our algorithms, which are described in an explicit manner, can easily be implemented. They lead to substantial gains in the processing time of both stages. Their efficiency was shown via intensive numerical tests.

Read this paper on arXiv…

Wed, 18 Dec 13
26/70