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Technical University of Crete
Technical University of Crete
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| URI: | http://purl.tuc.gr/dl/dias/DD27E75E-3E4F-4177-8D79-B3FABA179F1A | ||
| Year | 2008 | ||
| Type of Item | Conference Full Paper | ||
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| Bibliographic Citation | D. S. Papailiopoulos and G. N. Karystinos, “Efficient computation of the M-phase vector that maximizes a rank-deficient quadratic form,” in Proc. Conf. on Inform. Sc. and Syst. (CISS '08), pp. 1086-1090 doi: 10.1109/CISS.2008.4558680 https://doi.org/10.1109/CISS.2008.4558680 | ||
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The maximization of a full-rank quadratic form over a finite alphabet is NP-hard in both a worst-case sense and an average sense. Interestingly, if the rank of the form is not a function of it, then it can be maximized in polynomial time. An algorithm for the efficient computation of the M-phase vector that maximizes a rank-deficient quadratic form is developed based on an analytic procedure. Auxiliary hyperspherical coordinates are introduced and the multi-dimensional space is partitioned into a polynomial-size set of regions; each region corresponds to a unique M-phase vector. The M-phase vector that maximizes the rank-deficient quadratic form is shown to belong to the polynomial-size set of candidate vectors. Thus, the size of the feasible set is efficiently reduced from exponential to polynomial.
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