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グラフスペクトルによる 多項式時間最大クリーク抽出

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グラフスペクトルによる多項式時間最大クリーク抽出についてのプレゼン資料

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Part I contained a description of the single-modulus algorithm for reducing a matrix to Frobenius form, obtaining exact integral factors of the characteristic polynomial. Part II contains a description of the multiple-modulus algorithm. Since different moduli may yield different factorizations, an algorithm is given for determining which factorizations are not correct factorizations over the integers of the characteristic polynomial. Part II also contains a discussion of the selection of the moduli and numerical examples.
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A description is given of the Danilewski algorithm for reducing a matrix to Frobenius form using rational arithmetic. This algorithm is modified for use over the field of integers modulo p. The modified algorithm yields exact integral factors of the characteristic polynomial. A description of the single-modulus algorithm is given. Part II contains a description of the multiplemodulus algorithm. Since different moduli may yield different factorizations, an algorithm is given for determining which factorizations are not correct factorizations over the integers of the characteristic polynomial. (auth)
  • X.-D Zhang
X.-D. Zhang. The laplacian eigenvalues of graphs: a survey. arXiv preprint arXiv:1111.2897, 2011.