Mix-Matrix Transformation Method for Max-Сut Problem

The spectra of local minima in spin-glass models

“…Direct tests can confirm that the last relation in (13) agrees nicely with asymptotic expression (9). We assumed that with expressions (13) To make sure that expression (13) and data from table 1 do not give excessive values of the global minimum depth, we used the MM algorithm [18,26] which allows us to find the deepest local minima (but not the global minimum). The typical form of local minima spectra produced by this algorithm for 2D EA, 3D EA and SK models are given in figures 21-23 (the spectra for the SK* model are similar to those for the SK model, so we do not present them here).…”

“…and the energy-dimensionality dependence is reduced to expression The knowledge of the local minima spectrum is necessary in many fields of science. In informatics it is essential for tackling quadratic minimization problems [1][2][3][4][5][6][7][8][9][10], generating algorithms for searching the global minimum [11][12][13][14][15][16][17][18] and the optimal graph cross section [19][20][21][22][23][24][25][26]. In neuroinformatics the knowledge of spectra is necessary for building associative memory systems [27][28][29][30][31][32][33][60][61], developing neural nets and neural minimization algorithms [34][35][36][37][38][39][40].…”

“…Provided the sufficient computational resources, we also determined the deepest minimum E * and global minimum . δ which were determined by using the algorithms designed for finding deeper minima: MixMatrix-algorithm [18,26], DDK-algorithm [16], GRA-algorithm [11] and Branch&Bound method [15].…”

Global Minimum Depth in Edwards-Anderson Model

“…In many fields of science, it is necessary to know the global energy minimum for different systems. Namely, in informatics we use it when solving problems of quadratic optimization [1][2][3][4][5][6], developing search algorithms for the global minimum [7][8][9][10][11][12] and solving max-cut problems [13][14][15][16][17]. In neuroinformatics, we have to know the global minimum when developing associative memory systems [18][19][20][21] and constructing neural networks and neural network minimization algorithms [22][23][24].…”

Generalized approach to description of energy distribution of spin system

“…A more accurate expressions for the means and the variances of energy distributions in the microcanonical ensembles are given in papers [8][9][10]. These expressions were successfully used when deriving the minimization algorithms [8][9][10][11][12][13][14][15] and describing complex neuron systems [16][17][18][19].…”