The "largest element first" heuristic selects (i 1 ,j 1 )∈arg. max (i,j)∈I×J [a ij ], j 1 is assigned to i 1 and {i 1 ,j 1 } deleted to give I 1 =I-{i 1 }, J 1 =J-{j 1 }. The procedure is repeated with I 1 and J 1 , culminating in an assignment. ...
The home-away assignment problems and break minimization/maximization problems in sports scheduling Suppose that we have a timetable of a round-robin tournament with a number of teams, and distances between their homes. The home-away assignment problem is... A Suzuka,R Miyashiro,A Yoshise,......
In theDeterminant Maximizationproblem, given anpositive semi-definite matrixinand an integerk, we are required to find aprincipal submatrix ofhaving the maximum determinant. This problem is known to beNP-hard and further proven to beW[1]-hard with respect tokby Koutis (Inf Process Lett 100:8...
Smaller points have less uncertainty in the assignment. • Unlike the classical implementation of k-means, the general EM algorithm can be applied to both continuous and categorical variables. Algorithm 2: EM clustering algorithm 1. EM (k, X, eps); Input: Cluster number k, a databas...
EnglishEspañolDeutschFrançaisItalianoالعربية中文简体PolskiPortuguêsNederlandsNorskΕλληνικήРусскийTürkçeאנגלית 9 RegisterLog in Sign up with one click: Facebook Twitter Google Share on Facebook ...
The MI-SDP then jointly searches for the binary variables as well as the transformation matrix such that the maximum number of assignment conditions are satisfied. We present this idea more precisely in our following preliminary result. Result 4.4 The Problem 4.1 can be solved optimally for the ...
cover problem. In fact, f(S) is submodular even for arbitrary submodular functions g. It is monotone iff g is monotone. 4 The rank function of a matroid. Another important class of submodular functions arises in the context of matroids: Definition 1.4 (Matroid) A matroid is a pair ...
“hidden”nuisancevariablesJ,whichneedtobeintegratedout.Inparticular,wewanttomaximizetheposteriorprobabilityoftheparametersΘgiventhedataU,marginalizingoverJ:Θ∗=argmaxΘ�J∈JnP(Θ,J|U)(1)TheintuitionbehindEMisanoldone:alternatebetweenestimatingtheunknownsΘandthehiddenvariablesJ.Thisideahasbeenaroundfor...
For relaxed multi-demand models, a standard technique can reduce the problem to the unit demand case in the following way: each buyer i with demand di is replaced by di copies of buyer i, each requesting a single item. However, such a trick does not apply to the sharp demand model. ...
As a result, learning can be completed in a single step. However, we encounter undefined variational posteriors of log expectation. We overcome this problem by the use of lower bounds. When our cluster assignment also uses a MAP estimation, we have a global objective known as the maximization...