STYLIADH@GRPATVX1.BITNET (12/15/89)
I am dealing with the following NP_complete Let A be a three dimensional matrix A[1..n][1..m][1..w], of INTEGERS, xn[1..n] a one dimensional matrix of INTEGERS and N[1..n] a one dimensional matrix of integers in the range 1..n. Given the sums n (A) SUM A[i][j][k] foreach j in [1,m] ,k in [1,w]. i=1 m (B) SUM A[i][j][k] foreach i in [1,n],k in [1,w]. j=1 w (C) SUM A[i][j][k] foreach i in [1,n],j in [1,m] k=1 and the fact that : from the n elements A[i][j][k], j in [1,m],k in [1,w],N[i] of them have a known integer value xn[i] and n-N[i] of them have the value xn[i]+1. xn[i]>=0 foreach i. A[i][j][k] >=0 foreach i,j,k. which are the elements A[i][j][k] foreach i in [1,n],j in [1,m],k in [1,w]? The problem obviously is NP-complete. I wonder if anyone can help me with aproximation methods or clever heuristics or anything. I would welcome any coments,bibliography,ideas anything. Many thanks.