Class Tree  

Description 
The weighted latinsquare problem is a variant of the latinsquare problem. In the weighted latinsquare problem, we are given an n x n weights wt(i,j). We are also given a bound w. A weighted latinsequre is an n x n array a such that a. each entry contains an integer from {1,2,...,n} b. no row contains the same integer twice c. no column contains the same integer twice d. for every row i, 1<=i<=n, a(i,1)*wt(i,1) + a(i,2)*wt(i,2) + a(i,n)*wt(i,n) <= w The goal in the problem is to find a weighted latin square. Input Format ============ Input data are stored in a plain text file, a. The file starts with n lines num(1). num(2). ... num(n). which specify the number of rows and columns in the square and the rannge of integers to use. b. Then there are n^2 lines, each of the form weight wt(i,j)=v. c. Then there is a single line bound(w). Example: num(1). num(2). num(3). num(4). weight wt(1,1)=1. weight wt(1,2)=2. weight wt(1,3)=1. weight wt(1,4)=2. weight wt(2,1)=1. weight wt(2,2)=2. weight wt(2,3)=1. weight wt(2,4)=2. weight wt(3,1)=1. weight wt(3,2)=2. weight wt(3,3)=1. weight wt(3,4)=2. weight wt(4,1)=1. weight wt(4,2)=2. weight wt(4,3)=1. weight wt(4,4)=2. bound(15). Output Requirement ================== A solution must be specified in terms of a 3ary predicate "square", with the meaning of "square(i,j,k)": "square (i,j) contains integer k". For the input given above, the following is a valid weighted latin square: square(4,4,4) square(2,3,4) square(1,2,4) square(3,1,4) square(2,4,3) square(1,3,3) square(3,2,3) square(4,1,3) square(3,4,2) square(4,3,2) square(2,2,2) square(1,1,2) square(1,4,1) square(3,3,1) square(4,2,1) square(2,1,1) Thus, the output produced by the solver, when displaying the corresponding answer set must show these and only these atoms of the type "square" (and possibly some other atoms based on other predicates). Authors: Gayathri Namasivayam and Miroslaw Truszczynski Affiliation: University of Kentucky Email: {gayathri, mirek}@cs.uky.edu 
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