I've already asked for the name of a problem in which we search for a certain matrix with given sums of each row and column in the Math StackExchange:
Its name is Fixed-Charge Transportation Problem and it is also related to graph theory and integer programming.
I've also implemented some algorithms to solve it in javascript, but they are slow. Basically, it tests for every possibility.
Do somebody have already implemented, or knows some js lib with this (and maybe more) graph algorithm available?
EDIT 1
Only a fixed cost equal one is being considered. This is enough to solve my problem. I am after any solution at first, since it is possible to swap quantities in rectangularly positioned cells to find a local minimum.
This is my current recursive algorithm (variable names come from portuguese, so I added some comments for clarity):
var gra; //desired sums for rows
var dem; //desired sums for columns
var x; //current solution being built (bidimensional array); will be returned when one is found
var [iMax, jMax] = [gra.length, dem.length];
function passo(i, j) {
if (j == jMax - 1) { //if last column
var m = gra[i];
if (m > max[i][j]) {
return;
}
x[i][j] = m;
gra[i] -= m;
dem[j] -= m;
if (i == iMax - 1) {
if (gra[i] == 0 && dem[j] == 0) {
return true;
}
} else {
if (passo(i + 1, j)) return true;
}
gra[i] += m;
dem[j] += m;
} else {
if (i == iMax - 1) { //if last row
var m = dem[j];
if (m <= max[i][j] && m <= gra[i]) {
x[i][j] = m;
gra[i] -= m;
dem[j] -= m;
if (passo(0, j + 1)) return true;
gra[i] += m;
dem[j] += m;
}
} else {
for (var m = Math.min(max[i][j], gra[i], dem[j]); m >= 0; m--) {
x[i][j] = m;
gra[i] -= m;
dem[j] -= m;
if (passo(i + 1, j)) return true;
gra[i] += m;
dem[j] += m;
}
}
}
}
passo(0, 0);
