An Efficient Algorithm for Decomposition of Partially Ordered Sets

Algorithm 1

Find the width of a poset.

	Input:
	n: the number of elements of a poset P
	An × n: the incidence matrix of a poset P
	Output: the length of its largest antichain width (P)
	Begin
	width = 0
	while length of matrix A! = 0 do
	sum_column = sum(A, axis = 0)
	sum_row = sum(A, axis = 1)
	sum_cr =
	M = inf
	for j = 1 to n
	if (sum_cr [j] ≤ M):
	M = sum_cr [j]
	Index = j
	end
	end
	Index_row = []
	Index_column = []
	for j = 1 to n
	if (A[j, Index] == 1):
	Index_row.append(j)
	end
	if (A[Index, j] == 1):
	Index_column.append (j)
	end
	end
	Delete all columns and row when value = 1 in (rows = Index_row [:],
	columns = Index_column [:] and column = Index)
	width +=1
	end
	return the best population found (the width of its largest antichain)
	End