Question

Network flows let d = (dij) be a p q matrix with non-negative real entries and row sums ai and column sums bj . Show that it is possible to round each dij , ai , bj up or down to an integer (that is bc or de) so that the sum of the rounded entries in each row (column) equal the rounded row (resp. Column) sum. Give an algorithm to find such a rounding

Answer 1

non-negative real entries and row sums ai and column sums bj . Show that it is possible to round each dij , ai , bj up or down to an integer (that is bc or de) so that the sum of the rounded entries in each row (column) equal the rounded row (resp. Column) sum