Weighted Matroid

In combinatorics, a branch of mathematics, a weighted matroid is a matroid endowed with function with respect to which one can perform a greedy algorithm.

A weight function w : E → R+ for a matroid M=(E, I) assigns a strictly positive weight to each element of E. We extend the function to subsets of E by summation; w(A) is the sum of w(x) over x in A. A matroid with an associated weight function is called a weighted matroid.