1 Answers
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 + {\displaystyle w:E\rightarrow \mathbb {R} ^{+}} for a matroid M = {\displaystyle M=} assigns a strictly positive weight to each element of E {\displaystyle E}. We extend the function to subsets of E {\displaystyle E} by summation; w {\displaystyle w} is the sum of w {\displaystyle w} over x {\displaystyle x} in A {\displaystyle A}. A matroid with an associated weight function is called a weighted matroid.