Weighted Matroid
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High Quality Content by WIKIPEDIA articles! 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. There is a simple algorithm for finding a basis: Let A be the empty set. For each x in E o if A U {x} is independent, then set A to A U {x}. The result is clearly an independent set. It is a maximal independent set because if B U {x} is not independent for some subset B of A, then A U {x} is not independent either (the contrapositive follows from the hereditary property). Thus if we pass up an elem...
High Quality Content by WIKIPEDIA articles! 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. There is a simple algorithm for finding a basis: Let A be the empty set. For each x in E o if A U {x} is independent, then set A to A U {x}. The result is clearly an independent set. It is a maximal independent set because if B U {x} is not independent for some subset B of A, then A U {x} is not independent either (the contrapositive follows from the hereditary property). Thus if we pass up an element, we'll never have an opportunity to use it later. We will generalize this algorithm to solve a harder problem.
