# minimum spanning trees

Published articles for minimum spanning trees.

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## When Greedy Algorithms are Perfect: the Matroid

DevFeed: [When Greedy Algorithms are Perfect: the Matroid](<https://devfeed.tech/articles/when-greedy-algorithms-are-perfect-the-matroid-40364.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2014/08/26/when-greedy-algorithms-are-perfect-the-matroid/>)

Published: 2014-08-26T09:00:02Z

Content type: article

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Algorithms, Complexity](<https://devfeed.tech/topics/algorithms-complexity.md>), [graph theory](<https://devfeed.tech/topics/graph-theory.md>), [Graphs](<https://devfeed.tech/topics/graphs.md>), [math](<https://devfeed.tech/topics/math.md>)

Tags: [algorithms](<https://devfeed.tech/tags/algorithms.md>), [graph-theory](<https://devfeed.tech/tags/graph-theory.md>), [graphs](<https://devfeed.tech/tags/graphs.md>), [greedy](<https://devfeed.tech/tags/greedy.md>), [greedy-algorithm](<https://devfeed.tech/tags/greedy-algorithm.md>), [kruskal-s-algorithm](<https://devfeed.tech/tags/kruskal-s-algorithm.md>), [linear-independence](<https://devfeed.tech/tags/linear-independence.md>), [matroids](<https://devfeed.tech/tags/matroids.md>), [minimum-spanning-trees](<https://devfeed.tech/tags/minimum-spanning-trees.md>), [trees](<https://devfeed.tech/tags/trees.md>), [vertex](<https://devfeed.tech/tags/vertex.md>)

### AI overview

This article explains when greedy algorithms are guaranteed to produce optimal solutions. It introduces matroids as the framework characterizing that guarantee and uses the minimum spanning tree problem as an example, with background on matroid history and connections to linear algebra and graph theory.

### Source excerpt

Greedy algorithms are by far one of the easiest and most well-understood algorithmic techniques. There is a wealth of variations, but at its core the greedy algorithm optimizes something using the natural rule, "pick what looks best" at any step. So a greedy routing algorithm would say to a routing problem: "You want to visit all these locations with minimum travel time? Let's start by going to the closest one. And from there to the next closest one.