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# Minimum spanning tree example ### Spanning tree and Minimum Spanning tree with example - Quesco

Minimum Spanning Trees Example of Minimum Spanning Trees. Here we are going to find minimum spanning tree for the below graph. There are more... Minimum Spanning-Tree Algorithm. Application of Minimum Spanning Tree. Minimum Spanning Tree are widely used for designing networks. For example, we. What is a Minimum Spanning Tree? A minimum spanning tree is a special kind of tree that minimizes the lengths (or weights) of the edges of the tree. An example is a cable company wanting to lay line to multiple neighborhoods; by minimizing the amount of cable laid, the cable company will save money. A tree has one path joins any two vertices. A spanning tree of a graph is a tree that 6.3: Minimum Spanning Tree T.S. 3. Generic Algorithm. 0:def minimum spanningTree(G) 1:A = empty set of edges. 2:while A does not span all vertices yet: 3:add asafeedge to A. An edge of G issafeif by adding the edge to A, the resulting subgraph is still a subset of a minimum spanning tree Minimum Spanning Trees Suppose we are given a connected, undirected,weightedgraph. This is a graphG=(V,E) together with a functionw:E ! R that assigns a realweight w(e) to each edgee, which may be positive, negative, or zero

### Minimum Spanning Tree: Definition, Examples, Prim's Algorithm - Statistics How T

1. imum weight spanning tree for a weighted, connected, undirected graph is a spanning tree having a weight less than or equal to the weight of every other possible spanning tree. The weight of a spanning tree is the sum of weights given to each edge of the spanning tree
2. imal spanning tree T is a tree with
3. MST = Minimum Spanning Tree = 최소 신장 트리 각 간선의 가중치가 동일하지 않을 때 단순히 가장 적은 간선을 사용한다고 해서 최소 비용이 얻어지는 것은 아니다. MST는 간선에 가중치를 고려하여 최소 비용의 Spanning Tree를 선택하는 것을 말한다
4. MINIMUM spANNING Trees!By: Makenna , Emmely , and Jessica Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website
5. imum spanning tree (MST) can be defined on an undirected weighted graph. An MST follows the same definition of a spanning tree. The only catch here is that we need to select the
6. imum spanning tree (MST) is one which costs the least among all spanning trees. Here is an example of a
7. This implies that Kruskal's produces a Spanning Tree. On the default example, notice that after taking the first 2 edges: 0-1 and 0-3, in that order, Kruskal's cannot take edge 1-3 as it will cause a cycle 0-1-3-0. Kruskal's then take edge 0-2 but it cannot take edge 2-3 as it will cause cycle 0-2-3-0. X Esc

Example of a Spanning Tree. Let's understand the above definition with the help of the example below. The initial graph is: Weighted graph. The possible spanning trees from the above graph are: Minimum spanning tree - 1 Minimum spanning tree - 2 Minimum spanning tree - 3 Minimum spanning tree - 4. The minimum spanning tree from the above spanning trees is Minimum spanning tree has direct application in the design of networks. It is used in algorithms approximating the travelling salesman problem, multi-terminal minimum cut problem and minimum-cost weighted perfect matching. Other practical applications are: Cluster Analysis; Handwriting recognition; Image segmentation; There are two famous algorithms for finding the Minimum Spanning Tree

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1. weight set of edges that connects all of the vertices. 23 10 21 14 24 16 4 18 9 7 11 8 weight(T) = 50 = 4 + 6 + 8 + 5 + 11 + 9 + 7 5 6 Brute force: Try all possible spanning trees • problem 1: not so easy to implemen
2. Now, you can try to draw as many Spanning Tree as possible. While drawing the Spanning Trees, one thing that can be noted here is that, if we have e edges, then we are making spanning trees of having n-1 edges, where n is the number of vertices or nodes. So, the total number of possible spanning trees are: eC(n-1); here, e is the number of edges present in the graph and n is the total number.
3. imum spanning tree using Prim's algorithm. Kruskal's Algorithm: An algorithm to construct a Minimum Spanning Tree for a connected weighted graph. It is a Greedy Algorithm. The Greedy Choice is to put the smallest weight edge that does not because a cycle in the MST constructed so far
4. We have discussed Kruskal's algorithm for Minimum Spanning Tree. Like Kruskal's algorithm, Prim's algorithm is also a Greedy algorithm. It starts with an empty spanning tree. The idea is to maintain two sets of vertices. The first set contains the vertices already included in the MST, the other set contains the vertices not yet included

### Properties of Minimum Spanning Tree (MST) - GeeksforGeek

• imum spanning trees of the same weight having the
• imum cost spanning tree uses the greedy approach. This algorithm treats the graph as a forest and every node it has as an individual tree. A tree connects to another only and only if, it has the least cost among all available options and does.
• imum spanning tree, in a connected weighted graph, is a spanning tree that has the smallest possible sum of weights of its edges. Minimum Spanning Trees
• imum as possible then that spanning tree is called the

### [알고리즘] 최소 신장 트리(MST, Minimum Spanning Tree)란 - Heee's

Prim's Algorithm to Find Minimum Spanning Tree ExampleWatch More Videos athttps://www.tutorialspoint.com/videotutorials/index.htmLecture By: Mr. Arnab Chakr.. From the above figure, we see that we have now covered all the vertices in the graph and obtained a complete spanning tree with minimum cost. Now let us implement the Prim's algorithm in C++. Note that in this program as well, we have used the above example graph as the input so that we can compare the output given by the program along with the illustration Example for Prim's Minimum Spanning Tree Algorithm. Let's try to trace the above algorithm for finding the Minimum Spanning Tree for the graph in Fig. 2: Step A: Define key[] array for storing the key value(or cost) of every vertex. Initialize this to. Hence the resultant MST is-. The total cost of the tree is= 10+25+22+12+16+14=99. Hence the above tree is the resultant minimum spanning tree with cost 99. Note: If we have two graphs which are not connected to each other, no algorithm can find the MST from those two The weight of a spanning tree is the sum of all the weights assigned to each edge of the spanning tree. Example Kruskal's Algorithm. Kruskal's algorithm is a greedy algorithm that finds a minimum spanning tree for a connected weighted graph. It finds a tree of that graph which includes every vertex and the total weight of all the edges in the.

### Minimum Spanning Tree - SlideShar

1. Minimum Spanning Tree CSE 373: Data Structures and Algorithms Thanks to Kasey Champion, Ben Jones, Adam Blank, Michael Lee, Evan McCarty, Robbie Weber, Whitaker Brand, Zora Fung, Stuart Reges, Justin Hsia, Ruth Anderson, and many others for sample slides and materials.
3. imum spanning treeis a tree of

The Only Minimum Spanning Tree Algorithm algorithm in place of simple weight comparisons. SE takes as input four integers i, j,k,l, representing four (not necessarily distinct) vertices, and decides which of the two edges (i, j) and (k,l) has smaller weight.(Because the input graph undirected, the pairs (i, j) and (j,i) represent the same edge. Minimum spanning trees have direct applications in the design of networks, including computer networks, telecommunications networks, transportation networks, water supply networks, and electrical grids. 2 One example would be a telecommunications company laying cable to a new neighborhood. If it is constrained to bury the cable only. Minimum Spanning Tree Problem Minimum Spanning Tree Problem Given undirected graph G with vertices for each of n objects weights d( u; v) on the edges giving the distance and , Find the subgraphP T that connects all vertices and minimizes fu;vg2T d(u;v). T will be a tree. Why? If there was a cycle, we could remove any edge on the cycle to ge Minimum Spanning Tree Problem Must be necessarily a tree! 6 4 11 3 9 8 4 6 5 3 9 2 7 8 Street Networks, Wiring Electronic Components, Laying Pipes Weightsmay represent distances, costs, travel times, capacities, resistance etc. Applications 6.3: Minimum Spanning Tree T.S. Kruskal's Algorithm follows the Greedy Algorithm to construct a Minimum Spanning Tree for a connected, weighted, and undirected graph. This algorithm treats the graph as a forest and its vertices as an individual tree. The aim of this algorithm is to find a subset of the edges that forms a tree that includes every vertex with minimum edges

Building MST (Minimum Spanning Tree) is a method for constructing hierarchy of clusters. For example, we can also use local inconsistency remove edges significantly larger than their neighborhood edges. References Introduction to Data Mining, by P.-N. Tan, M. Steinbach, V. Kumar,. Let's visually run Dijkstra's algorithm for source node number 0 on our sample graph step-by-step: The shortest path between node 0 and node 3 is along the path 0->1->3. However, the edge between node 1 and node 3 is not in the minimum spanning tree. Therefore, the generated shortest-path tree is different from the minimum spanning tree

Example: Let's consider a couple of real-world examples on minimum spanning tree: One practical application of a MST would be in the design of a network. For instance, a group of individuals, who are separated by varying distances, wish to be connected together in a telephone network 3 Minimum Spanning Tree Minimum Spanning Tree (MST) is a spanning tree with the minimum total weight. In this section, we will rst learn the de nition of a spanning tree and then study some properties for Minimum Spanning Tree, which will be useful in proving the correctness of MST algorithms. Lecture 13: Shortest Path, Minimum Spanning Tree- #include <iostream> #include <vector> #include <utility> #include <algorithm> using namespace std; const int MAX = 1e4 + 5; int id[MAX], nodes, edges; pair <long long.

### How to Find Total Number of Minimum Spanning Trees in a Graph? Baeldung on Computer

Prim's Algorithm: Minimum Spanning Tree (mst) short example of prim's algorithm, graph is from cormen book. hijinks ensue as the mighty nein attempt subterfuge in order to carry out the mission of the knights of requital thanks to far cry 5 and d&d beyond for dijkstra algorithm for single source shortest path procedure examples time complexity drawbacks patreon explanation for the article. Now, you have two edges for your Minimum Spanning Tree. Next, as usual you have to check, which all vertices are reachable from Vertex/City 'a','b' and 'd'. Just remember, you have to exclude the edges/roads that are already included in the Minimum Spanning Tree. And, in this case Vertex/City 'c' is reachable from Vertex/City 'a' Minimum Spanning Trees Spanning trees A spanning tree of a graph is just a subgraph that contains all the vertices and is a tree. Note that if you have a path visiting all points exactly once, it's a special kind of tree. For instance in the example above, twelve of sixteen spanning trees are actually paths Example of Kruskal's Algorithm. Greedy algorithm approach is used to find the minimum cost spanning tree. Using this appraoch, Greedy Choice is made by putting the smallest weight edge. Below is the example of Kruskal's Algorithm with input- output constraint and the solution for the example. Input and Output of the Example ### Kruskal's algorithm (Minimum spanning tree) with real-life examples HackerEarth Blo

Lecture 12 Minimum Spanning Tree Motivating Example: Point to Multipoint Communication • Single source, Multiple Destinations • Broadcast - 1 2 All nodes in the network are destinations • Multicast - Some nodes in the network are destinations • Only one copy of the information travels along common edges Message replication along forking points only 4.3 Minimum Spanning Trees. Minimum spanning tree. An edge-weighted graph is a graph where we associate weights or costs with each edge. A minimum spanning tree (MST) of an edge-weighted graph is a spanning tree whose weight (the sum of the weights of its edges) is no larger than the weight of any other spanning tree.. Assumptions. To streamline the presentation, we adopt the following. The weight of a spanning tree is the sum of all the weights assigned to each edge of the spanning tree. Example Kruskal's Algorithm. Kruskal's algorithm is a greedy algorithm that finds a minimum spanning tree for a connected weighted graph. It finds a tree of that graph which includes every vertex and the total weight of all the edges in the. Maximum Spanning Tree: Given an undirected weighted graph, a maximum spanning tree is a spanning tree having maximum weight.It can be easily computed using Prim's algorithm.The goal here is to find the spanning tree with the maximum weight out of all possible spanning trees. Prim's Algorithm: Prim's algorithm is a greedy algorithm, which works on the idea that a spanning tree must have. Minimum Spanning Trees. If we just want a spanning tree, any \(n-1\) edges will do. If we have edge weights, we can ask for the spanning tree with the lowest total edge weights. This is the minimum spanning tree. For example, if we add some edge weights, what is the minimum spanning tree ### VisuAlgo - Minimum Spanning Tree (Prim's, Kruskal's

A spanning tree is a subset of Graph G, which has all the vertices covered with minimum possible number of edges. Hence, a spanning tree does not have cycles and it cannot be disconnected.. By this definition, we can draw a conclusion that every connected and undirected Graph G has at least one spanning tree minimum-spanning-tree. This project implements the algorithms of Kruskal, Prim and Boruvka for creating a minimum spanning tree (MST) of a weighted, undirected graph in C with parallelization via MPI. It was developed for the module Algorithm Engineering at the HTWK Leipzig Find the minimum spanning tree of the graph. Input. On the first line there will be two integers N - the number of nodes and M - the number of edges. (1 = N = 10000), (1 = M = 100000) M lines follow with three integers i j k on each line representing an edge between node i and j with weight k. The IDs of the nodes are between 1 and n inclusive

Minimum spanning tree is the spanning tree where the cost is the least among all the spanning trees. There also can be more than one minimum spanning tree. In simple words, in a minimum spanning tree, sum of weight of edges should be minimum and all vertices should be connected. For n number of vertices in the weighted graph, the number of. Hierarchical clustering in minimum spanning trees Meichen Yu,1,a) Arjan Hillebrand,1 Prejaas Tewarie,2 Jil Meier,3 Bob van Dijk,1 Piet Van Mieghem,3 and Cornelis Jan Stam1 1Department of Clinical Neurophysiology and MEG Center, VU University Medical Center, PO Box 1081 HV, Amsterdam, The Netherlands 2Department of Neurology, VU University Medical Center, Amsterdam, The Netherland

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The minimum spanning tree obtained by the application of Prim's Algorithm on the given graph is as shown below-. Now, Cost of Minimum Spanning Tree. = Sum of all edge weights. = 1 + 4 + 2 + 6 + 3 + 10. = 26 units kruskal's algorithm is a greedy algorithm that finds a minimum spanning tree for a connected weighted undirected graph.It finds a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized.This algorithm is directly based on the MST( minimum spanning tree) property

### Spanning Tree and Minimum Spanning Tree - Programi

• imum spanning tree for the graph representing communication links between offices as shown in Figure 19.16. Solution We start with any vertex and choose the one marked a. Add the edge ab which is the cheapest edge of those incident to a
• They are used for finding the Minimum Spanning Tree (MST) of a given graph. To apply these algorithms, the given graph must be weighted, connected and undirected. Some important concepts based on them are- Concept-01: If all the edge weights are distinct, then both the algorithms are guaranteed to find the same MST. Example
• spantree(G,'Method','sparse') uses Kruskal's algorithm for calculating the
• imum spanning tree is a graph consisting of the subset of edges which together connect all connected nodes, while
• imum spanning tree with a vertex chosen at random. Find all the edges that connect the tree to new vertices, find the
• imum spanning tree problems and applied them to benchmark instances . They showed that the performance of their metaheuristics depends not only on the characteristics of the instances but also on the cardinality. For example, the ant colony optimization approach is best for small, whereas the tabu search approach has advantage for large
• imum among all possible combinations. In Shortest Path, requirement is to.

### Minimum Spanning Tree Tutorials & Notes Algorithms HackerEart

• imal - that's why I'm following Prim's/Kruskal's to begin with! - OJFord Jun 13 '15 at 23:1
• imum spanning tree from a given connected, edge-weighted graph.It first appeared in Kruskal (1956), but it should not be confused with Kruskal's algorithm which appears in the same paper. If the graph is disconnected, this algorithm will find a
• imum total weight Example: CPS 616 GREEDY TECHNIQUE 9 - 2 Prim's.

### minimum spanning tree (mst) Code Exampl

Exercises 8 - minimal spanning trees (Prim and Kruskal) For example, you could stop it after k edges have been added to T. spanning tree is the same problem as finding the minimum spanning tree in a graph which had costs negated (relative to the originals) Minimum spanning trees. Basically a minimum spanning tree is a subset of the edges of the graph, so that there's a path form any node to any other node and that the sum of the weights of the edges is minimum. Here's the minimum spanning tree of the example: Look at the above image closely

Shortest-Path Trees and MSTs Last time, we saw how Dijkstra's algorithm and A* search can be used to find shortest path trees in a graph. Note that a shortest-path tree might not be an MST and vice-versa. 5 3 2 1 Minimum spanning tree in the graph. Minimum spanning tree in the graph. � A minimum spanning tree is a special kind of tree that minimizes the lengths or weights of the edges of the tree. example: A cable company wanting to lay line to multiple neighborhoods; by minimizing the amount of cable laid; the cable company will save money. A tree has one path joins any two vertices. A spanning tree of a graph is a tree that For example, let's say , and . We need to construct a graph with nodes and edges. The value of minimum spanning tree must be . The diagram belows shows a way to construct such a graph while keeping the lengths of all edges is as small as possible: Here the sum of lengths of all edges is Lecture 32: Minimum Spanning Trees Minimum spanning trees: Borůvka's, Prim's and Kruskal's algorithms. Early in the 20th century, the challenge of electrifying towns and cities was one of the pressing issues facing civil engineers. In 1926, a Moravian academic named Otakar Borůvka considered the problem and came up with a solution.A workable solution needed to

### Minimum Spanning Tree - AfterAcadem

• 先備知識與注意事項. 在上一篇文章Minimum Spanning Tree：Intro(簡介)介紹過MST的問題情境以及演算法概念，這篇文章要接著介紹尋找MST的演算法之一：Kruskal's Algorithm。. 說明演算法時將會用上專有名詞如「light edge」、「cross」，如果不太熟悉，可以參考上一篇文章�
• imum cost spanning tree using kruskal's algorithm example in C Program
• We have discussed Kruskal's algorithm for Minimum Spanning Tree.Like Kruskal's algorithm, Prim's algorithm is also a Greedy algorithm.It starts with an empty spanning tree. The idea is to maintain two sets of vertices. The first set contains the vertices already included in the MST, the other set contains the vertices not yet included
• imum spanning tree for a connected weighted undirected graph.It finds a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is ### Minimum Spanning Tree Algorithm

NUMERICAL EXAMPLE Input: the weight matrix M = [wij] n × n for the undirected Consider the following graph and its shows the various steps weighted graph G involved in the construction of the minimum cost spanning tree. Output: Minimum Cost Spanning Tree T of G. www.ijsrp.org International Journal of Scientific and Research Publications. Kruskal's algorithm for MST with example

### Prim's Minimum Spanning Tree (MST) Greedy Algo-5 - GeeksforGeek

• Minimum-cost spanning tree games arise in cost allocation problems in which a joint enterprise can be represented as a tree that connects agents to a common source (e.g., Claus 1973; Bird 1976). MSTGs are cost sharing games where players need to be connected to a certain service supplier and form coalitions , (i.e., subsets of users/vertices) to share the cost of this service
• imum cost spanning tree: The same tree is generated by Prim's algorithm if the start vertex is any of: A, B, or D; however if the start vertex is C the
• In this article, we will cover the problem of Minimum Spanning Tree.In my previous post, I covered the Disjoint Set Union problem.. NOTE: To make the article fun, we have wrapped an inter-galactic fictional story around it. Don't get confused by it. The Problem. Kapi has just conquered the universe. His childhood dream is finally a reality In this tutorial, we will learn about the Spanning Tree of the graph and its properties.We will also learn about the Minimum spanning tree for graph in C++ and its implementation using Prim's algorithm and Kruskal's algorithm.. We will take some examples to understand the concept in a better way. Spanning Tree . Spanning tree is the subset of graph G which has covered all the vertices V of. Kruskal's algorithm is a greedy algorithm to find the minimum spanning tree. Sort the edges in ascending order according to their weights. At every step, choose the smallest edge (with minimum weight). If this edge forms a cycle with the MST formed so far, discard the edge, else, add it to the MST

A minimum spanning tree is a tree. It is different from other trees in that it minimizes the total of the weights attached to the edges. Depending on what the graph looks like, there may be more than one minimum spanning tree. In a graph where all the edges have the same weight, every tree is a minimum spanning tree The Flowchart of Finding Minimum Spanning Tree 3.2.3 Design of Image Segmentation Result Generation Algorithm. In the design of this algorithm, some of the minimum range trees obtained will be. A minimum spanning tree is a spanning tree with weighted edges in which the total weight of all edges is minimized. For example, you might want to find the cheapest way to lay out a network of water pipes. Here's an example of a minimum spanning tree for a weighted undirected graph

### MST Introduction Minimum Spanning Tree Introduction - javatpoin

In this article we will briefly discuss about the Metric Travelling Salesman Probelm and an approximation algorithm named 2 approximation algorithm, that uses Minimum Spanning Tree in order to obtain an approximate path.. What is the travelling salesman problem ? Travelling Salesman Problem is based on a real life scenario, where a salesman from a company has to start from his own city and. Minimum spanning tree-Prim's algorithm, with C Program Example. Prim's algorithm to find the minimum cost spanning tree of for a weighted undirected graph, uses the greedy approach. Prim's algorithm, in contrast with Kruskal's algorithm, treats the nodes as a single tree and keeps on adding new nodes to the spanning tree from the given graph Kruskal's algorithm finds a minimum spanning forest of an undirected edge-weighted graph.If the graph is connected, it finds a minimum spanning tree. (A minimum spanning tree of a connected graph is a subset of the edges that forms a tree that includes every vertex, where the sum of the weights of all the edges in the tree is minimized Initialize the minimum spanning tree with a random vertex (initial vertex). Find all the edges that connect the tree to new vertices, find the minimum, and add it to the tree (greedy choice). Keep repeating step 2 until we get a minimum spanning tree (until all vertices are reached). We can look at an example to understand how Prim's. Algorithm for finding Minimum Spanning Tree• The Prims Algorithm• Kruskals Algorithm• Baruvkas Algorithm 5. About Prim's AlgorithmThe algorithm was discovered in 1930 bymathematician Vojtech Jarnik and later independentlyby computer scientist Robert C. Prim in 1957.The algorithm continuously increases the size of atree starting with a single vertex until it spans all thevertices Minimum weight spanning tree. Description. Six terminals located in different buildings need to be connected. The cost of connecting two terminals is proportional to the distance between them. Determine the connections to install to minimize the total cost. Further explanation of this example: 'Applications of optimization with Xpress-MP. Spanning Tree from PVST+ to Rapid-PVST Migration Configuration Example (ZIP - 46 KB) 18/Dec/2020. Spanning Tree Protocol (STP) / 802.1D. Configure a Layer 2 vPC Data Center Interconnect on a Nexus 7000 Series Switch 14/Aug/2015. Configure and Validate REP with STP 14/Feb/2018 A spanning tree is a subset of the graph G that includes all of the attributes with the minimum number of edges (that would have to be 2 because a tree with just one edge would only connect at most 2 attributes). In the graph above, there are three spanning trees.All spanning trees in this graph G must have the same number of attributes (3 in total) and edges (2 in total) Search for jobs related to Minimum spanning tree example with solution or hire on the world's largest freelancing marketplace with 20m+ jobs. It's free to sign up and bid on jobs Otakar Boruvka on minimum spanning tree problem˚ Translation of both the 1926 papers, comments, history Jaroslav Ne+setril∗, Eva Milkov-a, Helena Ne+setrilov-a Faculty of Mathematics and Physics, Department of Applied Mathematics, Malostranske nam 25, 118 00 Prague, Czech Republic Abstrac

For example, in minimum spanning tree, maybe you guess one of the edges that's in the right answer. And then, once you do that, you can reduce it to some other subproblems. And if you can solve those subproblems, you combine them and get an optimal solution to your original thing. So this is a familiar property sophisticated minimum spanning tree algorithms. 1 Introduction Motivation. The actual running time of implementations of parallel algorithms depends on two groups of parameters, namely software parameters such as, e.g., the number of memory accesses or the degree of a used broadcast tree, and hardware parameters such as, e.g., the. THE MINIMUM SPANNING TREE PROBLEM IN ARCHAEOLOGY Per Hage, Frank Harary, and Brent James The minimum spanning tree problem is a well-known problem of combinatorial optimization. It was independently discovered in archaeology by Renfrew and Sterud in their method of close proximity analysis The minimum spanning tree of a planar point set can be maintained fully dynamically for any signature of size n in expected time O(log n) per update. P roof . As shown by Mulmuley, by Schwarzkopf, and by Devillers et al. [ 51 ], we can maintain the Delaunay triangulation in this time bound Several algorithms were proposed to find a minimum spanning tree in #' a graph. #' #' Prim's algorithm was developed in 1930 by the mathematician Vojtech #' Jarnik, independently proposed by the computer scientist Robert C. Prim #' in 1957 and rediscovered by Edsger Dijkstra in 1959. This is a greedy #' algorithm that can find a minimum.