Know the difference between A* and Dijkstra's algorithm (pp. 241-243) Cost = AccumulativeCostTo(E.From) + E.Cost + Cost To (Target)Utilizing a heuristic in this way, the modified costs direct the search towardthe target node instead of radiating outward equally in all directions. Thisresults in fewer edges needing to be examined, thereby speeding up thesearch and is the primary difference between A* and Dijkstra's algorithm.NOTE If you set the heuristic cost to zero in A", the resulting search behavesexactly the same as Dijkstra's algorithm.Let's take a peek at how A* operates on the problem graphs used in thePathFinder program.A* in ActionScreenshot 5.8 shows the result of A* operating on the simple source-targetexample problem. As you can see, no extraneous edges have been consid-ered, and the path leads directly to the target. The heuristic function used isthe straight-line distance between two nodes.Time Claped for A Sanchis 5.96-005Graph Search Algorithms♫Screenshot 5.8. Do not pass Go, do not collect £200.Time laped for each351 06Screen shot 5.9Screen shot 5.9 is just as impressive. Observe how few edges the A* algo-rithm had to consider before finding the target. As a consequence of this,the time taken to perform the search is considerably less than for any of theother searches (even though an evil square root is required to calculate theheuristic cost).HJH210 E: 1220TLFEBOOKThe Secret Life of Graphs | 243NOTE A* is proven to be optimally efficient. In other words, no other searchalgorithm will expand fewer nodes in the quest for the least cost path betweensource and target. Graph Search Algorithmsdiagonal edges cost more to traverse than horizontal or vertical ones. Withthis in mind you can see how the algorithm has searched a similar distancein every direction before reaching the target.Screenshot 5.7 shows Dijkstra's algorithm operating on the more com-plex map.H²Time Espod for Dia's Search is 0.000274Screenshot 5.7The Secret Life of Graphs | 241H210 1220Like the BFS, Dijkstra's algorithm examines an awful lot of edges.Wouldn't it be great if the algorithm could be given hints as it progresses tonudge the search along in the correct direction? Well, luckily for us, this ispossible. Ladies and gentlemen, please put your hands together in a roundof applause and welcome A*!242 Chapter 5Dijkstra with a Twist: A*Dijkstra's algorithm searches by minimizing the cost of the path so far. Itcan be improved significantly by taking into account, when putting nodeson the frontier, an estimate of the cost to the target from each node underconsideration. This estimate is usually referred to as a heuristic, and thename given to the algorithm that uses this method of heuristically directedsearch is A* (pronounced ay-star). And jolly good it is too!If the heuristic used by the algorithm gives the lower bound on theactual cost (underestimates the cost) from any node to the target, then A* isguaranteed to give optimal paths. For graphs that contain spatial informa-tion, such as navigation graphs, there are several heuristic functions youcan use, the most straightforward being the straight-line distance betweenthe nodes in question. This is sometimes referred to as the Euclideandistance.TLFEBOOKGraph Search AlgorithmsA* proceeds in an almost identical fashion to Dijkstra's search algo-rithm. The only difference is in the calculation of the costs of the nodes onthe search frontier. The adjusted cost, F, to the node when positioned on thepriority queue (the search frontier), is calculated as:F=G+H(5.3)where G is the cumulative cost to reach a node and H is the heuristic esti-mate of the distance to the target. For an edge E that has just come off thefrontier and been added to the SPT, the pseudocode to calculate the cost toits destination node looks like this:Cost AccumulativeCostTo(E.From) + E.Cost + CostTo(Target)Utilizing a heuristic in this way, the modified costs direct the search toward

Dijkstra's algorithm is a greedy algorithm that works on graphs with non-negative edge weights. It…

Answered: Know the difference between A* and…

Know the difference between A* and Dijkstra's algorithm (pp. 241-243)

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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