Algorythms for finding paths in graphs

Algorithms for Finding Paths in Graphs The graph is a set of points, called nodes, connected by some lines called edges (not necessarily all the nodes are connected). You can imagine it like cities connected by roads.

BFS or Breadth-First Search The algorithm was developed independently by Moore and Lee for different applications in 1959 and 1961. This algorithm can be compared with the ignition of the neighboring vertices. First, we ignite one node (the one from which you start the way) and then fire spreads to all its neighboring nodes. As a consequence, the same happens with all the nodes. Thus, the fire spreads in "width". As a result of this, a shortcut to the desired nodes will be found.

Dijkstra's Algorithm This algorithm is named after the founder and had been developed in 1959. The algorithm checks each of the nodes of the graph and finds the shortest path to the source node. Standard realization works on a weighted graph (a graph in which each edge has a weight or value which we have to "pay" to pass this edge). In the standard implementation, edges have non-negative weight. At the checkered field, the weight of each edge of the graph is the same (for example 1).

A * (A "With an Asterisk") First, it was described in 1968 by Peter Hart, Nils Nilsson and Bertram Raphael. This algorithm is an extension of Dijkstra's algorithm, the acceleration is achieved by heuristics – in considering each node, the transition is made to the one where the estimated path is the shortest. At the same time, there are many different methods of counting the length of the proposed route from the top. The result of the work will also be the shortest path.

Best-First Search It is an enhanced version of the BFS algorithm, which differs from the original in the fact of the use of the heuristics. It first considers the nodes which are presumably more profitable. So using the heuristics it does for BFS is the same as A * does for Dijkstra's algorithm.

Iterative Deeping A It is a modified version of A *, and uses less memory due to the smaller number of deployed nodes. It works faster than A * in the case of a successful heuristic choice. The result of the work is the shortest path.

Jump Point Search The youngest of these algorithms was introduced in 2011. It is an improved A *. JPS accelerates the search path, "jumping" over many places that should be reviewed. Unlike similar algorithms, JPS requires pretreatment or additional memory costs.

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