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# The 5 Most Powerful Pathfinding Algorithms

Pathfinding algorithms are a crucial component in a wide range of applications, from video games to robotics and logistics. They enable machines to navigate efficiently through complex environments by *finding the shortest or most efficient path between two points*.

##### What are Pathfinding Algorithms?

The goal of a pathfinding algorithm is to explore a graph to find the optimal path from a starting point to a destination point, while considering obstacles, barriers, and other constraints (see Figure 3 as an example)

Over the years, numerous pathfinding algorithms have been developed, each with its own advantages and limitations. Some of the most well-known algorithms include Dijkstra’s algorithm, A* algorithm, the breadth-first search algorithm and the depth-first search algorithm; these last two have been previously discussed in our graph traversal algorithms article. Check out the following links for more on the broader graph data sceince or graph algorithms topics. The various algorithms mentioned above differ in their approach to exploring the graph and their use of heuristic information to guide the search.

In this article, we provide an overview of the most common pathfinding algorithms, their strengths and weaknesses, and their use cases. We explore how these algorithms work and provide examples of their application in real-world scenarios. By the end of this article, readers will have a better understanding of how pathfinding algorithms work, and which algorithm might be the best fit for a particular use case.

#### Top 5 Pathfinding Algorithms

##### Cycle detection

The Cycle Detection problem seeks to find all the cycles (loops) in a graph, that is, they must be paths that start and end at the same vertex but otherwise never visit any vertex twice.

Cycle detection is used to determine whether a loop exists in a set of connected elements or nodes. In the case of a graph network, a loop exists when a node is connected to itself, or when a set of nodes create a closed loop.

Overall, cycle detection algorithms are used to prevent infinite loops and ensure that a program or graph operates as expected. By detecting cycles, they enable efficient and safe navigation through a set of connected elements or nodes.

###### How does it work?

One way to detect cycles is to use the “depth-first search” algorithm.

This algorithm works by exploring all possible paths from a starting node until it reaches a dead-end or a previously visited node. During this exploration, the algorithm marks each visited node as “visited”. If the algorithm encounters a node that has already been visited and is not the immediate parent node, this indicates the presence of a cycle. Figure 1 graphically explains how the algorithm work.

##### Dijkstra’s algorithm

Dijkstra’s algorithm is used to find the shortest path between two points in a graph by evaluating each node in the graph and calculating the distance from the starting node to each node in the graph.

We start by evaluating the starting node and assigning it a distance of 0. We evaluate each of the neighboring nodes and calculate the distance to each node. The algorithm selects the node with the smallest distance and adds it to the list of visited nodes.

Afterwards we evaluate the neighboring nodes of the newly added node and calculate the distances. The algorithm adds the node with the smallest distance to the list of visited nodes and continues this process until it reaches the destination node. As the algorithm evaluates each node, it keeps track of the distances and the path taken to reach each node. If a node is revisited with a shorter distance, the algorithm updates the distance and path to reflect the better route.

Dijkstra’s algorithm is widely used in navigation systems, logistics, and transportation planning: by efficiently evaluating each node and keeping track of the path taken, it helps find the optimal route between two points in a graph.

###### How does it work?

The algorithm starts by evaluating the starting node and assigning it a distance of 0. It then evaluates each of the neighboring nodes and calculates the distance to each node. The algorithm selects the node with the smallest distance and adds it to the list of visited nodes. It evaluates the neighboring nodes of the newly added node and calculates their distances.

It adds the node with the smallest distance to the list of visited nodes and continues this process until it reaches the destination node. As the algorithm evaluates each node, it keeps track of the distances and the path taken to reach each node. If a node is revisited with a shorter distance, the algorithm updates the distance and path to reflect the better route. In the Figure 2, the shortest distance from node A to node G is the path A-B-D-E-G.

##### A* algorithm

A* algorithm (pronounced “A-star”) is a graph traversal and path search algorithm that uses heuristics to estimate the most efficient path.

The A* algorithm is a powerful tool for finding the shortest path between two points in a graph by exploring the graph. It uses a heuristic function to guide the search towards the destination. The heuristic function estimates the distance between the current node and the destination node and it is what makes the A* algorithm different from other pathfinding algorithms. This helps guide the algorithm towards the destination more efficiently, as it prioritizes nodes that are closer to the destination.

The A* algorithm is widely used in robotics, video games, and other applications where efficient navigation is required.

**How does it work?**

The algorithm starts by evaluating the starting point and calculating its “score”. This score includes the distance from the starting point to the current node, as well as an estimate of the remaining distance to the destination using a heuristic function.

Next, the algorithm explores the neighboring nodes of the current node and calculates their scores. It then selects the node with the lowest score and adds it to the list of visited nodes. The algorithm continues this process, evaluating nodes and adding them to the visited list, until it reaches the destination node.

Along the way, the algorithm keeps track of the path taken and the scores of the visited nodes. If a node is revisited with a lower score, the algorithm updates the node’s score and path to reflect the better route. Figure 3 visually shows how the A* algorithm finds the optimal path from the starting point to the destination.

##### Maximum Flow algorithm

The Maximum Flow algorithm is used to find the maximum amount of “flow” that can pass through a graph network of connected nodes or vertices.

The Maximum Flow algorithm can be useful in a variety of applications, such as optimizing transportation networks, traffic flow, or water management systems, finding the maximum amount of liquid that can pass through the pipes. By finding the maximum flow through a network, it can help identify areas where congestion or blockages are occurring and help optimize the flow to improve efficiency.

**How does it work?**

We assign capacities to the relationships between the nodes, which represent the maximum amount of flow that can pass through each relationship. The algorithm then attempts to find the path with the highest flow from a source node to a sink node.

To do this, we start by assigning an initial flow of zero to all the edges. We then find a path from the source node to the sink node, where the flow on each relationship is less than the capacity of that relationship. The algorithm increases the flow on each relationship along the path by the maximum amount possible, based on the capacities of the edges.

We continue finding paths and increase the flow until we can no longer find any paths from the source node to the sink node. At this point, we have found the maximum flow through the network. Figure 4 visually shows step by step how the algorithm work with an example, aiming at finding the maximum amount of flow between nodes A and G.

##### Minimum Spanning Trees algorithm

The Minimum Spanning Tree algorithm is used in weighed networks to find the shortest, most efficient way to connect all the nodes in a graph: it finds the minimum set of edges that connects all the nodes, without creating any loops or cycles.

The Minimum Spanning Tree algorithm can be used to optimize communication networks or designing transportation routes, as it identifies the most efficient way to connect different parts of a network or system.

**How does it work?**

We start by selecting any node in the graph and adding it to a decision tree. We then find the relationship with the smallest weight that connects the tree to a new node and adds that node and its connecting relationship to the tree. The algorithm continues this process, adding nodes and edges to the tree until all the nodes in the graph are connected.

As the algorithm adds relationship to the tree, it keeps track of the total weight of the tree. The goal is to find the minimum weight tree that connects all the nodes. Figure 5 shows in a graph example the minimum relationships connecting all nodes.

#### Conclusions

In conclusion, pathfinding algorithms are powerful tools for finding optimal paths in a graph network. Whether it is finding the shortest path between two points or navigating through a complex maze, these algorithms provide efficient and effective solutions.

The algorithms mentioned above have numerous applications in fields such as transportation, robotics, and logistics (e.g. A*, Dijkstra’s algorithms), providing a way to optimize the flow of traffic (e.g. Maximum Flow algorithm), identify the most efficient way to connect nodes in a graph (e.g. Minimum Spanning Tree algorithm). Overall, pathfinding algorithms offer numerous benefits and are widely used in a variety of fields.

As technology continues to advance, these algorithms will continue to play an increasingly important role in optimizing navigation, transportation, and resource allocation.

For a deeper dive on these and other algorithms discussed here as well as more advanced graph topics, check out our additional articles on the subject:

- Graph Traversal Algorithms (a.k.a Pathfinding algorithms)
- Closeness Centrality
- Degree Centrality
- Betweenness Centrality
- PageRank
- Graph Embeddings (for more on graph embedding algorithms)

Also read this related article on graph analytics for more on analytics within the graph database context.

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- What is Hume (GraphAware)?

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