What are pathfinding algorithms?
by Stephen M. Walker II, CoFounder / CEO
What are pathfinding algorithms?
Pathfinding algorithms are used to find the shortest, fastest, or most efficient route between two points in a graph or map. They typically involve traversing the graph by following edges and updating nodetonode distance estimates as new information is discovered. Some common pathfinding algorithms include Dijkstra's algorithm, A* search algorithm, breadthfirst search (BFS), depthfirst search (DFS), and greedy bestfirst search (GBFS).
Pathfinding algorithms are commonly used in various applications such as navigation systems, routing protocols for computer networks, and game AI for determining optimal paths or strategies. They can help improve efficiency, reduce travel times, minimize energy consumption, or optimize resource allocation by finding the most suitable routes between different locations or points of interest.
Different pathfinding algorithms have varying strengths and weaknesses in terms of their accuracy, computational complexity, memory requirements, and adaptability to dynamic changes or disturbances in the environment. Researchers must carefully consider these factors when selecting an appropriate algorithm for specific pathfinding tasks or applications.
What are some common pathfinding algorithms and how do they work?
Pathfinding algorithms are used to find the shortest or most efficient route between two points in a graph or map. Some common pathfinding algorithms include:

Dijkstra's algorithm — This is a classic greedy algorithm that computes the shortest distance from a source node to all other nodes in an unweighted or positive weighted graph. It iteratively updates the minimum distance estimates for each node, starting from the source node and traversing outwards along the edges of the graph until reaching the target node. The algorithm maintains a priority queue of nodes with their current minimum distance estimates and continually selects the node with the smallest estimate to explore its adjacent neighbors. Dijkstra's algorithm has a time complexity of
O(n log n)
for dense graphs andO(m + n log n)
for sparse graphs, wheren
is the number of nodes andm
is the number of edges in the graph. 
A* search algorithm — This is an extension of Dijkstra's algorithm that incorporates a heuristic function to guide the search towards the target node more efficiently. The A* algorithm maintains a priority queue of nodes with their estimated total costs (i.e., the sum of the minimum distance estimates and the heuristic cost estimates) and continually selects the node with the smallest estimated total cost to explore its adjacent neighbors. By choosing nodes that are likely to be closer to the target, A* search can often find the optimal path more quickly than Dijkstra's algorithm, especially in cases where the graph is large or the heuristic function is highly informative. The time complexity of A* search depends on the specific implementation and the choice of heuristic function but generally ranges from
O(n log n)
toO(m + n log n)
. 
Breadthfirst search (BFS) — This is a simple algorithm that explores the graph level by level, starting from the source node and traversing outwards along the edges of the graph until reaching the target node. BFS maintains a queue of nodes to visit and continually dequeues the next node to explore its adjacent neighbors. While BFS guarantees finding the shortest path in unweighted graphs, it can be computationally expensive for dense graphs with many levels or large numbers of nodes. The time complexity of BFS is
O(n + m)
for all graph types. 
Depthfirst search (DFS) — This is another simple algorithm that explores the graph by traversing deep into the tree structure before backtracking to explore alternative paths, starting from the source node and recursively visiting its adjacent neighbors. DFS maintains a stack of nodes to visit and continually pops the next node to explore its adjacent neighbors. While DFS can be useful for finding connected components or traversing treelike structures, it does not guarantee finding the shortest path between two points in a graph. The time complexity of DFS is
O(n + m)
for all graph types. 
Greedy bestfirst search (GBFS) — This algorithm iteratively selects the node with the smallest estimated remaining cost (i.e., the difference between the target distance and the current minimum distance estimate) to explore its adjacent neighbors. GBFS maintains a priority queue of nodes with their current minimum distance estimates and continually selects the node with the smallest estimated remaining cost to explore its adjacent neighbors. While GBFS can often find good solutions quickly, it does not guarantee finding the optimal path between two points in a graph and may suffer from suboptimal or even incorrect results if the heuristic function is too aggressive or misleading. The time complexity of GBFS depends on the specific implementation but generally ranges from
O(n + m)
toO(m log m)
.
These pathfinding algorithms offer various tradeoffs in terms of their accuracy, efficiency, and robustness to different types of graphs and heuristic functions. Researchers must carefully consider these factors when selecting an appropriate algorithm for specific pathfinding tasks or applications.
What are some common issues with pathfinding algorithms?
Pathfinding algorithms can encounter several issues that may affect their accuracy, efficiency, or robustness in specific contexts. Some common problems include:

Incomplete or incorrect information — In many realworld applications, the graph representing the environment may be partially known or contain erroneous data about edge weights or distances between nodes. This can lead to suboptimal or even incorrect pathfinding results if the algorithm relies too heavily on these inaccurate inputs.

Dynamic changes or disturbances — The environment may undergo continuous fluctuations or unpredictable disruptions that alter the structure of the graph and affect the validity of previously computed paths. This requires the algorithm to adapt its search strategy and update its distance estimates in realtime to maintain optimal performance.

Computational complexity and scalability — Some pathfinding algorithms have high time or space complexity, which can limit their applicability to large graphs or complex environments with many nodes and edges. This may require researchers to develop more efficient data structures or approximate techniques for handling these computational challenges.

Heuristic function selection and tuning — In algorithms like A* search that use heuristic functions to guide the search towards the target node, selecting an appropriate function and finetuning its parameters can be a challenging task that requires domain knowledge or empirical testing. An improper choice of heuristic function may lead to suboptimal results or even cause the algorithm to fail in certain cases.

Pathfinding in discrete spaces — In some applications, the environment is represented as a discrete grid or lattice rather than a continuous graph, which can introduce additional complexities and challenges for pathfinding algorithms. This requires researchers to develop specialized techniques for traversing these discrete spaces and handling obstacles, dead ends, or other irregularities within the map.
These issues highlight the importance of carefully selecting an appropriate pathfinding algorithm and tailoring its implementation to suit the specific requirements and constraints of the target application or environment.