Efficient Pathfinding on Grid Maps: Comparative Analysis of Classical Algorithms and Incremental Line Search

Pathfinding on grid maps is a cornerstone problem in robotics, autonomous navigation, and game develop- ment. Classical algorithms such as A*, Dijkstra's, and Breadth-First Search (BFS) are known for their ability to guarantee optimal solutions, while others like Depth-First Search (DFS) and Greedy Best-First Search prioritize speed over optimality. However, these algorithms can be computationally inefficient in large-scale or real-time environments. This paper introduces Incremental Line Search (ILS), a novel optimization strategy that incorporates Bresenham's line algorithm to define a dynamically adjustable corridor between the start and goal points. By restricting the search to this focused region and expanding only when necessary, ILS significantly reduces computational overhead while preserving optimality in cases where the underlying algorithm guarantees it, and delivering near-optimal paths in others. Extensive experiments were conducted to evaluate the performance of ILS across various metrics, including execution time, visited nodes, and path length, over a total of 6000 grid maps generated with obstacle densities of 10%, 20%, and 30%. On average, ILS achieved a 87.31% reduction in execution time and a 71.44% reduction in node expansions compared to their standard counterparts. Despite these improvements, path quality was preserved: Best-First Search showed a 63.24% improvement in path length, while DFS improved by 86.70%, confirming that ILS not only accelerates computation but also leads to smoother paths in most scenarios. These findings affirm ILS as a highly effective and resilient optimization technique for demanding pathfind- ing tasks. Its dynamic adaptability renders ILS especially suitable for applications in robotics, autonomous systems, and resource-constrained environments, setting the stage for future advancements in multi-agent navigation and real-time optimization.