Best-first search algorithms such as A* and Weighted A* are widely used tools. However, their high memory requirements often make them impractical for memory-constrained applications, such as on-board planning for interplanetary rovers, drones, and embedded systems. One popular strategy among memory-efficient approaches developed to address this challenge is to eliminate or sparsify the Closed list, a structure that tracks states explored by the search. However, such methods often incur substantial overhead in runtime, requiring recursive searches for solution reconstruction. In this work, we propose Attractor-based Closed List Search (ACLS), a novel framework that sparsely represents the Closed list using a small subset of states, termed attractors. ACLS intelligently identifies attractor states in a way that enables efficient solution reconstruction while preserving theoretical guarantees on the quality of the solution. Furthermore, we also introduce a lazy variant, Lazy-ACLS, which defers the computation of attractor states until necessary, substantially improving planning speed. We demonstrate the efficacy of ACLS used in conjunction with A*, Weighted A*, and Dijkstra’s searches across multiple domains including 2D and 3D navigation, Sliding Tiles, and Towers of Hanoi. Our experimental results demonstrate that ACLS significantly reduces memory usage, maintaining only 9% of the states typically stored in a Closed list, while achieving comparable planning times and outperforming state-of-the-art approaches. Source code can be found at github.com/alvin-ruihua-zou/ACLS.