Validation and Implementation of ILBFS

TL;DR

The paper addresses the challenge of memory-efficient yet difficult-to-implement RBFS by introducing Iterative Linear Best-First Search (ILBFS) as a simpler, iterative alternative that preserves linear-space search. It presents the first ILBFS implementation, validates equivalence with RBFS in memory usage and node-expansion order, and analyzes key implementation details such as tie-breaking and explicit removal from the open list using collapse/restore memory management ($O(n)$-like behavior). The study provides empirical results on the 8-puzzle, showing that ILBFS maintains linear memory and, with correct tie-breaking, matches RBFS in node expansion order, albeit with up to ~3x slower runtime due to open-list maintenance. Overall, ILBFS is demonstrated as an accessible stepping stone that facilitates the adoption of RBFS-like algorithms while preserving memory efficiency. These findings support using ILBFS as a pedagogical and practical bridge toward RBFS for researchers and practitioners.

Abstract

Recursive Best-First Search (RBFS) is a heuristic search algorithm known for its efficient memory usage compared to traditional best-first search methods like A*. Despite its theoretical advantages, RBFS is complex and difficult to teach and to implement, limiting its widespread adoption. To address these challenges, Iterative Linear Best-First Search (ILBFS) was introduced as a simpler, more intuitive alternative while maintaining the linear space complexity of RBFS. In this paper, we present the first implementation of ILBFS, validate its memory usage and node expansion order claims, and explore critical aspects of its implementation, such as tie-breaking and node deletion mechanisms. Our findings demonstrate that ILBFS can serve as an effective stepping stone for researchers and practitioners looking to use memory efficient best-first search methods, facilitating the adoption of RBFS-like algorithms.

Figures (2)

• Figure 1: Example scenario where the ILBFS algorithm could result in an infinite loop for certain tie-breakings. The algorithm could potentially switch back and forth between a and b (left and right).
• Figure 2: Comparison of Average Memory Usage by Solution Length for RBFS and ILBFS Variants.