Bidirectional Search for Longest Paths: Case for Front-to-Front Heuristics

2026-06-06 · Source: cs.AI updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

BiXDFBnB is a novel bidirectional depth-first branch-and-bound algorithm designed for Generalized Longest Simple Path (GLSP) problems, including Longest Simple Path (LSP), Snakes, and Coil-in-the-Box (CIB). It adapts the Single-Frontier Bidirectional Search (SFBDS) framework, originally for shortest-path problems, to maximization problems by operating on paired states. This approach naturally integrates front-to-front (F2F) heuristics, eliminating the high overhead typically associated with bidirectional frontier management. The algorithm employs a simultaneous Cartesian node expansion strategy to guarantee valid path meetings and effectively prunes the search space using F2F bounds. Empirical evaluation across grids, mazes, and CIB domains demonstrates that BiXDFBnB F2F significantly reduces node expansions, often by up to two orders of magnitude, and frequently improves overall runtime compared to unidirectional search, A*, and XMM, while mitigating exponential memory constraints.

Key takeaway

For AI scientists and research scientists working on NP-hard longest-path problems, BiXDFBnB offers a superior approach. You should consider integrating this bidirectional depth-first branch-and-bound algorithm to overcome memory limitations and achieve significant performance gains. Its efficient front-to-front heuristic pruning and simultaneous expansion strategy can drastically reduce computation time and node expansions for GLSP variants like LSP and Snake-in-the-Box.

Key insights

BiXDFBnB uses paired-state bidirectional search and front-to-front heuristics to efficiently solve complex longest-path problems.

Principles

• Paired-state search avoids frontier-matching overhead.
• F2F heuristics enable powerful pruning in MAX problems.
• Simultaneous expansion guarantees path validity.

Method

BiXDFBnB uses a depth-first branch-and-bound approach, recursively evaluating paired forward and backward states. It prunes branches based on F2F heuristic upper bounds and expands simultaneously via Cartesian product of successors.

In practice

• Apply to Longest Simple Path (LSP) problems.
• Use for Snake-in-the-Box and Coil-in-the-Box.
• Adapt for other constrained maximization problems.

Topics

• Bidirectional Search
• Longest Path Problems
• Front-to-Front Heuristics
• Depth-First Branch-and-Bound
• Generalized Longest Simple Path
• NP-hard Problems

Code references

• tzurshubi/BiHS

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.