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

2026-06-04 · Source: Artificial Intelligence · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

A new algorithm, BiXDFBnB, is proposed for solving Generalized Longest Simple Path (GLSP) problems, which are maximization (MAX) problems. This algorithm adapts the Single-Frontier Bidirectional Search (SFBDS) framework, previously used for shortest-path (MIN) problems, to the GLSP setting. BiXDFBnB leverages SFBDS's inherent operation on paired states to enable efficient front-to-front (F2F) heuristic evaluation, thereby circumventing the high overhead typically associated with bidirectional frontier management. The algorithm is designed to handle overlapping constraints effectively. Empirical evaluation demonstrates that BiXDFBnB frequently reduces the number of node expansions across various longest-path problems, including Longest Simple Path (LSP), Snakes, and Coil-in-the-Box (CIB), and in some cases, also improves overall runtime.

Key takeaway

For AI scientists working on complex pathfinding or optimization problems, particularly those involving longest paths, you should evaluate BiXDFBnB. This algorithm offers a novel approach to reduce computational effort by efficiently integrating front-to-front heuristics, potentially improving runtime for problems like Longest Simple Path, Snakes, or Coil-in-the-Box. Consider prototyping with BiXDFBnB to assess its performance gains on your specific maximization tasks, especially where traditional bidirectional search overhead is a concern.

Key insights

Adapting Single-Frontier Bidirectional Search to maximization problems enables efficient front-to-front heuristics.

Principles

• Bidirectional search can reduce effort for backward-amenable problems.
• Front-to-front heuristics can reduce node expansions.
• Paired-state operations can avoid F2F overhead.

Method

BiXDFBnB adapts SFBDS for GLSP, using paired states for natural F2F heuristic evaluation, efficiently handling overlapping constraints in depth-first branch-and-bound.

In practice

• Apply BiXDFBnB to Longest Simple Path problems.
• Consider BiXDFBnB for Snakes and Coil-in-the-Box tasks.

Topics

• Bidirectional Search
• Longest Path Problems
• Heuristic Search
• Branch-and-Bound
• SFBDS Framework
• Optimization Algorithms

Best for: Research Scientist, AI Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Artificial Intelligence.