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

2026-06-04

AI Summary

This work addresses the inefficiency of traditional bidirectional heuristic search in longest-path maximization problems, which stems from the high computational cost of front-to-front heuristic evaluation. To overcome this challenge, we propose BiXDFBnB, an algorithm that extends the single-front bidirectional search framework to the generalized longest simple path problem for the first time. By integrating a depth-first branch-and-bound strategy, BiXDFBnB naturally accommodates front-to-front heuristic estimation while effectively handling overlapping constraints, substantially reducing both the search space and the number of node expansions. Experimental results demonstrate that BiXDFBnB significantly decreases node expansions on benchmark problems—including the longest simple path, Snakes, and Coil-in-the-Box—and achieves substantial runtime improvements across multiple instances.

Abstract

Bidirectional heuristic search can potentially reduce search effort for problems amenable to backward search. Therein, it is well-known that front-to-front heuristics can reduce the number of node expansions, but their overhead is so high that overall runtime almost always increases. We propose BiXDFBnB, a bidirectional depth-first branch-and-bound algorithm that adapts the Single-Frontier Bidirectional Search (SFBDS) framework - originally developed for shortest-path (MIN) problems - to the Generalized Longest Simple Path (GLSP) setting. Because SFBDS inherently operates on paired states, front-to-front (F2F) heuristic evaluation arises naturally and avoids the overhead typically associated with bidirectional frontier management. We show that this adaptation can be successfully applied to maximization (MAX) problems while efficiently handling overlapping constraints. BiXDFBnB is applied to several types of longest-path problems: Longest Simple Path (LSP), Snakes, and Coil-in-the-Box (CIB). Empirical evaluation shows that the new algorithm frequently reduces the number of node expansions and, in some cases, also improves overall runtime.

Problem

• bidirectional search
• longest path
• front-to-front heuristics
• branch-and-bound
• combinatorial optimization

Innovation

• Bidirectional Search
• Front-to-Front Heuristic
• Branch-and-Bound
• Longest Path Problem
• Single-Frontier Bidirectional Search