# Iterative Budgeted Exponential Search

## TL;DR

This paper introduces a new iterative search framework that significantly reduces the number of node expansions in heuristic search algorithms, improving efficiency from exponential or quadratic to near-linear logarithmic in the optimal solution cost.

## Contribution

The paper presents a novel iterative expansion control framework that yields new graph and tree search algorithms with improved theoretical bounds and practical robustness.

## Key findings

- Algorithms achieve $O(n \, \log C)$ expansions.
- New algorithms outperform existing methods in challenging scenarios.
- No overhead in tree search scenarios where IDA* performs well.

## Abstract

We tackle two long-standing problems related to re-expansions in heuristic search algorithms. For graph search, A* can require $\Omega(2^{n})$ expansions, where $n$ is the number of states within the final $f$ bound. Existing algorithms that address this problem like B and B' improve this bound to $\Omega(n^2)$. For tree search, IDA* can also require $\Omega(n^2)$ expansions. We describe a new algorithmic framework that iteratively controls an expansion budget and solution cost limit, giving rise to new graph and tree search algorithms for which the number of expansions is $O(n \log C)$, where $C$ is the optimal solution cost. Our experiments show that the new algorithms are robust in scenarios where existing algorithms fail. In the case of tree search, our new algorithms have no overhead over IDA* in scenarios to which IDA* is well suited and can therefore be recommended as a general replacement for IDA*.