Fast greedy algorithm improves airplane refueling scheduling accuracy
A Fast Greedy Algorithm with a 0.45 Approximation Guarantee for the Airplane Refueling Problem
Data Structures and AlgorithmsDiscrete Mathematics
Summary
The airplane refueling problem involves deciding the order and timing for mid-air refueling to keep planes flying efficiently. The authors studied a simple rule-based approach that quickly decides the refueling schedule. They showed this fast method guarantees a solution close to optimal better than before, with improved mathematical backing. They also found a way to run this method using clever data structures that keep the calculations quick and memory-friendly.
What this means in practice
- •For logistics planners: Generate near-optimal in-flight refueling schedules rapidly to improve fuel use and timing in complex air operations.
- •For algorithm engineers: Implement a fast baseline algorithm for the airplane refueling problem that integrates efficiently with larger optimization frameworks handling large inputs.
Authors
Oleg Lomachenko, Arnold Enikeev
Abstract
We study a natural greedy algorithm for the Airplane Refueling Problem (ARP), based on a well-known priority rule. We show that this algorithm achieves an approximation guarantee of $9/20$, noticeably improving the previously known $1/12$ guarantee for a fast algorithm. We also show that the same priority rule can be implemented in $O(n\log n)$ time and $O(n)$ space using a dynamic convex-hull data structure. These results provide a worst-case approximation guarantee for an existing greedy priority rule and establish an efficient implementation. In the real-RAM model, the running-time bound is independent of the magnitude of the processing times. The resulting method is also suitable as a fast primal routine inside more complex exact and approximation algorithms for large instances. These results narrow the gap between theoretically strong but complex approximation schemes and lightweight algorithms that can be used directly in computational pipelines. The algorithm combines a simple selection rule with a provable performance bound, making it a useful baseline for further algorithmic studies of ARP.