2024/11/27 by Shreya Gupta, Gupta, Shreya, Boyang Huang +3
Business, Management and Accounting · Economics, Econometrics and Finance · #Banking stability, regulation, efficiency #Computational Complexity (cs.CC) #Digital Platforms and Economics #Economic Theory and Policy #FOS: Computer and information sciences
paper · pdf · doi:10.48550/arxiv.2411.18137
openalex publication_date 2024/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Coin Change problem, also known as the Change-Making problem, is a well-studied combinatorial optimization problem, which involves minimizing the number of coins needed to make a specific change amount using a given set of coin denominations. A natural and intuitive approach to this problem is the greedy algorithm. While the greedy algorithm is not universally optimal for all sets of coin denominations, it yields optimal solutions under most real-world coin systems currently in use, making it an efficient heuristic with broad practical applicability. Researchers have been studying ways to determine whether a given coin system guarantees optimal solutions under the greedy approach, but surprisingly little attention has been given to understanding the general computational behavior of the greedy algorithm applied to the coin change problem. To address this gap, we introduce the Greedy Coin Change problem and formalize its decision version: given a target amount W and a set of denominations C, determine whether a specific coin is included in the greedy solution. We prove that this problem is \mathbf P-complete under log-space reductions, which implies it is unlikely to be efficiently parallelizable or solvable in limited space.