20 IJSGS FUGUSAU VOL. 10 (4) WEBSITE: https://fugus-ijsgs.com.ng DOI: https://doi.org/10.57233/ijsgs.v10i4.730 ISSNp: 2488-9229; ISSNe: 3027-1118 INTERNATIONAL JOURNAL OF SCIENCE FOR GLOBAL SUSTAINABILITY (A PUBLICATION OF FACULTY OF SCIENCE, FEDERAL UNIVERSITY GUSAU, NIGERIA) Towards Enhancing Energy Consumption and Time Complexity of Combinatorial Algorithms for Solving the Knapsack Problem Saminu Isah Kanoma *1 , Bashar Bin Usman 2 Danlami Gabi 3 Abubakar Sidiq Nurudeen 4 Hassan Umar Suru 5 1 ICT Directorate Federal University Gusau, Zamfara State Nigeria 2 National Hajj Commission of Nigeria. 3 Department of Computer Science, Kebbi State University of Science and Technology Aliero, Kebbi State Nigeria. 4 Federal Polytechnic Kaltungo 5 Department of Computer Science, Kebbi State University of Science and Technology Aliero, Kebbi State Nigeria. *Corresponding Author: Email: sikanoma4u@gmail.com Received on: October, 2024 Revised and Accepted on: November, 2024 Published on: December, 2024 ABSTRACT The increasing demand for energy-efficient and time-optimized computational systems has driven research into combinatorial algorithms, particularly those used to solve the knapsack problem. The knapsack problem is one of the most significant in combinatorial optimization, which involves determining the optimal selection of items to include in a knapsack while adhering to specific constraints, such as weight or profit limits. This study compares the energy consumption and time complexity of the greedy and dynamic programming algorithms applied to this problem. Using power models to measure total energy consumption and execution time, the research reveals that the greedy algorithm is far more efficient, with negligible energy consumption across various scenarios. In contrast, the dynamic programming algorithm, while delivering accurate solutions, consumes more energy and takes longer due to its memory-intensive operations. These findings highlight the need to consider energy and time efficiency in algorithm design, contributing to more sustainable computing practices. Future research will explore larger datasets and focus on instruction-level energy analysis to optimize algorithm performance. Keywords: knapsack problem, power model, energy consumption, time complexity greedy and dynamic programming algorithms 1.0 INTRODUCTION The rapid advancement of computational technologies has revolutionized numerous domains further, particularly in the realm of combinatorial optimization. Modern combinatorial algorithms are integral to solving complex decision-making problems, offering innovative solutions to challenges in diverse applications, such as supply chain optimization, investment strategies, and energy-efficient computing (Ghosh & Sarkar, 2021). Among these, the knapsack problem continues to be a cornerstone in combinatorial optimization research due to its broad applicability in real-world scenarios. This problem entails selecting an optimal subset of items to maximize a specific objective, such as profit, while adhering to constraints like weight or capacity limits (Pisinger & Righini, 2022). Algorithms developed to address this problem utilize systematic approaches to evaluate possible solutions, ensuring robust and efficient outcomes. Recent advancements in algorithmic design and computational models have significantly enhanced their scalability and performance, further solidifying their importance in tackling real-world optimization challenges. However, the increasing complexity of these algorithms has led to a significant rise in their computational demands, including both time and energy consumption (Al-Enazi et al., 2021). As these algorithms grow in sophistication, so do their requirements for computational resources, making energy and time efficiency increasingly critical. In today’s technology-driven world, where sustainability is paramount, the energy and time efficiency of combinatorial algorithms presents a growing challenge. The growing emphasis on sustainable and energy-efficient computing practices has positioned the measurement and optimization of energy consumption in algorithms as a central theme in recent research (Jiang et al., 2023). Understanding the interplay between energy consumption and time complexity in combinatorial algorithms has become increasingly critical. This knowledge not only aids in optimizing algorithmic performance but also supports the development of sustainable and energy- efficient computing solutions. Recent advancements in energy profiling and computational modeling enable precise analysis, driving significant improvements in algorithm design and the underlying systems that execute them (Kumar et al., 2023)