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Within the Advanced Configuration and Power Interface (ACPI) framework,\n                    <jats:italic>Dynamic Power Management<\/jats:italic>\n                    (DPM) and\n                    <jats:italic>Dynamic Voltage and Frequency Scaling<\/jats:italic>\n                    (DVFS) reduce static and dynamic energy consumption; however, applying them to dependent-task workflows under deadline constraints introduces complex trade-offs among static, frequency-independent, and frequency-dependent energy components. To address these challenges, this article presents\n                    <jats:italic>Scheduling for Energy Saving<\/jats:italic>\n                    (\n                    <jats:italic>S4eS<\/jats:italic>\n                    ), a compile-time energy-aware scheduling algorithm with provably lower-bound time complexity.\n                    <jats:italic>S4eS<\/jats:italic>\n                    integrates a DPM module that selects compute nodes for switch-off using a theory-grounded criterion based on frequency-independent energy, and a DVFS module that determines task-level frequency scaling to maximize net energy savings while respecting deadlines. Theoretical analysis establishes the lower-bound complexity of both modules, ensuring scalability for large-scale environments. Experimental results on synthetic and real-world workflows show that\n                    <jats:italic>S4eS<\/jats:italic>\n                    achieves average energy savings of 20.08%, outperforming related methods while maintaining reduced computational overhead.\n                  <\/jats:p>","DOI":"10.1007\/s10586-026-06216-4","type":"journal-article","created":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T17:37:54Z","timestamp":1781631474000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["S4eS: a lower-bound complexity scheduling algorithm for energy savings on DVFS-enabled platforms"],"prefix":"10.1007","volume":"29","author":[{"given":"Tarek","family":"Hagras","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gamal A.","family":"El-Sayed","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,16]]},"reference":[{"key":"6216_CR1","unstructured":"International Energy Agency: Data Centres and Data Transmission Networks. 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