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We leverage flexibility from different parallelization degrees and frequency levels (DVFS) for the tasks, keeping application throughput constraints and communication bandwidth limitations while minimizing overall cost (including device\/edge resource energy, communication cost and cloud resource renting). We present several offline algorithmic solutions with a global view of the environment: an integer linear program (ILP) extending the crown scheduling approach for multi-layer distributed systems, a variant leveraging symmetries in application and system structure, and a greedy heuristic algorithm. We also expanded the problem formulation to consider the dynamic joining of application task graphs, introducing a dynamic approach based on the proposed ILP and greedy heuristic algorithm. Our experimental evaluation for several real-world and synthetic scenarios shows that the time required for solving the scheduling problem to cost-optimality by the ILP is feasible for nontrivial scenarios. The heuristic achieves about 3% worse cost efficiency on average, yet operates much faster (by 1\u20132 orders of magnitude), allowing to scale up the problem size more than the ILP approach. The symmetry-folding applied to the ILP approach improves its optimization time by about 1 order of magnitude, at the expense of less than a 5% increase in cost compared to a non-folded static ILP solution. The heuristic is likewise accelerated by leveraging symmetry, though to a minor extent. The dynamic incremental variant of the ILP approach reduces the long optimization time of the static ILP method with a minor cost penalty compared to a clean-slate offline solution.<\/jats:p>","DOI":"10.1007\/s10586-026-06234-2","type":"journal-article","created":{"date-parts":[[2026,7,25]],"date-time":"2026-07-25T18:52:11Z","timestamp":1785005531000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Mapping and scheduling swarms of moldable streaming applications for energy-efficient computing in the heterogeneous edge-cloud continuum"],"prefix":"10.1007","volume":"29","author":[{"given":"Sajad","family":"Khosravi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christoph","family":"Kessler","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sebastian","family":"Litzinger","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00f6rg","family":"Keller","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,7,25]]},"reference":[{"key":"6234_CR1","doi-asserted-by":"crossref","unstructured":"Asghar, H., Jung, E.: A survey on scheduling techniques in the edge cloud: Issues, challenges and future directions (2022). https:\/\/arxiv.org\/abs\/2202.07799","DOI":"10.21203\/rs.3.rs-1360831\/v1"},{"key":"6234_CR2","unstructured":"Gurobi Optimization, LLC: Gurobi Optimizer Reference Manual (2023). https:\/\/www.gurobi.com"},{"issue":"1","key":"6234_CR3","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1109\/TC.2019.2937867","volume":"69","author":"I Hautala","year":"2019","unstructured":"Hautala, I., Boutellier, J., Silv\u00e9n, O.: TTADF: Power efficient dataflow-based multicore co-design flow. 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