Authors - Nikolaos Lazaropoulos, Ioannis Vaxevanakis, Ioannis Sigalas, Ioannis Lamprou, Vassilis Zissimopoulos Abstract - Cloud Native Functions (CNFs) support automated and dynamic orchestration of containerized network services, replacing traditional hardware-based architectures. These deployments consist of modular microservices that enable elastic scalability and collaborative service delivery. This paper presents an approximation framework for capacity constrained CNF resource allocation, modeled as variants of the Group Generalized Assignment Problem (Group GAP). The main contributions are: (1) a 1 2 -approximation algorithm for CNF placement when each function’s footprint is at most half the cluster capacity and (2) a 1 2 (1 − e−1/d)-approximation for shared microservices among multiple CNFs, where d is the degree of sharing, supported by experimental evaluation of the algorithm relative error.
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