Computing Power Network (CPN) unifies wide-area computing resources through coordinated network control, while cloud-native abstractions enable flexible resource orchestration and on-demand service provisioning atop the elastic infrastructure CPN provides. However, current approaches fall short of fully integrating computing resources via network-enabled coordination as envisioned by CPN. In particular, optimally mapping services to an underlying infrastructure to maximize resource efficiency and service satisfaction remains challenging. To overcome this challenge, we formally define the service mapping problem in CPN, establish its theoretical intractability, and identify key challenges in practical optimization. We propose Adaptive Bilevel Search (ABS), a modular framework featuring (1) graph partitioning-based reformulation to capture variable coupling, (2) a bilevel optimization architecture for efficient global exploration with best-response solving of local subproblems, and (3) fragmentation-aware evaluation for long-term performance guidance. Implemented using distributed particle swarm optimization, ABS is extensively evaluated across diverse CPN scenarios, consistently outperforming existing approaches. Notably, in complex scenarios, ABS achieves up to 73.2% higher computing resource utilization and a 60.2% higher service acceptance ratio compared to the best-performing baseline.

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