Network slicing across multiple administrative domains raises two coupled challenges: enforcing slice-specific trust constraints while enabling fast online admission and placement decisions. This paper considers a multi-domain infrastructure where each slice request specifies a VNF chain, resource demands, and a set of (un)trusted operators, and formulates the problem as a Node-Link (NL) integer program to obtain an optimal benchmark, before proposing a Path-Link (PL) formulation that pre-generates trust and order-compliant candidate paths to enable real-time operation. To mitigate congestion, resource prices are made dynamic using a Kleinrock congestion function, which inflates marginal costs as utilization approaches capacity, steering traffic away from hotspots. Extensive simulations across different congestion levels and slice types show that: (i) PL closely tracks NL with negligible gaps at low load and moderate gaps otherwise, (ii) dynamic pricing significantly reduces blocking under scarce resources, and (iii) PL reduces computation time by about 3x-6x compared to NL, remaining within a few seconds even at high load. These results demonstrate that the proposed PL and dynamic pricing framework achieves near-optimal performance with practical runtime for online multi-domain slicing under trust constraints.

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