arXiv:2606.25553v2 Announce Type: replace Abstract: Latency-sensitive Internet of Things (IoT) applications are increasingly deployed as interdependent microservices across heterogeneous edge-cloud infrastructures. Placing them under resource and network constraints is an NP-hard combinatorial optimisation problem. This study proposes EP-NCO, a graph-based neural combinatorial optimisation framework for service placement in compute continuum platforms. The objective accounts for execution latency, direct-link communication delay, and an approximate sharing of bandwidth among dependency flows that coexist in the resulting placement. Across held-out graph sizes generated by the same synthetic framework, the EP-NCO variant trained on Large instances with hard decoding achieved the lowest mean aggregate latency cost at every scale. It was 6.0%-12.5% lower than a genetic algorithm (GA), 14.4%-20.8% lower than particle swarm optimisation (PSO), and 1.2%-9.4% lower than the strongest reinforcement learning ablation. On Small instances, its mean cost was 10.5% below the best Gurobi solutions found and close to Gurobi's mean lower bound. The observed inference time of the EP-NCO variants was 0.88-1.03 s per instance, compared with 85-97 s for GA and PSO. As a result, the one-off training cost of the EP-NCO variant trained on Large instances with hard decoding is recovered after roughly 1,000 placements.