Novel network infrastructures require the distribution of computing and network resource control to meet stringent requirements in terms of latency, reliability and bitrate. 5G systems bring a key novelty in systems design that it the 'network slice'as a new resource provisioning entity. A network slice is meant to serve end-to-end services as a composition of different network and system resources as radio, link, storage and computing resources. Conventionally, each resource is managed by a distinct decision-maker, platform, provider, orchestrator or controller. Naturally, centralized slice orchestration approaches are proposed in the literature, where a multi-domain orchestrator allocates the resources, for instance using a multi-resource allocation rule. Nonetheless, while simplifying the algorithmic approach, centralization can come at the expense of scalability and performance. In this paper, we propose new ways to distribute the slice multi-resource resource allocation problem, using cascade and parallel resource allocations that are functionally compatible with novel software platforms. We also show how to adapt the proposed algorithms to make them able to guarantee service level agreements on the minimum resource needed, and to take into account deadline priority policy scheduling. We provide an exhaustive analysis of the advantages and disadvantages of the different approaches, including a numerical analysis for a realistic setting.