The virtualization of network functions enables innovative new network services which can be deployed quickly and at low cost on (distributed) cloud computing infrastructure. This paper initiates the algorithmic study of the fundamental underlying problem of how to efficiently route traffic through a given set of Virtualized Network Functions (VNFs). We are given a link-capacitated network G=(V,E) , a source-destination pair (s,t)∈V2 and a set of waypoints W⊂V (the VNFs). In particular, we consider the practically relevant but rarely studied case of bidirected networks. The objective is to find a (shortest) route from s to t such that all waypoints are visited. We show that the problem features interesting connections to classic combinatorial problems, present different algorithms, and derive hardness results.

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