Hardness of Virtual Network Embedding with Replica Selection

Abstract: Efficient embedding virtual clusters in physical network is a challenging problem. In this paper we consider a scenario where physical network has a structure of a balanced tree. This assumption is justified by many real- world implementations of datacenters. We consider an extension to virtual cluster embedding by introducing replication among data chunks. In many real-world applications, data is stored in distributed and redundant way. This assumption introduces additional hardness in deciding what replica to process. By reduction from classical NP-complete problem of Boolean Satisfia- bility, we show limits of optimality of embedding. Our result holds even in trees of edge height bounded by three. Also, we show that limiting repli- cation factor to two replicas per chunk type does not make the problem simpler.