Hardness of Virtual Network Embedding with Replica Selection

TL;DR

This paper investigates the complexity of embedding virtual clusters with data replication in tree-structured data center networks, demonstrating the problem's NP-hardness even under simplified conditions.

Contribution

It extends virtual network embedding complexity analysis by incorporating data replication, proving NP-hardness in balanced tree networks with limited replicas.

Findings

Embedding with replication is NP-hard even in trees of height three.

Limiting to two replicas per data chunk does not reduce complexity.

Optimal embedding decision is computationally intractable under these conditions.

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.