The rise of Software-Defined Networking (SDN) and Network Function Virtualization (NFV) introduces opportunities for service providers to reduce CAPEX/OPEX and to offer and quickly deploy novel network services. In particular, SDN and NFV enable the flexible composition of network functions, a generic service concept known as Network Service Chaining (NSC).However, the control of resources, management and configuration of network service chains is challenging. In particular, there typically exist multiple options on how an abstract network service can be decomposed into more refined, interconnected network functions. Moreover, efficient algorithms have to be devised to allocate the network functions. The underlying algorithmic problem can be seen as a novel generalization of the Virtual Network Embedding Problem (VNEP), where there exist multiple realization options. The joint optimization of decomposition and embedding has not been studied in the literature before. This paper studies the problem of how to optimally decompose and embed network services. In particular, we propose two novel algorithms to map NSCs to the network infrastructure while allowing possible decompositions of network functions. The first algorithm is based on Integer Linear Programming which minimizes the cost of the mapping based on the NSCs requirements and infrastructure capabilities. The second one is a heuristic algorithm to solve the scalability issue of the ILP formulation. It targets to minimize the mapping cost by making a reasonable selection of the network function decompositions. The experimental results indicate that considering network function decompositions at the time of the embedding significantly improves the embedding performance in terms of acceptance ratio while decreasing the mapping cost in the long run in both optimal and heuristic solutions.

Modern Internet applications, from HD video-conferencing to health monitoring and remote control of power-plants, pose stringent demands on network latency, bandwidth and availability. Centralized inter-domain routing brokers is an approach to support such applications and provide inter-domain guarantees, enabling new avenues for innovation. These entities centralize routing control for missioncritical traffic across domains, working in parallel to BGP. In this work, we propose using IXPs as natural points for stitching interdomain paths under the control of inter-domain routing brokers.To evaluate the potential of this approach, we first map the global substrate of inter-IXP pathlets that IXP members could offer, based on measurements for 229 IXPs worldwide. We show that using IXPs as stitching points has two useful properties. Up to 91% of the total IPv4 address space can be served by such inter-domain routing brokers when working in concert with just a handful of large IXPs and their associated ISP members. Second, path diversity on the inter-IXP graph increases by up to 29 times, as compared to current BGP valley-free routing. To exploit the rich path diversity, we introduce algorithms that inter-domain routing brokers can use to embed paths, subject to bandwidth and latency constraints. We show that our algorithms scale to the sizes of the measured graphs and can serve diverse simulated path request mixes. Our work highlights a novel direction for SDN innovation across domains, based on logically centralized control and programmable IXP fabrics.

The Virtual Network Embedding Problem (VNEP) captures the essence of many resource allocation problems. In the VNEP, customers request resources in the form of Virtual Networks. An embedding of a virtual network on a shared physical infrastructure is the joint mapping of (virtual) nodes to physical servers together with the mapping of (virtual) edges onto paths in the physical network connecting the respective servers. This work initiates the study of approximation algorithms for the VNEP for general request graphs. Concretely, we study the offline setting with admission control: given multiple requests, the task is to embed the most profitable subset while not exceeding resource capacities. Our approximation is based on the randomized rounding of Linear Programming (LP) solutions. Interestingly, we uncover that the standard LP formulation for the VNEP exhibits an inherent structural deficit when considering general virtual network topologies: its solutions cannot be decomposed into valid embeddings. In turn, focusing on the class of cactus request graphs, we devise a novel LP formulation, whose solutions can be decomposed. Proving performance guarantees of our rounding scheme, we obtain the first approximation algorithm for the VNEP in the resource augmentation model. We propose different types of rounding heuristics and evaluate their performance in an extensive computational study. Our results indicate that good solutions can be achieved even without resource augmentations. Specifically, heuristical rounding achieves 77.2% of the baseline's profit on average while respecting capacities.

This paper makes the case for a parametrized complexity approach to tackle the fundamental but notoriously hard Virtual Network Embedding Problem. In particular, we show that the structure of the to-be-embedded virtual network requests can be exploited toward fast (i.e.,fixed-parameter tractable) approximation algorithms, using dynamic as well as linear programming algorithms. Our approach does provide formal guarantees on the runtime and solution quality and can safeguard also latency constraints. Using extensive computational experiments we demonstrate the practical relevance of our novel approach.

We consider the task of computing (combined) function mapping and routing for requests in Software-Defined Networks (SDNs). Function mapping refers to the assignment of nodes in the substrate network to various processing stages that requests must undergo. Routing refers to the assignment of a path in the substrate network that begins in a source node of the request, traverses the nodes that are assigned functions for this request, and ends in a destination of the request.The algorithm either rejects a request or completely serves a request, and its goal is to maximize the sum of the benefits of the served requests. The solution must abide edge and vertex capacities.We follow the framework suggested by Even et al. [1] for the specification of the processing requirements and routing of requests via processing-and-routing graphs (PR-graphs). In this framework, each request has a demand, a benefit, and PR-graph.Our main result is a randomized approximation algorithm for path computation and function placement with the following guarantee. Let m denote the number of links in the substrate network, ε denote a parameter such that 0 < ε < 1, and opt f denote the maximum benefit that can be attained by a fractional solution (one in which requests may be partly served and flow may be split along multiple paths). Let c min denote the minimum edge capacity, and let d max denote the maximum demand. Let ∆ max denote an upper bound on the number of processing stages a request undergoes. If c min /(∆ max · d max ) = Ω((log m)/ε 2 ), then with probability at least 1 − 1 m − exp(−Ω(ε 2 · opt f /(b max · d max ))), the algorithm computes a (1 − ε)-approximate solution.