We currently witness the emergence of interesting new network topologies optimized towards the traffic matrices they serve, such as demand-aware datacenter interconnects (e.g., ProjecToR) and demand-aware overlay networks (e.g., SplayNets). This paper introduces a formal framework and approach to reason about and design such topologies. We leverage a connection between the communication frequency of two nodes and the path length between them in the network, which depends on the entropy of the communication matrix. Our main contribution is a novel robust, yet sparse, family of network topologies which guarantee an expected path length that is proportional to the entropy of the communication patterns.
The design of robust networks especially has been of prime interest to researchers for many decades. In the field of network design, survivable networks are explored that remain functional when links are severed or nodes fail, that is, network services can be restored in the event of catastrophic failures @cite_6 @cite_18 . Recently, researchers have proposed an interesting generic and declarative approach to network design @cite_13 .
@cite_18 @cite_13 @cite_6
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In the survivable network design problem (SNDP), the goal is to find a minimum-cost spanning subgraph satisfying certain connectivity requirements. We study the vertex-connectivity variant of SNDP in which the input specifies, for each pair of vertices, a required number of vertex-disjoint paths connecting them. We give the first strong lower bound on the approximability of SNDP, showing that the problem admits no efficient @math ratio approximation for any fixed @math , unless @math . We show hardness of approximation results for some important special cases of SNDP, and we exhibit the first lower bound on the approximability of the related classical NP-hard problem of augmenting the connectivity of a graph using edges from a given set. One way to improve the reliability of a network is through physical diversity, i.e., via routing of traffic between a given pair of nodes in the network over two or more physically-disjoint paths such that if a node or a physical link fails on one of the disjoint paths, not all of the traffic is lost. Alternatively, enough spare capacity may be allocated on the individual paths such that the lost traffic due to a node or physical link failure can be routed immediately over the predetermined paths. In this paper, we present optimal algorithms for K-disjoint paths (K spl ges 2) in a graph of vertices (or nodes) and edges (or links). These algorithms are simpler than those given in the past. We discuss how such algorithms can be used in the design of survivable mesh networks based on the digital cross-connect systems (DCS). We also discuss the generation of optimal network topologies which permit K>2 disjoint paths and upon which survivable networks may be modeled. The study is of particular relevance to fiber networks. Network survivability--the ability to maintain operation when one or a few network components fail--is indispensable for present-day networks. In this paper, we characterize three main components in establishing network survivability for an existing network, namely, (1) determining network connectivity, (2) augmenting the network, and (3) finding disjoint paths. We present a concise overview of network survivability algorithms, where we focus on presenting a few polynomial-time algorithms that could be implemented by practitioners and give references to more involved algorithms. We consider robust (undirected) network design (RND) problems where the set of feasible demands may be given by an arbitrary convex body. This model, introduced by Ben-Ameur and Kerivin [Ben-Ameur W, Kerivin H (2003) New economical virtual private networks. Comm. ACM 46(6):69–73], generalizes the well-studied virtual private network (VPN) problem. Most research in this area has focused on constant factor approximations for specific polytope of demands, such as the class of hose matrices used in the definition of VPN. As pointed out in Chekuri [Chekuri C (2007) Routing and network design with robustness to changing or uncertain traffic demands. SIGACT News 38(3):106–128], however, the general problem was only known to be APX-hard (based on a reduction from the Steiner tree problem). We show that the general robust design is hard to approximate to within polylogarithmic factors. We establish this by showing a general reduction of buy-at-bulk network design to the robust network design problem. Gupta pointed...