Merlin: A Language for Provisioning Network Resources

This paper presents Merlin, a new framework for managing resources in software-defined networks. With Merlin, administrators express high-level policies using programs in a declarative language. The language includes logical predicates to identify sets of packets, regular expressions to encode forwarding paths, and arithmetic formulas to specify bandwidth constraints. The Merlin compiler uses a combination of advanced techniques to translate these policies into code that can be executed on network elements including a constraint solver that allocates bandwidth using parameterizable heuristics. To facilitate dynamic adaptation, Merlin provides mechanisms for delegating control of sub-policies and for verifying that modifications made to sub-policies do not violate global constraints. Experiments demonstrate the expressiveness and scalability of Merlin on real-world topologies and applications. Overall, Merlin simplifies network administration by providing high-level abstractions for specifying network policies and scalable infrastructure for enforcing them

Degrees and distances in random and evolving Apollonian networks

This paper studies Random and Evolving Apollonian networks (RANs and EANs), in d dimension for any d>=2, i.e. dynamically evolving random d dimensional simplices looked as graphs inside an initial d-dimensional simplex. We determine the limiting degree distribution in RANs and show that it follows a power law tail with exponent tau=(2d-1)/(d-1). We further show that the degree distribution in EANs converges to the same degree distribution if the simplex-occupation parameter in the n-th step of the dynamics is q_n->0 and sum_{n=0}^infty q_n =infty. This result gives a rigorous proof for the conjecture of Zhang et al. that EANs tend to show similar behavior as RANs once the occupation parameter q->0. We also determine the asymptotic behavior of shortest paths in RANs and EANs for arbitrary d dimensions. For RANs we show that the shortest path between two uniformly chosen vertices (typical distance), the flooding time of a uniformly picked vertex and the diameter of the graph after n steps all scale as constant times log n. We determine the constants for all three cases and prove a central limit theorem for the typical distances. We prove a similar CLT for typical distances in EANs