Understanding edge-connectivity in the Internet through core-decomposition

Internet is a complex network composed by several networks: the Autonomous Systems, each one designed to transport information efficiently. Routing protocols aim to find paths between nodes whenever it is possible (i.e., the network is not partitioned), or to find paths verifying specific constraints (e.g., a certain QoS is required). As connectivity is a measure related to both of them (partitions and selected paths) this work provides a formal lower bound to it based on core-decomposition, under certain conditions, and low complexity algorithms to find it. We apply them to analyze maps obtained from the prominent Internet mapping projects, using the LaNet-vi open-source software for its visualization

Solving the Transportation Problem

A simplified description of a new computing procedure for the Hitchcock-Koopmans transportation problem is given, together with a step by step solution of an illustrative example. The procedure is based on Kuhn's combinatorial algorithm for the assignment problem and a simple "labeling process" for solving maximal flow problems in networks. The proposed computation appears to be considerably more efficient than the specialized form of the simplex method which is in common use.