On fractionality of the path packing problem

In this paper, we study fractional multiflows in undirected graphs. A fractional multiflow in a graph G with a node subset T, called terminals, is a collection of weighted paths with ends in T such that the total weights of paths traversing each edge does not exceed 1. Well-known fractional path packing problem consists of maximizing the total weight of paths with ends in a subset S of TxT over all fractional multiflows. Together, G,T and S form a network. A network is an Eulerian network if all nodes in N\T have even degrees. A term "fractionality" was defined for the fractional path packing problem by A. Karzanov as the smallest natural number D so that there exists a solution to the problem that becomes integer-valued when multiplied by D. A. Karzanov has defined the class of Eulerian networks in terms of T and S, outside which D is infinite and proved that whithin this class D can be 1,2 or 4. He conjectured that D should be 1 or 2 for this class of networks. In this paper we prove this conjecture.Comment: 18 pages, 5 figures in .eps format, 2 latex files, main file is kc13.tex Resubmission due to incorrectly specified CS type of the article; no changes to the context have been mad

Boosting the Efficiency of Byzantine-tolerant Reliable Communication

Reliable communication is a fundamental primitive in distributed systems prone to Byzantine (i.e. arbitrary, and possibly malicious) failures to guarantee integrity, delivery and authorship of messages exchanged between processes. Its practical adoption strongly depends on the system assumptions. One of the most general (and hence versatile) such hypothesis assumes a set of processes interconnected through an unknown communication network of reliable and authenticated links, and an upper bound on the number of Byzantine faulty processes that may be present in the system, known to all participants. To this date, implementing a reliable communication service in such an environment may be expensive, both in terms of message complexity and computational complexity, unless the topology of the network is known. The target of this work is to combine the Byzantine fault-tolerant topol-ogy reconstruction with a reliable communication primitive, aiming to boost the efficiency of the reliable communication service component after an initial (expensive) phase where the topology is partially reconstructed. We characterize the sets of assumptions that make our objective achievable, and we propose a solution that, after an initialization phase, guarantees reliable communication with optimal message complexity and optimal delivery complexity