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The two-connected network with bounded meshes problem is discussed. This problem poses a central challenge in the development of fiber-optic backbone networks. A branch-and-cut model is applied to several families of valid inequalities and their corresponding separation algorithms.

In blockchains, transactions fees are fixed by the users. The probability for a transaction to be processed quickly increases with the fee level. In this paper, we study the transactions fees optimization problem in Ethereum blockchain. This problem consists in determining the minimum price a user should pay in order that its transaction be processed with a given probability in a given amount of time. To reach this goal, we define a new solution method based on a Monte Carlo approach to predict the probability that a transaction be mined within a given time limit. Numerical results on real data highlight the quality of the results.