Gossiping (also called total exchange or all-to-all communication) is the process of information di usion in which each node of a network holds a packet that must be communicated to all other nodes in the network. We consider here gossiping in the store-and-forward, fullduplex and -port (or shouting) model. In such a model, the protocol consists of a sequence of rounds and during each round, each node can send (and receive) messages from all its neighbors. The great majority of the previous works on gossiping problems allows the messages to be freely concatenated and so messages of arbitrary length can be transmitted during a round. Here we restrict the problem to the case where at each round communicating nodes can exchange exactly one packet. We give a lower bound of N ?1 , where is the minimum degree, and show that it is attained in Cayley symmetric digraphs with some additional properties. That implies the existence of an optimal gossiping protocol for classical networks like hypercubes, k-dimensional tori, and star-graphs.

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In this paper, we propose a method which enables us to construct almost optimal broadcast schemes on an n-dimensional hypercube in the circuit switched, -port model. In this model, an initiator must inform all the nodes of the network in a sequence of rounds. During a round, vertices communicate along arc-disjoint dipaths. Our construction is based on particular sequences of nested binary codes having the property that each code can inform the next one in a single round. This last property is insured by a flow technique and results about symmetric flow networks.We apply the method to design new schemes improving and generalizing the previous results. Our schemes are the best possible algebraic schemes, and they are optimal in the case n = 2 p , 1.

The phenomenon of women's underrepresentation in engineering is well known. However, the slow progress in achieving better gender equality here compared with other domains has accentuated the 'numbers' issue, while the quality aspects have been largely ignored. This study aims to shed light on both these aspects via the lens of mentors, who are at the coalface of guiding female engineers through their education and subsequent careers. Based on data collected from 25 mentors (8 men and 17 women from 8 countries), the paper explores their experiences of being mentors, as well as their views on recommended actions for nurturing female engineers. The findings reveal that the primary motivation for becoming a mentor was personal for men and women. Many mentors from countries with relatively lower female labour participation rates perceive their roles as guarantors of their mentees' successful future career paths, and a similar trend can be found in mentors in academia. The study underscores the need for invigorating mentors' roles in order to secure a more equitable future for engineering education.