AbstracL A secret sharing scheme permits a secret to be shared among participants in such a way that only qualified subsets of participants can recover the secret, but any nonqualified subset has absolutely no information on the secret. The set of all qualified subsets defines the access structure to the secret. Sharing schemes are useful in the management of cryptographic keys and in multiparty secure protocols.We analyze the relationships among the entropies of the sample spaces from which the shares and the secret are chosen. We show that there are access structures with four participants for which any secret sharing scheme must give to a participant a share at least 50% greater than the secret size. This is the first proof that there exist access structures for which the best achievable information rate (i.e., the ratio between the size of the secret and that of the largest share) is bounded away from 1. The bound is the best possible, as we construct a secret sharing scheme for the above access structures that meets the bound with equality.

Two mobile agents (robots) having distinct labels and located in nodes of an unknown anonymous connected graph, have to meet. We consider the asynchronous version of this well-studied rendezvous problem and we seek fast deterministic algorithms for it. Since in the asynchronous setting meeting at a node, which is normally required in rendezvous, is in general impossible, we relax the demand by allowing meeting of the agents inside an edge as well. The measure of performance of a rendezvous algorithm is its cost: for a given initial location of agents in a graph, this is the number of edge traversals of both agents until rendezvous is achieved. If agents are initially situated at a distance D in an infinite line, we show a rendezvous algorithm with cost O(D|L min | 2) when D is known and O((D + |L max |) 3) if D is unknown, where |L min | and |L max | are the lengths of the shorter and longer label of the agents, respectively. These results still hold for the case of the ring of unknown size but then we also give an optimal algorithm of cost O(n|L min |), if the size n of the ring is known, and of cost O(n|L max |), if it is unknown. For arbitrary graphs, we show that rendezvous is feasible if an upper bound on the size of the graph is known and we give an optimal algorithm of cost O(D|L min |) if the topology of the graph and the initial positions are known to agents.

Abstract. We derive new limitations OIL the information rate and the average information rate of secret sharing schemes for access structure represented by graphs. We give the first proof of t h e existcnce u l Access structures w i l h optimal information rate and optimal average information rate less that 1/2 + c, where E is an arbitrary positive constant. We also provide several general lower Luunds on inlormation rate and average information rate of graphs In particular, we show that any graph with vertices admits a secret sharing scheme with infvimation rate

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A recently introduced novel community detection strategy is based on a label propagation algorithm (LPA) which uses the diffusion of information in the network to identify communities. Studies of LPAs showed that the strategy is effective in finding a good community structure. Label propagation step can be performed in parallel on all nodes (synchronous model) or sequentially (asynchronous model); both models present some drawback, e.g., algorithm termination is nor granted in the first case, performances can be worst in the second case. In this paper, we present a semi-synchronous version of LPA which aims to combine the advantages of both synchronous and asynchronous models. We prove that our models always converge to a stable labeling. Moreover, we experimentally investigate the effectiveness of the proposed strategy comparing its performance with the asynchronous model both in terms of quality, efficiency and stability. Tests show that the proposed protocol does not harm the quality of the partitioning. Moreover it is quite efficient; each propagation step is extremely parallelizable and it is more stable than the asynchronous model, thanks to the fact that only a small amount of randomization is used by our proposal.