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In this paper, we consider methods whereby a subset of players in a ( k, n)-threshold scheme can 'repair' another player's share in the event that their share has been lost or corrupted. This will take place without the participation of the dealer who set up the scheme. The repairing protocol should not compromise the (unconditional) security of the threshold scheme, and it should be efficient, where efficiency is measured in terms of the amount of information exchanged during the repairing process. We study two approaches to repairing. The first method is based on the 'enrollment protocol' from Nojoumian et al. (IET Inf Secur 4: 202-211, 2010) which was originally developed to add a new player to a threshold scheme (without the participation of the dealer) after the scheme was set up. The second method distributes 'multiple shares' to each player, as defined by a suitable combinatorial design. This method results in larger shares, but lower communication complexity, as compared to the first method. [ABSTRACT FROM AUTHOR]

Li et al. (Retransmission ≠ repeat: simple retransmission permutation can resolve overlapping channel collisions, ) introduced a technique for resolving overlapping channel transmissions that used an interesting new type of combinatorial structure. In connection with this problem, they provided an example of a 4 × 4 array having certain desirable properties. We define a class of combinatorial structures, which we term retrans mission permutation arrays, that generalise the example that Li et al. provided. We show that these arrays exist for all possible orders. We also define some extensions having additional properties, for which we provide some partial results. [ABSTRACT FROM AUTHOR]

By researching on the node scheduling problem of m-covered and connected sensor networks, a new concept of two-hops-cluster is proposed in this paper, and based on it, a new distributed node scheduling algorithm THCNS for allocating all nodes in the sensor network into k( k ⩽ m) different groups {0, 1, ..., k} is designed, without requiring location information. Our algorithm guarantees that each group to be connected and maintains the coverage ratio with high possibility. Theoretical analysis and simulation results show that it has better performance than previous randomized scheduling scheme, and can prolong the lifetime of the sensor network effectively. [ABSTRACT FROM AUTHOR]