This special issue contains papers selected from the ones submitted in response to the call for papers. Each paper was reviewed by three referees who provided comments on the quality and relevance of these papers. The problem of dynamic tree embedding has been well studied on various models of computing. Li's paper deals with tree embedding problem on hypercubes. Recurrence relations are developed that characterize the expected load in randomized tree embeddings where a tree grows by letting its nodes take random walks of short distance.
Load balancing is an important problem in parallel computing.
Nikoletseas, Palem, Spirakis, and Yung provide a new model of random graphs in their paper. The new model is a random regular graph with edge faults obtained by selecting the edges of a random number of the set of all regular graphs of degree r independently and with probability p . They also study some connectivity properties of the new model. Sun's paper deals with the problem of secret sharing. In a secret sharing scheme a dealer shares a secret among a set of participants in such a way that only qualified subsets of participants can reconstruct the secret.