Fault tolerance on improved distributed spanning tree structure

To improve the fault tolerance of the distributed spanning tree (DST) structure, we present an improved DST structure through orderly storing the elements in groups. Further, we give a representative selection rule, and based on which the node arrival and departure algorithms are proposed to balance the distribution of representatives in the structure. The maximal difference of the probabilities of any node to be selected as representatives by other nodes in the groups within the same level is not more than 1/a(a-1). Finally, we discuss the fault tolerance on the improved DST structure in a random failures model and an adversarial failures model. The results show that the improved DST structure is high resilient to fault even if the failures are carefully targeted. At most O(f/logN) nodes are lost when f nodes failed, and it is better than skip graph.