Optimal Tree Structures for Group Key Tree Management Considering Insertion and Deletion Cost

Authors:
Weiwei Wu;Minming Li;Enhong Chen
Affiliations:
USTC-CityU Joint Research Institute Department of Computer Science, University of Science and Technology of China,Department of Computer Science, City University of Hong Kong,;Department of Computer Science, City University of Hong Kong,;Department of Computer Science, University of Science and Technology of China,
Venue:
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Year:
2008

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Abstract

We study the optimal structure for group broadcast problem where the key tree model is extensively used. The objective is usually to find an optimal key tree to minimize the cost based on certain assumptions. Under the assumption that nmembers arrive in the initial setup period and only member deletions are allowed after that period, previous works show that when only considering the deletion cost, the optimal tree can be computed in O(n2) time. In this paper, we first prove a semi-balance property for the optimal tree and use it to improve the running time from O(n2) to O(loglogn). Then we study the optimal tree structure when insertion cost is also considered. We show that the optimal tree is such a tree where any internal node has at most degree 7 and children of nodes with degree not equal to 2 or 3 are all leaves. Based on this result we give a dynamic programming algorithm with O(n2) time to compute the optimal tree.