Optimal tree structure with loyal users and batch updates

Yu-Ki Chan (), Minming Li () and Weiwei Wu ()
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Yu-Ki Chan: City University of Hong Kong
Minming Li: City University of Hong Kong
Weiwei Wu: City University of Hong Kong

Journal of Combinatorial Optimization, 2011, vol. 22, issue 4, No 11, 630-639

Abstract: Abstract We study the probabilistic model in the key tree management problem. Users have different behaviors. Normal users have probability p to issue join/leave request while the loyal users have probability zero. Given the numbers of such users, our objective is to construct a key tree with minimum expected updating cost. We observe that a single LUN (Loyal User Node) is enough to represent all loyal users. When 1−p≤0.57 we prove that the optimal tree that minimizes the cost is a star. When 1−p>0.57, we try to bound the size of the subtree rooted at every non-root node. Based on the size bound, we construct the optimal tree using dynamic programming algorithm in O(n⋅K+K 4) time where K=min {4(log (1−p)−1)−1,n} and n is the number of normal users.

Keywords: Key trees; Group keys; Optimality; Probability; Updating cost (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10878-010-9312-z

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