Paper Info
Title
Minimum certificate dispersal with tree structures
Abstract
Given an n -vertex graph G =(V ,E ) and a set R ⊆{{x ,y }|x ,y ∈V } of requests, we consider to assign a set of edges to each vertex in G so that for every request {u , v } in R the union of the edge sets assigned to u and v contains a path from u to v . The Minimum Certificate Dispersal Problem (MCD) is defined as one to find an assignment that minimizes the sum of the cardinality of the edge set assigned to each vertex, which is originally motivated by the design of secure communications in distributed computing. This problem has been shown to be LOGAPX-hard for general directed topologies of G and R . In this paper, we consider the complexity of MCD for more practical topologies of G and R , that is, when G or R forms an (undirected) tree; tree structures are frequently adopted to construct efficient communication networks. We first show that MCD is still APX-hard when R is a tree, even a star. We then explore the problem from the viewpoint of the maximum degree Δ of the tree: MCD for tree request set with constant Δ is solvable in polynomial time, while that with Δ=Ω(n ) is 2.78-approximable in polynomial time but hard to approximate within 1.01 unless P=NP. As for the structure of G itself, we show that if G is a tree, the problem can be solved in O (n 1+ε |R |), where ε is an arbitrarily small positive constant number.
Year
DOI
Venue
2012
10.1007/978-3-642-29952-0_51
theory and applications of models of computation
Keywords
DocType
Volume
practical topology,efficient communication network,maximum degree,tree structure,minimum certificate dispersal problem,tree request,polynomial time,small positive constant number,set r,minimum certificate dispersal,vertex graph,data structure
Conference
abs/1106.5845
Citations 
PageRank 
References 
0
0.34
16
Authors
4
Name
Order
Citations
PageRank
Taisuke Izumi128439.02
Tomoko Izumi214121.33
Hirotaka Ono340056.98
Koichi Wada431954.11