Minimum certificate dispersal with tree structures

Taisuke Izumi, Tomoko Izumi, Hirotaka Ono, Koichi Wada

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish
Title of host publicationTheory and Applications of Models of Computation - 9th Annual Conference, TAMC 2012, Proceedings
Number of pages12
Publication statusPublished - 2012
Event9th Annual Conference on Theory and Applications of Models of Computation, TAMC 2012 - Beijing, China
Duration: May 16 2012May 21 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7287 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other9th Annual Conference on Theory and Applications of Models of Computation, TAMC 2012

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


Dive into the research topics of 'Minimum certificate dispersal with tree structures'. Together they form a unique fingerprint.

Cite this