Split and join: Strong partitions and universal steiner trees for graphs

Costas Busch, Chinmoy Dutta, Jaikumar Radhakrishnan, Rajmohan Rajaraman, Srivathsan Srinivasagopalan

Research output: Contribution to journalConference article

7 Scopus citations

Abstract

We study the problem of constructing universal Steiner trees for undirected graphs. Given a graph G and a root node r, we seek a single spanning tree T of minimum stretch, where the stretch of T is defined to be the maximum ratio, over all terminal sets X, of the cost of the minimal sub-tree TX of T that connects X to r to the cost of an optimal Steiner tree connecting X to r in G. Universal Steiner trees (USTs) are important for data aggregation problems where computing the Steiner tree from scratch for every input instance of terminals is costly, as for example in low energy sensor network applications. We provide a polynomial time UST construction for general graphs with 2 O(√log n)-stretch. We also give a polynomial time polylogarithmic-stretch construction for minor-free graphs. One basic building block of our algorithms is a hierarchy of graph partitions, each of which guarantees small strong diameter for each cluster and bounded neighbourhood intersections for each node. We show close connections between the problems of constructing USTs and building such graph partitions. Our construction of partition hierarchies for general graphs is based on an iterative cluster merging procedure, while the one for minor-free graphs is based on a separator theorem for such graphs and the solution to a cluster aggregation problem that may be of independent interest even for general graphs. To our knowledge, this is the first sub polynomial-stretch (o(nε) for any ε > 0) UST construction for general graphs, and the first polylogarithmic-stretch UST construction for minor-free graphs.

Original languageEnglish (US)
Article number6375285
Pages (from-to)81-90
Number of pages10
JournalProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
DOIs
StatePublished - 2012
Externally publishedYes
Event53rd Annual IEEE Symposium on Foundations of Computer Science, FOCS 2012 - New Brunswick, NJ, United States
Duration: Oct 20 2012Oct 23 2012

Keywords

  • graph clustering
  • hierarchical graph partition
  • minor-free graphs
  • universal Steiner tree

ASJC Scopus subject areas

  • Computer Science(all)

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