On the Steiner Tree 3/2-Approximation for Quasi-Bipartite Graphs
DOI:
https://doi.org/10.7146/brics.v6i39.20108Resumé
Let G = (V,E) be an undirected simple graph and w : E -> R+ be
a non-negative weighting of the edges of G. Assume V is partitioned
as R union X. A Steiner tree is any tree T of G such that every node
in R is incident with at least one edge of T. The metric Steiner tree
problem asks for a Steiner tree of minimum weight, given that w is a
metric. When X is a stable set of G, then (G,R,X) is called quasi-bipartite.
In [1], Rajagopalan and Vazirani introduced the notion of
quasi-bipartiteness and gave a ( 3/2 + epsilon) approximation algorithm
for the metric Steiner tree problem, when (G,R,X) is quasi-bipartite. In this
paper, we simplify and strengthen the result of Rajagopalan and Vazirani.
We also show how classical bit scaling techniques can be adapted
to the design of approximation algorithms.
Key words: Steiner tree, local search, approximation algorithm, bit scaling.
Downloads
Publiceret
Citation/Eksport
Nummer
Sektion
Licens
Authors who publish with this journal agree to the following terms:- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).