| author: | Hadas Shachnai and Lisa Zhang |
|---|---|
| title: | The master ring problem |
| keywords: | Master ring, shortest common supersequence, optical networks, exact algorithms. |
| abstract: |
We consider the master ring problem (MRP) which
often arises in optical network design. Given a network
which consists of a collection of interconnected rings
R
,
1
…
,
R
, with
K
n
,
1
…
,
n
distinct nodes, respectively, we need to find an
ordering of the nodes in the network that respects the
ordering of every individual ring, if one exists. Our main
result is an exact algorithm for MRP whose running time
approaches
K
Q·∏
for some polynomial
k=1
K
(n
k
/√
2
)
Q
, as the
n
values become large. For the ring clearance
problem, a special case of practical interest, our
algorithm achieves this running time for rings of
any size
k
n
. This yields the first nontrivial improvement, by
factor of
k
≥2
(2√
, over the running time of the naive algorithm, which
exhaustively enumerates all
2
)
K
≈ (2.82)
K
∏
possible solutions.
k=1
K
(2n
k
)
|
| If your browser does not display the abstract correctly (because of the different mathematical symbols) you may look it up in the PostScript or PDF files. | |
| reference: | Hadas Shachnai and Lisa Zhang (2005), The master ring problem, in 2005 International Conference on Analysis of Algorithms, Conrado Martínez (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AD, pp. 287-296 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
| ps.gz-source: | dmAD0126.ps.gz (105 K) |
| ps-source: | dmAD0126.ps (259 K) |
| pdf-source: | dmAD0126.pdf (154 K) |
The first source gives you the `gzipped' PostScript, the second the plain PostScript and the third the format for the Adobe accrobat reader. Depending on the installation of your web browser, at least one of these should (after some amount of time) pop up a window for you that shows the full article. If this is not the case, you should contact your system administrator to install your browser correctly.
Due to limitations of your local software, the two formats may show up differently on your screen. If eg you use xpdf to visualize pdf, some of the graphics in the file may not come across. On the other hand, pdf has a capacity of giving links to sections, bibliography and external references that will not appear with PostScript.