This is a template for an open problem database entry ("problem file") for
The Open Problems Project, currently at
.
It is simply an ASCII file, with various fields starting a new line with a *
preceding the field name. The template gives a rough definition of the
contents of each field. The field contents can be written in LaTeX.
Delete the explanatory text and insert your own; or leave blank as appropriate.
Nearly all fields are optional; use `' for an empty field.
When in doubt, leave a note for the editors, who will edit the problem before
posting it. After the template is one sample, for Problem 1. See the web page
for the correspondence between the "problem file" and the displayed version.
---------------------------------------------------------
TEMPLATE
---------------------------------------------------------
* Number: To be filled in by the editors.
* Problem: Concise and informative name of problem.
Each major word capitalized.
* Statement:
Clear statement of the problem,
defining most(?) unusual technical terms.
* Origin: Uncertain, pending investigation.
That's the default. Fill in more if you know it.
* Status/Conjectures: Open.
Again that's the default.
* Motivation:
A new field, added Nov. 2001. Infrequently used.
Leave out entirely if not needed.
* Partial and Related Results:
A paragraph or two about related results.
Use \cite{key} where key is from the geom.bib Computational
Geometry community bibliography. If you don't have access to
this, or your reference is not there, provide the reference
information in bib format and I'll add it to my copy of
geom.bib.
* Related Open Problems:
That's the default. Can reference other problems
like this: Problem~\ref{Problem.23}.
* Reward:
That's the default.
* Appearances:
Where else has the problem appeared as an open problem,
e.g., in some other list. Default is , which could
mean "I don't know."
* Categories:
List of categories on the line, separated by semicolons.
There is no approved list of categories. We will let these
evolve and cluster naturally. Try to think of at least one category.
* Entry Revision History:
J. O'Rourke, 2 Aug. 2001; Name, Date; Name, Date.
---------------------------------------------------------
NB: This final line of dashes is needed to separate one problem from the next!
Follow the file with bibliographic entries not in geom.bib,
preferably in bibtex format, or notes for the moderators.
---------------------------------------------------------
EXAMPLE
---------------------------------------------------------
* Number: 1
* Problem: Minimum Weight Triangulation
* Statement:
Can a mininimum weight triangulation of a planar point set
be found in polynomial time?
The \emph{weight} of a triangulation is its total edge length.
* Origin: Perhaps E. L. Lloyd, 1977: \cite{l-tspp-77},
cited in Garey and Johnson~\cite{gj-cigtn-79}.
* Status/Conjectures: Open.
This problem is one
of the few from Garey and Johnson~\cite[p.~288]{gj-cigtn-79} whose
complexity status remains unknown.
* Partial and Related Results:
The best approximation algorithms achieve a (large) constant times
the optimal length~\cite{lk-qgtam-96};
good heuristics are known~\cite{dmm-naefm-95}.
If Steiner points are allowed, again constant-factor
approximations are known~\cite{e-amwst-94,cl-qrsam-98},
but it is open to decide even if a minimum-weight Steiner triangulation
exists (the minimum might be approached only
in the limit).
* Related Open Problems:
* Reward:
* Appearances:
\cite{mo-cgc42-01}
* Categories: triangulations
* Entry Revision History:
J. O'Rourke, 31 Jul. 2001.
---------------------------------------------------------