6 research outputs found
Fixed parameter tractability of crossing minimization of almost-trees
We investigate exact crossing minimization for graphs that differ from trees
by a small number of additional edges, for several variants of the crossing
minimization problem. In particular, we provide fixed parameter tractable
algorithms for the 1-page book crossing number, the 2-page book crossing
number, and the minimum number of crossed edges in 1-page and 2-page book
drawings.Comment: Graph Drawing 201
Data-Collection for the Sloan Digital Sky Survey: a Network-Flow Heuristic
The goal of the Sloan Digital Sky Survey is ``to map in detail one-quarter of
the entire sky, determining the positions and absolute brightnesses of more
than 100 million celestial objects''. The survey will be performed by taking
``snapshots'' through a large telescope. Each snapshot can capture up to 600
objects from a small circle of the sky. This paper describes the design and
implementation of the algorithm that is being used to determine the snapshots
so as to minimize their number. The problem is NP-hard in general; the
algorithm described is a heuristic, based on Lagriangian-relaxation and
min-cost network flow. It gets within 5-15% of a naive lower bound, whereas
using a ``uniform'' cover only gets within 25-35%.Comment: proceedings version appeared in ACM-SIAM Symposium on Discrete
Algorithms (1998
Parameterized Complexity of 1-Planarity
We consider the problem of finding a 1-planar drawing for a general graph,
where a 1-planar drawing is a drawing in which each edge participates in at
most one crossing. Since this problem is known to be NP-hard we investigate the
parameterized complexity of the problem with respect to the vertex cover
number, tree-depth, and cyclomatic number. For these parameters we construct
fixed-parameter tractable algorithms. However, the problem remains NP-complete
for graphs of bounded bandwidth, pathwidth, or treewidth.Comment: WADS 201