Gerhard J. Woeginger

Complexity of Coloring Graphs without Forbidden Induced Subgraphs

We give a complete characterization of parameter graphs H for which the problem of coloring H-free graphs is polynomial and for which it is NP-complete. We further initiate a study of this problem for two forbidden subgraphs.

An on-line scheduling heuristic with better worst case ratio than Graham's list scheduling

The problem of on-line scheduling a set of independent jobs on m machines is considered. The goal is to minimize the makespan of the schedule. Graham’s List Scheduling heuristic [R. L. Graham, SIAM J. Appl. Math., 17(1969), pp. 416–429] guarantees a worst case performance of

Polynomial graph-colorings

2 - \frac{1} {m}

Drawing graphs in the plane with high resolution

for this problem. This worst case bound cannot be improved for

On the recognition of permuted bottleneck Monge matrices

m = 2

A New Efficiently Solvable Special Case of the Three-Dimensional Axial Bottleneck Assignment Problem

and

Epsilon-Nets for Halfplanes

m = 3

Polynomial Graph-Colorings

. For

Complexity and approximability results for slicing floorplan designs

m \geqslant 4

On the Recognition of Permuted Bottleneck Monge Matrices

, approximation algorithms with worst case performance at most