Gerhard J. Woeginger

Bio: Gerhard J. Woeginger is an academic researcher from University of Graz. The author has contributed to research in topics: Planar graph & Cache. The author has an hindex of 5, co-authored 8 publications receiving 459 citations. Previous affiliations of Gerhard J. Woeginger include University of Pittsburgh.

Complexity of Coloring Graphs without Forbidden Induced Subgraphs

Abstract: 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

Abstract: 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 $2 - \frac{1} {m}$ for this problem. This worst case bound cannot be improved for $m = 2$ and $m = 3$. For $m \geqslant 4$, approximation algorithms with worst case performance at most $2 - \frac{1}{m} - \varepsilon _m $ are presented, where $\varepsilon _m $ is some positive real depending only on m.

Drawing graphs in the plane with high resolution

Abstract: This paper presents the problem of drawing a graph in the plane so that edges appear as straight lines and the minimum angle formed by any pair of incident edges is maximized. The resolution of a layout is defined to be the size of the minimum angle formed by incident edges of the graph, and the resolution of a graph to be the maximum resolution of any layout of the graph. The resolution R of a graph is characterized in terms of the maximum node degree d of the graph by proving that $\Omega (\frac{1}{{d^2 }}) \leqslant R \leqslant \frac{{2\pi }}{d}$ for any graph. Moreover, it is proved that $R = \Theta (\frac{1}{d})$ for many graphs including planar graphs, complete graphs, hypercubes, multidimensional meshes and tori, and other special networks. It is also shown that the problem of deciding if $R = \frac{{2\pi }}{d}$ for a graph is NP-hard for $d = 4$, and by using a counting argument that $R = O(\frac{{\log d}}{{d^2 }})$ for many graphs.

Drawing graphs in the plane with high resolution

Abstract: The problem of drawing a graph in the plane so that edges appear as straight lines and the minimum angle formed by any pair of incident edges is maximized is studied. The resolution of a layout is defined to be the size of the minimum angle formed by incident edges of the graph, and the resolution of a graph is defined to be the maximum resolution of any layout of the graph. The resolution R of a graph is characterized in terms of the maximum node degree d of the graph by proving that Omega (1/d/sup 2/) >

Linear Assignment Problems and Extensions

Abstract: Assignment problems deal with the question how to assign n items (eg jobs) to n machines (or workers) in the best possible way They consist of two components: the assignment as underlying combinatorial structure and an objective function modeling the ”best way”

A Review of Machine Scheduling: Complexity, Algorithms and Approximability

Abstract: The scheduling of computer and manufacturing systems has been the subject of extensive research for over forty years. In addition to computers and manufacturing, scheduling theory can be applied to many areas including agriculture, hospitals and transport. The main focus is on the efficient allocation of one or more resources to activities over time. Adopting manufacturing terminology, a job consists of one or more activities, and a machine is a resource that can perform at most one activity at a time. We concentrate on deterministic machine scheduling for which it is assumed that all data that define a problem instance are known with certainty.

Drawing planar graphs using the canonical ordering

Abstract: We introduce a new method to optimize the required area, minimum angle, and number of bends of planar graph drawings on a grid. The main tool is a new type of ordering on the vertices and faces of triconnected planar graphs. Using this method linear-time-and-space algorithms can be designed for many graph-drawing problems. Our main results are as follows: Every triconnected planar graphG admits a planar convex grid drawing with straight lines on a (2n−4)×(n−2) grid, wheren is the number of vertices. Every triconnected planar graph with maximum degree 4 admits a planar orthogonal grid drawing on ann×n grid with at most [3n/2]+4 bends, and ifn>6, then every edge has at most two bends. Every planar graph with maximum degree 3 admits a planar orthogonal grid drawing with at most [n/2]+1 bends on an [n/2]×[n/2] grid. Every triconnected planar graphG admits a planar polyline grid drawing on a (2n−6)×(3n−9) grid with minimum angle larger than 2/d radians and at most 5n−15 bends, withd the maximum degree.