SIAM Journal on Computing
An efficient parallel algorithm for the minimal elimination ordering (MEO) of an arbitrary graph
Theoretical Computer Science
An Approximate Minimum Degree Ordering Algorithm
SIAM Journal on Matrix Analysis and Applications
On treewidth and minimum fill-in of asteroidal triple-free graphs
Ordal'94 Selected papers from the conference on Orders, algorithms and applications
Characterizations and algorithmic applications of chordal graph embeddings
Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
A practical algorithm for making filled graphs minimal
Theoretical Computer Science
SIAM Journal on Matrix Analysis and Applications
Minimal Elimination Ordering Inside a Given Chordal Graph
WG '97 Proceedings of the 23rd International Workshop on Graph-Theoretic Concepts in Computer Science
A wide-range algorithm for minimal triangulation from an arbitrary ordering
Journal of Algorithms
Treewidth computations I. Upper bounds
Information and Computation
Fast minimal triangulation algorithm using minimum degree criterion
Theoretical Computer Science
Hi-index | 5.23 |
Elimination Game is a well-known algorithm that simulates Gaussian elimination of matrices on graphs, and it computes a triangulation of the input graph. The number of fill edges in the computed triangulation is highly dependent on the order in which Elimination Game processes the vertices, and in general the produced triangulations are neither minimum nor minimal. In order to obtain a triangulation which is close to minimum, the Minimum Degree heuristic is widely used in practice, but until now little was known on the theoretical mechanisms involved. In this paper we show some interesting properties of Elimination Game; in particular that it is able to compute a partial minimal triangulation of the input graph regardless of the order in which the vertices are processed. This results in a new algorithm to compute minimal triangulations that are sandwiched between the input graph and the triangulation resulting from Elimination Game. One of the strengths of the new approach is that it is easily parallelizable, and thus we are able to present the first parallel algorithm to compute such sandwiched minimal triangulations. In addition, the insight that we gain through Elimination Game is used to partly explain the good behavior of the Minimum Degree algorithm. We also give a new algorithm for producing minimal triangulations that is able to use the minimum degree idea to a wider extent.