The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
Approximating treewidth, pathwidth, frontsize, and shortest elimination tree
Journal of Algorithms
SIAM Journal on Discrete Mathematics
On the vertex ranking problem for trapezoid, circular-arc and other graphs
Discrete Applied Mathematics
Parallelizing Elimination Orders with Linear Fill
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Edge ranking of weighted trees
Discrete Applied Mathematics
Constructing a minimum height elimination tree of a tree in linear time
Information Sciences: an International Journal
Optimal vertex ranking of block graphs
Information and Computation
Minimal k-rankings and the rank number of Pn2
Information Processing Letters
Hi-index | 0.89 |
In this paper we consider the vertex ranking problem of weighted trees. We show that this problem is strongly NP-hard. We also give a polynomial-time reduction from the problem of vertex ranking of weighted trees to the vertex ranking of (simple) chordal graphs, which proves that the latter problem is NP-hard. In this way we solve an open problem of Aspvall and Heggernes. We use this reduction and the algorithm of Bodlaender et al.'s for vertex ranking of partial k-trees to give an exact polynomial-time algorithm for vertex ranking of a tree with bounded and integer valued weight functions. This algorithm serves as a procedure in designing a PTAS for weighted vertex ranking problem of trees with bounded weight functions.