Reconstructing the shape of a tree from observed dissimilarity data
Advances in Applied Mathematics
Doubly lexical orderings of matrices
SIAM Journal on Computing
An optimal synchronizer for the hypercube
PODC '87 Proceedings of the sixth annual ACM Symposium on Principles of distributed computing
A tradeoff between space and efficiency for routing tables
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Doubly lexical ordering of dense 0–1 matrices
Information Processing Letters
Tree spanners: spanning trees that approximate distances
Tree spanners: spanning trees that approximate distances
SIAM Journal on Discrete Mathematics
Incidence graphs of biacyclic hypergraphs
Discrete Applied Mathematics
Tree 3-spanners on interval, permutation and regular bipartite graphs
Information Processing Letters
Restrictions of minimum spanner problems
Information and Computation
SIAM Journal on Discrete Mathematics
Distance approximating trees for chordal and dually chordal graphs
Journal of Algorithms
A note on distance approximating trees in graphs
European Journal of Combinatorics
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Tree spanners in planar graphs
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Tree Spanners on Chordal Graphs: Complexity, Algorithms, Open Problems
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Distance Approximating Spanning Trees
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Estimating All Pairs Shortest Paths in Restricted Graph Families: A Unified Approach
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
SIAM Journal on Discrete Mathematics
Spanners for bounded tree-length graphs
Theoretical Computer Science
Additive Spanners for Circle Graphs and Polygonal Graphs
Graph-Theoretic Concepts in Computer Science
Navigating in a Graph by Aid of Its Spanning Tree Metric
SIAM Journal on Discrete Mathematics
Collective additive tree spanners for circle graphs and polygonal graphs
Discrete Applied Mathematics
Eccentric counts, connectivity and chordality
Information Processing Letters
| Hi-index | 5.23 |
In this paper, we show that every chordal graph with n vertices and m edges admits an additive 4-spanner with at most 2n - 2 edges and an additive 3-spanner with at most O(n log n) edges. This significantly improves results of Peleg and Schäffer from [Graph Spanners, J. Graph Theory 13 (1989) 99-116]. Our spanners are additive and easier to construct. An additive 4-spanner can be constructed in linear time while an additive 3-spanner is constructable in O(m log n) time. Furthermore, our method can be extended to graphs with largest induced cycles of length k. Any such graph admits an additive (k + 1)-spanner with at most 2n - 2 edges which is constructable in O(nk + m) time.