2004 | OriginalPaper | Chapter
Sparse Additive Spanners for Bounded Tree-Length Graphs
Authors : Yon Dourisboure, Cyril Gavoille
Published in: Structural Information and Communication Complexity
Publisher: Springer Berlin Heidelberg
Included in: Professional Book Archive
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This paper concerns construction of additive stretched spanners with few edges for n-vertex graphs having a tree-decomposition into bags of diameter at most δ, i.e., the tree-length δ graphs. For such graphs we construct additive 2δ-spanners with O(δnlog n) edges, and additive 4δ-spanners with O(δn) edges. This provides new upper bounds for chordal graphs for which δ=1. We also show a lower bound, and prove that there are graphs of tree-length δ for which every multiplicative δ-spanner (and thus every additive (δ–1)-spanner) requires Ω(n1 + 1/Θ(δ)) edges.