Spanners for bounded tree-length graphs

Authors:
Yon Dourisboure;Feodor F. Dragan;Cyril Gavoille;Chenyu Yan
Affiliations:
LaBRI, Université Bordeaux 1, France;Department of Computer Science, Kent State University, United States;LaBRI, Université Bordeaux 1, France;Department of Computer Science, Kent State University, United States
Venue:
Theoretical Computer Science
Year:
2007

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Abstract

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 @d, i.e., the tree-length @d graphs. For such graphs we construct additive 2@d-spanners with O(@dn+nlogn) edges, and additive 4@d-spanners with O(@dn) edges. This provides new upper bounds for chordal graphs for which @d=1. We also show a lower bound, and prove that there are graphs of tree-length @d for which every multiplicative @d-spanner (and thus every additive (@d-1)-spanner) requires @W(n^1^+^1^/^@Q^(^@d^)) edges.