Sparse Additive Spanners for Bounded Tree-Length Graphs

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 , i.e., the tree-length graphs. For such graphs we construct additive 2-spanners with O(n log n) edges, and additive 6-spanners with O(n) edges. We also show a lower bound, and prove that there are graphs of tree-length for which every multiplicative -spanner (and thus every additive ( 1)-spanner) requires 1+1=() ) edges