The Computer Journal
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
NP-completeness of minimum spanner problems
Discrete Applied Mathematics
SIAM Journal on Discrete Mathematics
Computing edge-connectivity augmentation function in Õ(nm) time
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
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
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Strategies for Hotlink Assignments
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
Proximity-Preserving Labeling Schemes and Their Applications
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Approximating Minimum Max-Stretch spanning Trees on unweighted graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Finding the best shortcut in a geometric network
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
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A tree t-spanner T of a graph G is a spanning tree of G whose max-stretch is t, i.e., the distance between any two vertices in T is at most t times their distance in G. If G has a tree t-spanner but not a tree (t–1)-spanner, then G is said to have max-stretch of t. In this paper, we study the Max-Stretch Reduction Problem: for an unweighted graph G = (V,E), find a set of edges not in E originally whose insertion into G can decrease the max-stretch of G. Our results are as follows: (i) For a ring graph, we give a linear-time algorithm which inserts k edges improving the max-stretch optimally. (ii) For a grid graph, we give a nearly optimal max-stretch reduction algorithm which preserves the structure of the grid. (iii) In the general case, we show that it is $\mathcal{NP}$-hard to decide, for a given graph G and its spanning tree of max-stretch t, whether or not one-edge insertion can decrease the max-stretch to t – 1. (iv) Finally, we show that the max-stretch of an arbitrary graph on n vertices can be reduced to s′≥ 2 by inserting O(n/s′) edges, which can be determined in linear time, and observe that this number of edges is optimal up to a constant.