Sparse Hypercube 3-spanners

W. Duckworth, M. Zito
2000 Discrete Applied Mathematics  
A t-spanner of a graph G = (V; E), is a sub-graph SG = (V; E ), such that E ⊆ E and for every edge {u; v} ∈ E, there is a path from u to v in SG of length at most t. A minimum-edge t-spanner of a graph G, S G , is the t-spanner of G with the fewest edges. For general graphs and for t = 2, the problem of determining for a given integer s, whether |E(S G )|6s is NP-Complete (Peleg and Scha er, J. Graph Theory 13(1) (1989) 99 -116). Peleg and Ullman (SIAM J. Comput. 18(4) (1989) 740 -747), give a
more » ... ethod for constructing a 3-spanner of the n-vertex Hypercube with fewer than 7n edges. In this paper we give an improved construction giving a 3-spanner of the n-vertex Hypercube with fewer than 4n edges and we present a lower bound of 3n=2 − o(1) on the size of the optimal Hypercube 3-spanner. ?
doi:10.1016/s0166-218x(99)00246-2 fatcat:wezq7n547vgbvne3aj6xnoanuy