A t-spanner of a graph G is a spanning subgraph H such that the distance between any two vertices in H is at most t times their distance in G. Spanners arise in the context of approximating the original graph by a sparse subgraph 23]. The MINIMUM t-SPANNER problem seeks to nd a t-spanner with the minimum number of edges for the given graph. In this paper, we completely settle the complexity status of this problem for various values of t, on Chordal graphs, Split graphs, Bipartite graphs and Convex Bipartite graphs. Our results settle an open question raised in 7] and also greatly simplify some of the proofs presented in 7, 8]. We also give a factor two approximation algorithm for the MINIMUM 2-SPANNER problem on interval graphs. Finally, we provide approximation algorithms for the bandwidth minimization problem on Convex Bipartite graphs and Split graphs using the notion of tree spanners.
Venkatesan et al. REF revealed the complexity of Minimum Multiplicative t-Spanner Problem for several graph classes such as chordal graphs, convex bipartite graphs, and split graphs.
Restrictions of Minimum Spanner Problems
Inf. Comput.
Inf. Comput.
Mathematics Computer Science