An (α, β)-spanner of a graph G is a subgraph H such that dH (u, w) ≤ α · dG (u, w) + β for every pair of vertices u, w, where dG' (u, w) denotes the distance between two vertices u and v in G'. It is known that every graph G has a polynomially constructible (2k - 1,0)-spanner (a.k.a. multiplicative (2k - 1)-spanner) of size O(n1+1/k) for every integer k ≥ 1, and a polynomially constructible (1, 2)-spanner (a.k.a. additive 2-spanner) of size Õ(n3/2). This paper explores hybrid spanner constructions (involving both multiplicative and additive factors) for general graphs and shows that the multiplicative factor can be made arbitrarily close to 1 while keeping the spanner size arbitrarily close to O(n), at the cost of allowing the additive term to be a sufficiently large constant. More formally, we show that for any constant ε, δ > 0 there exists a constant β = β(ε, δ) such that for every n-vertex graph G there is an efficiently constructible (1+ε,β)-spanner of size O(n1+δ). It follows that for any constant ε, δ > 0 and graph G, there exists a spanning subgraph H with O(n1+δ) edges which behaves like a multiplicative (1 + ε)-spanner for "sufficiently distant" pairs of vertices.
|Number of pages||10|
|Journal||Conference Proceedings of the Annual ACM Symposium on Theory of Computing|
|State||Published - 1 Jan 2001|
|Event||33rd Annual ACM Symposium on Theory of Computing - Creta, Greece|
Duration: 6 Jul 2001 → 8 Jul 2001
ASJC Scopus subject areas