The Weak Gap Property in Metric Spaces of Bounded Doubling Dimension

We introduce the weak gap property for directed graphs whose vertex set S is a metric space of size n. We prove that, if the doubling dimension of S is a constant, any directed graph satisfying the weak gap property has O(n) edges and total weight O(log n) · wt(MST(S)), where wt(MST(S)) denotes the weight of a minimum spanning tree of S. We show that 2-optimal TSP tours and greedy spanners satisfy the weak gap property.

• Type: Conference
• Year: 2009
• Where: BIRTHDAY
• Authors: Michiel H. M. Smid
• Keywords: Applied Computing, BIRTHDAY 2009, Directed Graph, Minimum Spanning Tree, Weak Gap Property