The Weak Gap Property in Metric Spaces of Bounded Doubling Dimension
نویسنده
چکیده
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.
منابع مشابه
The Gap Property in Doubling Metrics
We introduce the weak gap property as a variant of the gap property. We show that in any metric space of bounded doubling dimension, any directed graph whose vertex set S has size n and which satisfies the weak gap property has total weight O(wt(MST (S)) log n), 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...
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