Survival Network Design of Doubling Dimension Metrics
نویسنده
چکیده
We investigate the MinimumWeight 2-Edge-Connected Spanning Subgraph (2-ECSS) problem in an arbitrary metric space of doubling dimension and show a polynomial time randomized (1+ǫ)-approximation algorithm.
منابع مشابه
Bounded Geometries, Fractals, and Low-Distortion Embeddings
The doubling constant of a metric space (X; d) is the smallest value such that every ball in X can be covered by balls of half the radius. The doubling dimension of X is then defined as dim(X) = log2 . A metric (or sequence of metrics) is called doubling precisely when its doubling dimension is bounded. This is a robust class of metric spaces which contains many families of metrics that occur i...
متن کاملGreedy spanners are optimal in doubling metrics
We show that the greedy spanner algorithm constructs a (1+ )-spanner of weight −O(d)w(MST) for a point set in metrics of doubling dimension d, resolving an open problem posed by Gottlieb [11]. Our result generalizes the result by Narasimhan and Smid [15] who showed that a point set in d-dimension Euclidean space has a (1+ )-spanner of weight at most −O(d)w(MST). Our proof only uses the packing ...
متن کاملApproximation Algorithms for Bounded Dimensional Metric Spaces
The study of finite metrics is an important area of research, because of its wide applications to many different problems. The input of many problems (for instance clustering, near-neighbor queries and network routing) naturally involves a set of points on which a distance function has been defined. Hence, one would be motivated to store and process metrics in an efficient manner. The central i...
متن کاملCompact Routing Schemes in Networks of Low Doubling Dimension
We consider compact routing schemes in networks of low doubling dimension, where the doubling dimension is the least value α such that any ball in the network can be covered by at most 2 balls of half radius. There are two variants of routing scheme design: (i) labeled (name-dependent) routing, where the designer is allowed to rename the nodes so that the names (labels) can contain additional r...
متن کاملA $(1 + {\varepsilon})$-Embedding of Low Highway Dimension Graphs into Bounded Treewidth Graphs
Graphs with bounded highway dimension were introduced in [Abraham et al., SODA 2010] as a model of transportation networks. We show that any such graph can be embedded into a distribution over bounded treewidth graphs with arbitrarily small distortion. More concretely, if the highway dimension of G is constant we show how to randomly compute a subgraph of the shortest path metric of the input g...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1210.5729 شماره
صفحات -
تاریخ انتشار 2012