Algorithms on negatively curved spaces

d abstract] Robert Krauthgamer ∗ IBM Almaden James R. Lee † Institute for Advanced Study We initiate the study of approximate algorithms on negatively curved spaces. These spaces have recently become of interest in various domains of computer science including networking and vision. The classical example of such a space is the real-hyperbolic space Hd for d ≥ 2, but our approach applies to a more general family of spaces characterized by Gromov's (combinatorial) hyperbolic condition. We give ef cient algorithms and data structures for problems like approximate nearest-neighbor search and compact, low-stretch routing on subsets of negatively curved spaces of xed dimension (including Hd as a special case). In a different direction, we show that there is a PTAS for the Traveling Salesman Problem when the set of cities lie, for example, in Hd . This generalizes Arora's results for Rd . Most of our algorithms use the intrinsic distance geometry of the data set, and only nee...

• Type: Conference
• Year: 2006
• Where: FOCS
• Authors: Robert Krauthgamer, James R. Lee
• Keywords: Algorithms, Curved Space, FOCS 2006, Real-hyperbolic Space Hd, Theoretical Computer Science