Low-dimensional embedding with extra information

12 years 9 months ago
Low-dimensional embedding with extra information
A frequently arising problem in computational geometry is when a physical structure, such as an ad-hoc wireless sensor network or a protein backbone, can measure local information about its geometry (e.g., distances, angles, and/or orientations), and the goal is to reconstruct the global geometry from this partial information. More precisely, we are given a graph, the approximate lengths of the edges, and possibly extra information, and our goal is to assign coordinates to the vertices that satisfy the given constraints up to a constant factor away from the best possible. We obtain the first subexponential-time (quasipolynomial-time) algorithm for this problem given a complete graph of Euclidean distances with additive error and no extra information. For general graphs, the analogous problem is NP-hard even with exact distances. Thus, for general graphs, we consider natural types of extra information that make the problem more tractable, including approximate angles between edges, th...
Mihai Badoiu, Erik D. Demaine, Mohammad Taghi Haji
Added 30 Jun 2010
Updated 30 Jun 2010
Type Conference
Year 2004
Authors Mihai Badoiu, Erik D. Demaine, Mohammad Taghi Hajiaghayi, Piotr Indyk
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