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...

• Type: Conference
• Year: 2004
• Where: COMPGEOM
• Authors: Mihai Badoiu, Erik D. Demaine, Mohammad Taghi Hajiaghayi, Piotr Indyk
• Keywords: Algorithms, COMPGEOM 2004, Extra Information, General Graphs