Conditions for unique graph realizations
SIAM Journal on Computing
Efficient algorithms for inverting evolution
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Reconstructing a three-dimensional model with arbitrary errors
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
On the approximability of numerical taxonomy (fitting distances by tree metrics)
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
The Cricket location-support system
MobiCom '00 Proceedings of the 6th annual international conference on Mobile computing and networking
The cricket compass for context-aware mobile applications
Proceedings of the 7th annual international conference on Mobile computing and networking
Approximation algorithm for embedding metrics into a two-dimensional space
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
GPS-Free Positioning in Mobile ad-hoc Networks
HICSS '01 Proceedings of the 34th Annual Hawaii International Conference on System Sciences ( HICSS-34)-Volume 9 - Volume 9
Low-distortion embeddings of general metrics into the line
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Localization and routing in sensor networks by local angle information
Proceedings of the 6th ACM international symposium on Mobile ad hoc networking and computing
Theory of semidefinite programming for sensor network localization
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Ordinal embeddings of minimum relaxation: general properties, trees, and ultrametrics
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A semidefinite programming approach to tensegrity theory and realizability of graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Distributed localization using noisy distance and angle information
Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing
Plane embeddings of planar graph metrics
Proceedings of the twenty-second annual symposium on Computational geometry
GPS-Free node localization in mobile wireless sensor networks
MobiDE '06 Proceedings of the 5th ACM international workshop on Data engineering for wireless and mobile access
Ordinal embeddings of minimum relaxation: General properties, trees, and ultrametrics
ACM Transactions on Algorithms (TALG)
Localization and routing in sensor networks by local angle information
ACM Transactions on Sensor Networks (TOSN)
A linear-space algorithm for distance preserving graph embedding
Computational Geometry: Theory and Applications
Connectivity-based localization of large-scale sensor networks with complex shape
ACM Transactions on Sensor Networks (TOSN)
Managing cohort movement of mobile sensors via GPS-free and compass-free node localization
Journal of Parallel and Distributed Computing
Beyond triangle inequality: sifting noisy and outlier distance measurements for localization
INFOCOM'10 Proceedings of the 29th conference on Information communications
Beyond triangle inequality: Sifting noisy and outlier distance measurements for localization
ACM Transactions on Sensor Networks (TOSN)
| Hi-index | 0.00 |
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, the order type of vertices, a model of coordinate noise, or knowledge about the range of distance measurements. Our quasipolynomial-time algorithm for no extra information can also beviewed as a polynomial-time algorithm given an "extremum oracle" as extra information. We give several approximation algorithms and contrasting hardness results for these scenarios.