Algorithms for clustering data
Algorithms for clustering data
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Incremental algorithms for collision detection between solid models
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Incremental collision detection for polygonal models
Proceedings of the eleventh annual symposium on Computational geometry
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Data structures for mobile data
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Kinetic collision detection between two simple polygons
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Kinetic binary space partitions for intersecting segments and disjoint triangles
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Computing nearest neighbors for moving points and applications to clustering
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
The analysis of a simple k-means clustering algorithm
Proceedings of the sixteenth annual symposium on Computational geometry
Kinetic connectivity for unit disks
Proceedings of the sixteenth annual symposium on Computational geometry
Faster kinetic heaps and their use in broadcast scheduling
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic issues in modeling motion
ACM Computing Surveys (CSUR)
An Efficient k-Means Clustering Algorithm: Analysis and Implementation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Smooth kinetic maintenance of clusters
Proceedings of the nineteenth annual symposium on Computational geometry
Maintaining Nets and Net Trees under Incremental Motion
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Kinetic convex hulls and delaunay triangulations in the black-box model
Proceedings of the twenty-seventh annual symposium on Computational geometry
Tracking moving objects with few handovers
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Competitive query strategies for minimising the ply of the potential locations of moving points
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We propose a generic computational framework for maintaining a discrete geometric structure defined by a collection of static and mobile objects. We assume that the mobile objects move incrementally, that is, in discrete time steps. We assume that the structure to be maintained is a function of the current locations of the mobile and static objects (independent of their prior motion). Unlike other models for kinetic computation, we place no restrictions on the motion nor on its predictability.In order to handle unrestricted incremental motion, our framework is based on the coordination of two computational entities. The first is the incremental motion algorithm. It is responsible for maintaining the structure and a set of certificates, or conditions, that prove the structure's correctness. The other entity, called the motion processor, is responsible for handling all the low-level aspects of motion, including computing and/or tracking the motion of the mobile objects, answering queries about their current positions and velocities, and validating that the object motions satisfy simple motion estimates, which are generated by the incremental motion algorithm. Computational efficiency is measured in terms of the number of interactions between these two entities.