- Author:
- Julien Basch,
- Adviser:
- Leonidas J. Guibas
Modeling the physical world in the computer raises problems that intertwine discrete and continuous aspects. For example, physical objects move along continuous trajectories; yet every so often discrete events occur, such as collisions between objects.
In a model of objects in space, there are many discrete attributes that one may want to compute: the closest pair, the convex hull, the minimum spanning tree, etc. When the objects are in motion, the values of these attributes change over time, and it becomes necessary to keep track of them as the objects move.
In this thesis, we introduce a general approach, and an analysis framework, for solving this type of problems. To keep track of a discrete attribute, we create a new type of data structure, called a kinetic data structure. A kinetic data structure is made of a proof of correctness of the attribute which is animated through time by a discrete event simulation.
Cited By
- Rahmati Z, Whitesides S and King V Kinetic and stationary point-set embeddability for plane graphs Proceedings of the 20th international conference on Graph Drawing, (279-290)
- Rahmati Z and Zarei A Kinetic euclidean minimum spanning tree in the plane Proceedings of the 22nd international conference on Combinatorial Algorithms, (261-274)
- Yu J, Vishwanathan S, Günter S and Schraudolph N (2010). A Quasi-Newton Approach to Nonsmooth Convex Optimization Problems in Machine Learning, The Journal of Machine Learning Research, 11, (1145-1200), Online publication date: 1-Mar-2010.
Xu Z and Jacobsen H Processing proximity relations in road networks Proceedings of the 2010 ACM SIGMOD International Conference on Management of data, (243-254)- Durocher S and Paul C (2009). Kinetic maintenance of mobile k-centres on trees, Discrete Applied Mathematics, 157:7, (1432-1446), Online publication date: 1-Apr-2009.
- Durocher S and Paul C Kinetic maintenance of mobile k-centres on trees Proceedings of the 18th international conference on Algorithms and computation, (341-352)
- Xu Z and Jacobsen A Adaptive location constraint processing Proceedings of the 2007 ACM SIGMOD international conference on Management of data, (581-592)
- Bereg S, Bhattacharya B, Kirkpatrick D and Segal M (2006). Competitive algorithms for maintaining a mobile center, Mobile Networks and Applications, 11:2, (177-186), Online publication date: 1-Apr-2006.
- Palpanas T, Vlachos M, Keogh E, Gunopulos D and Truppel W Online Amnesic Approximation of Streaming Time Series Proceedings of the 20th International Conference on Data Engineering
- Kaplan H, Tarjan R and Tsioutsiouliklis K Faster kinetic heaps and their use in broadcast scheduling Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms, (836-844)
- Bespamyatnikh S, Bhattacharya B, Kirkpatrick D and Segal M Mobile facility location (extended abstract) Proceedings of the 4th international workshop on Discrete algorithms and methods for mobile computing and communications, (46-53)
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