Data structures and network algorithms
Data structures and network algorithms
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Realistic input models for geometric algorithms
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Kinetic connectivity of rectangles
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Data structures for mobile data
Journal of Algorithms
Kinetic connectivity for unit disks
Proceedings of the sixteenth annual symposium on Computational geometry
Clustering algorithms for wireless ad hoc networks
DIALM '00 Proceedings of the 4th international workshop on Discrete algorithms and methods for mobile computing and communications
Dynamic subgraph connectivity with geometric applications
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Testing bipartiteness of geometric intersection graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Kinetic and dynamic data structures for convex hulls and upper envelopes
Computational Geometry: Theory and Applications
Kinetic and dynamic data structures for closest pair and all nearest neighbors
ACM Transactions on Algorithms (TALG)
Testing bipartiteness of geometric intersection graphs
ACM Transactions on Algorithms (TALG)
Dynamic Connectivity: Connecting to Networks and Geometry
SIAM Journal on Computing
Smoothed analysis of left-to-right maxima with applications
ACM Transactions on Algorithms (TALG)
| Hi-index | 0.00 |
We consider the problem of maintaining connected components in a set of moving objects using the kinetic data structure (KDS) framework. We assume that the motion of each object can be specified by a low-degree algebraic trajectory; this trajectory, however, can be modified in an on-line fashion. While the objects move continuously, their connectivity changes at discrete times. A straightforward dynamic graph approach for maintaining connectivity of n objects has three shortcomings: the graph can have &OHgr;(n2) edges, the update bounds are amortized, and the algorithm is very complicated. Our first result shows that the connectivity for a set of n moving hypercubes can be maintained using a very simple, easy to determine graph with &Ogr;(n) edges. But this graph still requires a general-purpose dynamic graph scheme for connectivity maintenance. Our main result is a simplified connectivity data structure for moving rectangles in the plane. For this special but important case, we are able to overcome all three shortcomings mentioned above: our graph has &Ogr;(n) edges; our data structure supports updates in &Ogr;(log2 n) worst-case time; and the algorithm and data structures are quite a bit simpler than those based on a general dynamic graph scheme.