Arboricity and subgraph listing algorithms
SIAM Journal on Computing
The Hamiltonian cycle problem is linear-time solvable for 4-connected planar graphs
Journal of Algorithms
Data structures for mobile data
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Voronoi Diagrams of Moving Points in the Plane
WG '91 Proceedings of the 17th International Workshop
On embedding an outer-planar graph in a point set
Computational Geometry: Theory and Applications
Parametric and Kinetic Minimum Spanning Trees
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Kinetic data structures
Curve-constrained drawings of planar graphs
Computational Geometry: Theory and Applications
Each maximal planar graph with exactly two separating triangles is Hamiltonian
Discrete Applied Mathematics
Kinetic and dynamic data structures for closest pair and all nearest neighbors
ACM Transactions on Algorithms (TALG)
Improved bounds and new techniques for Davenport--Schinzel sequences and their generalizations
Journal of the ACM (JACM)
Davenport-Schinzel Sequences and their Geometric Applications
Davenport-Schinzel Sequences and their Geometric Applications
On the hardness of point-set embeddability
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
The point-set embeddability problem for plane graphs
Proceedings of the twenty-eighth annual symposium on Computational geometry
Kinetic Euclidean minimum spanning tree in the plane
Journal of Discrete Algorithms
Kinetic pie delaunay graph and its applications
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Kinetic data structures for all nearest neighbors and closest pair in the plane
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We investigate a kinetic version of point-set embeddability. Given a plane graph G(V,E) where |V|=n, and a set P of n moving points where the trajectory of each point is an algebraic function of constant maximum degree s, we maintain a point-set embedding of G on P with at most three bends per edge during the motion. This requires reassigning the mapping of vertices to points from time to time. Our kinetic algorithm uses linear size, O(nlogn) preprocessing time, and processes O(n2β2s+2(n)logn) events, each in O(log2n) time. Here, βs(n)=λs(n)/ n is an extremely slow-growing function and λs(n) is the maximum length of Davenport-Schinzel sequences of order s on n symbols.