Transitions in geometric minimum spanning trees (extended abstract)

2. We study some combinatorial and algorithmic problems related to transitions in Euclidean minimum spanning trees arising from an arbitrary motion of one or more points of the input set.

[1]  Robert E. Tarjan,et al.  A data structure for dynamic trees , 1981, STOC '81.

[2]  J..  SOME DYNAMIC COMPUTATIONAL GEOMETRY PROBLEMS , 2009 .

[3]  Tetsuo Asano,et al.  Clustering algorithms based on minimum and maximum spanning trees , 1988, SCG '88.

[4]  Charles T. Zahn,et al.  Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters , 1971, IEEE Transactions on Computers.

[5]  Andrew Chi-Chih Yao,et al.  On Constructing Minimum Spanning Trees in k-Dimensional Spaces and Related Problems , 1977, SIAM J. Comput..

[6]  H. D. Ratliff,et al.  A Cut Approach to the Rectilinear Distance Facility Location Problem , 1978, Oper. Res..

[7]  Robert L. Scot Drysdale,et al.  Voronoi diagrams based on convex distance functions , 1985, SCG '85.

[8]  Herbert Edelsbrunner,et al.  Algorithms in Combinatorial Geometry , 1987, EATCS Monographs in Theoretical Computer Science.

[9]  Robert W. Irving,et al.  Parametric Stable Marriage and Minimum Cuts , 1989, Inf. Process. Lett..

[10]  M. Atallah.  Some dynamic computational geometry problems , 1985 .

[11]  Robert E. Tarjan,et al.  A Fast Parametric Maximum Flow Algorithm and Applications , 1989, SIAM J. Comput..

[12]  Martin E. Dyer,et al.  On a Multidimensional Search Technique and its Application to the Euclidean One-Centre Problem , 1986, SIAM J. Comput..

[13]  J. Picard,et al.  Selected Applications of Minimum Cuts in Networks , 1982 .

[14]  William H. Cunningham,et al.  Optimal attack and reinforcement of a network , 1985, JACM.

[15]  Dan Gusfield,et al.  Parametric Combinatorial Computing and a Problem of Program Module Distribution , 1983, JACM.

[16]  Clyde L. Monma,et al.  Transitions in geometric minimum spanning trees , 1991, SCG '91.

[17]  Robert E. Tarjan,et al.  A data structure for dynamic trees , 1981, STOC '81.

[18]  Richard Cole,et al.  New Upper Bounds for Neighbor Searching , 1986, Inf. Control..