Maintaining Center and Median in Dynamic Trees

We show how to maintain centers and medians for a collection of dynamic trees where edges may be inserted and deleted and node and edge weights may be changed. All updates are supported in O(log n) time, where n is the size of the tree(s) involved in the update.

[1]  Michael E. Saks,et al.  The cell probe complexity of dynamic data structures , 1989, STOC '89.

[2]  R. Tamassia,et al.  Dynamic expression trees and their applications , 1991, SODA '91.

[3]  O. Kariv,et al.  An Algorithmic Approach to Network Location Problems. II: The p-Medians , 1979 .

[4]  G. Handler.  Minimax Location of a Facility in an Undirected Tree Graph , 1973 .

[5]  Greg N. Frederickson,et al.  Data Structures for On-Line Updating of Minimum Spanning Trees, with Applications , 1985, SIAM J. Comput..

[6]  Roberto Tamassia,et al.  On-line maintenance of the four-connected components of a graph , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[7]  Stephen B. Peckham.  Maintaining Tree Projections in Amortized $O$(log $n$) Time. , 1989 .

[8]  Siu-Wing Cheng,et al.  Isomorphism testing and display of symmetries in dynamic trees , 1996, SODA '96.

[9]  Bezalel Gavish,et al.  Computing the 2-median on tree networks in O(n lg n) time , 1995, Networks.

[10]  Robert E. Tarjan,et al.  Dynamic trees as search trees via euler tours, applied to the network simplex algorithm , 1997, Math. Program..

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

[12]  Roberto Tamassia,et al.  Combine and Conquer , 1997, Algorithmica.

[13]  Mikkel Thorup,et al.  Minimizing Diameters of Dynamic Trees , 1997, ICALP.

[14]  Roberto Tamassia,et al.  On-Line Graph Algorithms with SPQR-Trees , 1990, ICALP.

[15]  Robert E. Tarjan,et al.  A Class of Algorithms which Require Nonlinear Time to Maintain Disjoint Sets , 1979, J. Comput. Syst. Sci..

[16]  Zvi Galil,et al.  Maintaining Biconnected Components of Dynamic Planar Graphs , 1991, ICALP.

[17]  Monika Henzinger,et al.  Randomized dynamic graph algorithms with polylogarithmic time per operation , 1995, STOC '95.

[18]  Greg N. Frederickson,et al.  Data structures for on-line updating of minimum spanning trees , 1983, STOC.

[19]  La Poutre,et al.  Alpha-algorithms for incremental planarity testing , 1994 .

[20]  Andrew V. Goldberg,et al.  Use of dynamic trees in a network simplex algorithm for the maximum flow problem , 1991, Math. Program..

[21]  Han La Poutré,et al.  Alpha-algorithms for incremental planarity testing (preliminary version) , 1994, STOC '94.

[22]  Greg N. Frederickson,et al.  Parametric Search and Locating Supply Centers in Trees , 1991, WADS.

[23]  A. J. Goldman.  Optimal Center Location in Simple Networks , 1971 .

[24]  S. L. HAKIMIt.  AN ALGORITHMIC APPROACH TO NETWORK LOCATION PROBLEMS. , 1979 .

[25]  Tomasz Radzik.  Implementation of dynamic trees with in-subtree operations , 1998, JEAL.

[26]  José A. Pino,et al.  A generalized algorithm for centrality problems on trees , 1989, JACM.

[27]  Mimmo Parente,et al.  Dynamic and Static Algorithms for Optimal Placement of Resources in a Tree , 1996, Theor. Comput. Sci..

[28]  Han La Poutré.  Maintenance of Triconnected Components of Graphs (Extended Abstract) , 1992, ICALP.

[29]  Roberto Tamassia,et al.  Incremental Planarity Testing (Extended Abstract) , 1989, IEEE Annual Symposium on Foundations of Computer Science.

[30]  Greg N. Frederickson.  Ambivalent Data Structures for Dynamic 2-Edge-Connectivity and k Smallest Spanning Trees , 1997, SIAM J. Comput..

[31]  Roberto Tamassia,et al.  Incremental planarity testing , 1989, 30th Annual Symposium on Foundations of Computer Science.