TY - GEN

T1 - Maintenance of a minimum spanning forest in a dynamic planar graph

AU - Eppstein, David

AU - Italiano, Giuseppe F.

AU - Tamassia, Roberto

AU - Tarjan, Robert E.

AU - Westbrook, Jeffery

AU - Yung, Moti

N1 - Funding Information:
*Computer Science Laboratory, Xerox PARC, 3333 Coyote Hill Rd., Palo Alto, CA 94304. This work was done while the author was at the Department of Computer Science, Columbia University, New York, NY 10027. **Department of Computer Science, Columbia University, New York, NY 10027 and Dipartmento di Informatica e Sis-temistica, Universitb di Roma, Rome, Italy. ***Department of Computer Science, Brown University, Box 1910, Providence, RI 02912-1910. #Department of Computer Science, Princeton University, Princeton, NJ 08544, and AT&T Bell Laboratories, Murray Hill, New Jersey 07974. ##Department of Computer Science, Stanford University, Stanford, CA 94305. This work was done while the author was at Department of Computer Science, Princeton University, Princeton, NJ 08544. ###IBM Research Division, T. J. Watson Research Center, Yorktown Heights, NY 10598. + Research supported in part by NSF grant CCR-8X-14977, NSF grant DCR-86-05962, ONR Contract N00014-87-H-0467 and Esprit II Basic Research Actions Program of the European Communities Contract No. 3075.

PY - 1990/1/1

Y1 - 1990/1/1

N2 - We give efficient algorithms for maintaining a minimum spanning forest of a planar graph subject to on-line modifications. The modifications supported include changes in the edge weights, and insertion and deletion of edges and vertices. To implement the algorithms, we develop a data structure called an edge-ordered dynamic tree, which is a variant of the dynamic tree data structure of Sleator and Tarjan. Using this data structure, our algorithms run in O(logn) time per operation and O(n) space. The algorithms can be used to maintain the connected components of a dynamic planar graph in O(logn) time per operation.

AB - We give efficient algorithms for maintaining a minimum spanning forest of a planar graph subject to on-line modifications. The modifications supported include changes in the edge weights, and insertion and deletion of edges and vertices. To implement the algorithms, we develop a data structure called an edge-ordered dynamic tree, which is a variant of the dynamic tree data structure of Sleator and Tarjan. Using this data structure, our algorithms run in O(logn) time per operation and O(n) space. The algorithms can be used to maintain the connected components of a dynamic planar graph in O(logn) time per operation.

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M3 - Conference contribution

AN - SCOPUS:85031912028

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1

EP - 11

BT - Proceedings of the 1st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1990

PB - Association for Computing Machinery

T2 - 1st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1990

Y2 - 22 January 1990 through 24 January 1990

ER -