Years and Authors of Summarized Original Work
2000; Holm, de Lichtenberg, Thorup
Problem Definition
Let \( G=(V,E) \) be an undirected weighted graph. The problem considered here is concerned with maintaining efficiently information about a minimum spanning tree of G (or minimum spanning forest if G is not connected), when G is subject to dynamic changes, such as edge insertions, edge deletions and edge weight updates. One expects from the dynamic algorithm to perform update operations faster than recomputing the entire minimum spanning tree from scratch.
Throughout, an algorithm is said to be fully dynamic if it can handle both edge insertions and edge deletions. A partially dynamic algorithm can handle either edge insertions or edge deletions, but not both: it is incremental if it supports insertions only, and decremental if it supports deletions only.
Key Results
The dynamic minimum spanning forest algorithm presented in this section builds upon the dynamic connectivity algorithm...
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Recommended Reading
Alberts D, Cattaneo G, Italiano GF (1997) An empirical study of dynamic graph algorithms. ACM J Exp Algorithm 2
Cattaneo G, Faruolo P, Ferraro Petrillo U, Italiano GF (2002) Maintaining dynamic minimum spanning trees: an experimental study. In: Proceeding 4th workshop on algorithm engineering and experiments (ALENEX 02), 6–8 Jan, pp 111–125
Eppstein D (1992) Finding the k smallest spanning trees. BIT 32:237–248
Eppstein D (1994) Tree-weighted neighbors and geometric k smallest spanning trees. Int J Comput Geom Appl 4:229–238
Eppstein D, Galil Z, Italiano GF, Nissenzweig A (1997) Sparsification – a technique for speeding up dynamic graph algorithms. J Assoc Comput Mach 44(5):669–696
Eppstein D, Italiano GF, Tamassia R, Tarjan RE, Westbrook J, Yung M (1992) Maintenance of a minimum spanning forest in a dynamic plane graph. J Algorithms 13:33–54
Feder T, Mihail M (1992) Balanced matroids. In: Proceeding 24th ACM symposium on theory of computing, Victoria, 04–06 May, pp 26–38
Frederickson GN (1985) Data structures for on-line updating of minimum spanning trees. SIAM J Comput 14:781–798
Frederickson GN (1991) Ambivalent data structures for dynamic 2-edge-connectivity and k smallest spanning trees. In: Proceeding 32nd symposium on foundations of computer science, San Juan, 01–04 Oct, pp 632–641
Frederickson GN, Srinivas MA (1989) Algorithms and data structures for an expanded family of matroid intersection problems. SIAM J Comput 18:112–138
Henzinger MR, King V (2001) Maintaining minimum spanning forests in dynamic graphs. SIAM J Comput 31(2):364–374
Henzinger MR, King V (1999) Randomized fully dynamic graph algorithms with polylogarithmic time per operation. J ACM 46(4):502–516
Holm J, de Lichtenberg K, Thorup M (2001) Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity. J ACM 48:723–760
Paul J, Simon W (1980) Decision trees and random access machines. In: Symposium über Logik und Algorithmik; See also Mehlhorn K (1984) Sorting and searching. Springer, Berlin, pp 85–97
Tarjan RE, Vishkin U (1985) An efficient parallel biconnectivity algorithm. SIAM J Comput 14:862–874
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Italiano, G.F. (2016). Fully Dynamic Minimum Spanning Trees. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_156
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