Decremental dynamic connectivity
- Univ. of Copenhagen (Denmark)
We consider Las Vegas randomized dynamic algorithms for on-line connectivity problems with deletions only. In particular, we show that starting from a graph with m edges and n nodes, we can maintain a spanning forest during m deletions in O(min(n{sup 2}, m log n) + {radical}nm log{sup 2.5} n) expected total time. This is amortized constant time per operation if we start with a complete graph. The deletions may be interspersed with connectivity queries, each of which is answered in constant time. The previous best bound was O(m log{sup 2} n) by Henzinger and Thorup, which covered both insertions and deletions. Our bound is stronger for m/n = {omega}(log n). The result is based on a general randomized reduction of many deletions-only queries to few deletions and insertions queries. Similar results are thus derived for 2-edge-connectivity, bipartiteness, and q-weights minimum spanning tree. For the decremental dynamic {kappa}-edge-connectivity problem of deleting the edges of a graph starting with m edges and n nodes, we get a total running time of O(k{sup 2}n{sup 2}polylog n). The previous best bound was O(kmnpolylog n). Also improved running times are achieved for the static consensus tree problem, with applications to computational biology and relational data bases.
- OSTI ID:
- 471686
- Report Number(s):
- CONF-970142-; TRN: 97:001377-0035
- Resource Relation:
- Conference: 8. annual Association for Computing Machinery (ACM)-Society for Industrial and Applied Mathematics (SIAM) symposium on discrete algorithms, New Orleans, LA (United States), 5-7 Jan 1997; Other Information: PBD: 1997; Related Information: Is Part Of Proceedings of the eighth annual ACM-SIAM symposium on discrete algorithms; PB: 798 p.
- Country of Publication:
- United States
- Language:
- English
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