Decremental dynamic connectivity

Conference · Sun Jun 01 04:00:00 EDT 1997

OSTI ID:471686

Thorup, M ^[1]

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1. 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--
• Country of Publication: United States
• Language: English

Related Subjects

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