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- Valerie King
- FOCS
- 1999

This paper presents the first fully dynamic algorithms for maintaining all-pairs shortest paths in digraphs with positive integer weights less than b. For approximate shortest paths with an error factor of (2 +), for any positive constant , the amortized update time is O(n 2 log 2 n= log log n); for an error factor of (1 +) the amortized update time is O(n… (More)

This paper presents an eecient fully dynamic graph algorithm for maintaining the transitive closure of a directed graph. The algorithm updates the adjacency matrix of the transitive closure with each update to the graph. Hence, each reachability query of the form \Is there a directed path from i to j?" can be answered in O(1) time. The algorithm is… (More)

This paper solves a longstanding open problem in fully dynamic algorithms: We present the first fully dynamic algorithms that maintain connectivity, bipartiteness, and approximate minimum spanning trees in polylogarithmic time per edge insertion or deletion. The algorithms are designed using a new dynamic technique that combines a novel graph decomposition… (More)

We are given a set T = {T 1 , T 2 ,. .. , T k } of rooted binary trees, each T i leaf-labeled by a subset L(T i) ⊂ {1, 2,. .. , n}. If T is a tree on {1, 2,. .. , n}, we let T |L denote the minimal subtree of T induced by the nodes of L and all their ancestors. The consensus tree problem asks whether there exists a tree T * such that, for every i, T * |L(T… (More)

This paper solves a longstanding open problem in dynamic algorithms: We present the first dynamic algorithms that maintain connectivity, 2-edge connectivity, bipartiteness, cycle-equivalence, and approximate minimum spanning trees in polylogarithmic time per operation. The algorithms are designed using a new dynamic technique which combines a novel graph… (More)

- Valerie King
- WADS
- 1995

The problem considered here is that of determining whether a given spanning tree is a minimal spanning tree. In 1984 Koml6s presented an algorithm which required only a linear number of comparisons, but nonlinear overhead to determine which comparisons to make. We simplify his algorithm and give a linear-time procedure for its implementation in the unit… (More)

We consider a wireless sensor network in which each sensor is able to transmit within a disk of radius one. We show with elementary techniques that there exists a constant c such that if we throw cN sensors into an n × n square (of area N) independently at random, then with high probability there will be exactly one connected component which reaches all… (More)

We describe a deterministic version of a 1990 Cheriyan, Hagerup, and Mehlhorn randomized algorithm for computing the maximum flow on a directed graph with <italic>n</italic> nodes and <italic>m</italic> edges which runs in time <italic>O</italic>(<italic>mn</italic> + <italic>n</italic><supscrpt>2+ε</supscrpt>, for any constant <italic>ε</italic>.… (More)