The authors provide data structures that maintain a graph as edges are inserted and deleted, and keep track of the following properties: minimum spanning forests, best swap, graph connectivity, and… Expand

All algorithms are based on a new technique that transforms an algorithm for sparse graphs into one that will work on any graph, which is calledsparsification, and results speed up the insertion times to match the bounds of known partially dynamic algorithms.Expand

This paper uses F-heaps to obtain fast algorithms for finding minimum spanning trees in undirected and directed graphs and can be extended to allow a degree constraint at one vertex.Expand

The techniques used for designing the most efficient algorithms for finding a maximum cardinality or weighted matching in (general or bipartite) graphs are surveyed.Expand

This paper shows how to transform these algorithms to solve the all pairs shortest paths (APSP), in the same time complexity, up to a polylogarithmic factor.Expand

Dynamic programming solutions to a number of different recurrence equations for sequence comparison and for RNA secondary structure prediction are considered, when the weight functions used in the recurrences are taken to be linear.Expand

This work shows how to solve agreement in the presence of crash failures using O(n) messages which is optimal, thus settling a thirteen year old open problem.Expand

An attempt is made to provide a unifying theoretical framework for this growing body of algorithms that have been proposed to solve the set union problem and its variants.Expand