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On the Exponent of the All Pairs Shortest Path Problem
An algorithm of timeO(n?log3n),?=(3+?)/2, for the case of edge lengths in {?1, 0, 1}.
Sparsification-a technique for speeding up dynamic graph algorithms
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
Sparsification—a technique for speeding up dynamic graph algorithms
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.
Efficient algorithms for finding minimum spanning trees in undirected and directed graphs
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.
Efficient algorithms for finding maximum matching in graphs
  • Z. Galil
  • Computer Science, Mathematics
  • 1 March 1986
The techniques used for designing the most efficient algorithms for finding a maximum cardinality or weighted matching in (general or bipartite) graphs are surveyed.
All Pairs Shortest Paths for Graphs with Small Integer Length Edges
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.
Sparse dynamic programming I: linear cost functions
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.
Resolving message complexity of Byzantine Agreement and beyond
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.
Data structures and algorithms for disjoint set union problems
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.