A Faster All-Pairs Shortest Path Algorithm for Real-Weighted Sparse Graphs
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Improved Shortest Paths on the Word RAM
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Improved Algorithms for Finding Level Ancestors in Dynamic Trees
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
On the Comparison-Addition Complexity of All-Pairs Shortest Paths
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Experimental Evaluation of a New Shortest Path Algorithm
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
Path Minima in Incremental Unrooted Trees
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Improved Algorithms for Detecting Negative Cost Cycles in Undirected Graphs
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Improved algorithm for the symmetry number problem on trees
Information Processing Letters
Algorithms and theory of computation handbook
A scaling algorithm for maximum weight matching in bipartite graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Sensitivity analysis of minimum spanning trees in sub-inverse-ackermann time
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
A simple reduction from maximum weight matching to maximum cardinality matching
Information Processing Letters
Linear-Time Approximation for Maximum Weight Matching
Journal of the ACM (JACM)
On multiprocessor temperature-aware scheduling problems
Journal of Scheduling
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This paper presents an algorithm for maximum matching on general graphs with integral edge weights, running in time O(n3/4m lg N), where n, m and N are the number of vertices, number of edges, and largest edge weight magnitude, respectively. The best previous bound is O(n(mlg lg lgd n + n lg n)) where d is the density of the graph. The algorithm finds augmenting paths in batches by scaling the weights. The algorithm extends to degree-constrained subgraphs and hence to shortest paths on undirected graphs, the Chinese postman problem and finding a maximum cut of a planar graph. It speeds up Christofides' travelling salesman approximation algorithm from O(n3) to O(n2.75 lg n). A list splitting problem that arises in Edmonds' matching algorithm is solved in O(mα(m,n)) time, where m is the number of operations on a universe of n elements; the list splitting algorithm does not use set merging. Applications are given to update problems for red-green matching, the cardinality Chinese postman problem and the maximum cardinality plane cut problem; also to the all-pairs shortest paths problem on undirected graphs with lengths plus or minus one.