Priority queues with variable priority and an O(EV log V) algorithm for finding a maximal weighted matching in general graphs

We define two generalized types of a priority queue by allowing some forms of changing the priorities of the elements in the queue. We show that they can be implemented efficiently. Consequently, each operation takes O(log n) time. We use these generalized priority queues to construct an O(EV log V) algorithm for finding a maximal weighted matching in general graphs.

[1]  Harold N. Gabow,et al.  A Note on Degree-Constrained Star Subgraphs of Bipartite Graphs , 1976, Inf. Process. Lett..

[2]  Robert E. Tarjan,et al.  Scaling and related techniques for geometry problems , 1984, STOC '84.

[3]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[4]  Harold N. Gabow.  A good algorithm for smallest spanning trees with a degree constraint , 1978, Networks.

[5]  Eugene W. Myers,et al.  Finding All Spanning Trees of Directed and Undirected Graphs , 1978, SIAM J. Comput..

[6]  Robert E. Tarjan,et al.  A linear-time algorithm for a special case of disjoint set union , 1983, J. Comput. Syst. Sci..

[7]  Harold N. Gabow,et al.  An efficient reduction technique for degree-constrained subgraph and bidirected network flow problems , 1983, STOC.

[8]  Zvi Galil,et al.  Efficient Algorithms for Finding Maximal Matching in Graphs , 1983, CAAP.

[9]  Harold N. Gabow,et al.  Scaling algorithms for network problems , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[10]  R. E. Bellman,et al.  Review: Eugene L. Lawler, Combinatorial optimization: networks and matroids , 1978 .

[11]  Harold N. Gabow.  Algorithmic proofs of two relations between connectivity and the 1-factors of a graph , 1979, Discret. Math..

[12]  Harold N. Gabow,et al.  Two Algorithms for Generating Weighted Spanning Trees in Order , 1977, SIAM J. Comput..

[13]  Harold N. Gabow.  Some Improved Bounds on the Number of 1-Factors of n-Connected Graphs , 1976, Inf. Process. Lett..

[14]  D. Sleator.  An 0 (nm log n) algorithm for maximum network flow , 1980 .

[15]  Leon J. Osterweil,et al.  On Two Problems in the Generation of Program Test Paths , 1976, IEEE Transactions on Software Engineering.

[16]  Harold N. Gabow,et al.  Using euler partitions to edge color bipartite multigraphs , 1976, International Journal of Computer & Information Sciences.

[17]  Amnon Naamad,et al.  An O(EVlog²V) Algorithm for the Maximal Flow Problem , 1980, J. Comput. Syst. Sci..

[18]  Harold Gabow,et al.  Decomposing symmetric exchanges in matroid bases , 1976, Math. Program..

[19]  Robert E. Tarjan,et al.  Efficient Algorithms for a Family of Matroid Intersection Problems , 1984, J. Algorithms.

[20]  Robert E. Tarjan,et al.  Efficient algorithms for simple matroid intersection problems , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[21]  Jack Edmonds,et al.  Maximum matching and a polyhedron with 0,1-vertices , 1965 .

[22]  Harold N. Gabow.  A Linear-Time Recognition Algorithm for Interval Dags , 1981, Inf. Process. Lett..

[23]  Harold N. Gabow,et al.  Algorithms for edge coloring bipartite graphs , 1978, STOC '78.

[24]  Harold N. Gabow,et al.  An Augmenting Path Algorithm for the Parity Problem on Linear Matroids , 1984, FOCS.

[25]  Harold N. Gabow,et al.  An Efficient Implementation of Edmonds' Algorithm for Maximum Matching on Graphs , 1976, JACM.

[26]  Harold Neil Gabow,et al.  Implementation of algorithms for maximum matching on nonbipartite graphs , 1973 .

[27]  A. V. Karzanov,et al.  Determining the maximal flow in a network by the method of preflows , 1974 .

[28]  Harold N. Gabow,et al.  An Almost-Linear Algorithm for Two-Processor Scheduling , 1982, JACM.

[29]  Harold N. Gabow,et al.  A Counting Approach to Lower Bounds for Selection Problems , 1979, JACM.

[30]  Harold N. Gabow,et al.  Algorithms for Edge Coloring Bipartite Graphs and Multigraphs , 1982, SIAM J. Comput..