Data structures and network algorithms
Data structures and network algorithms
An O(EV log V) algorithm for finding a maximal weighted matching in general graphs
SIAM Journal on Computing
Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Efficient Algorithms for Shortest Paths in Sparse Networks
Journal of the ACM (JACM)
A data structure for manipulating priority queues
Communications of the ACM
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Implementation of algorithms for maximum matching on nonbipartite graphs.
Implementation of algorithms for maximum matching on nonbipartite graphs.
Faster scaling algorithms for general graph matching problems
Journal of the ACM (JACM)
A general approximation technique for constrained forest problems
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
A parallel algorithm for computing minimum spanning trees
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Data structures for weighted matching and nearest common ancestors with linking
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Combinatorial Optimization by Dynamic Contraction
Journal of Heuristics
Meldable RAM priority queues and minimum directed spanning trees
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A linear-time approximation algorithm for weighted matchings in graphs
ACM Transactions on Algorithms (TALG)
Incremental assignment problem
Information Sciences: an International Journal
Randomized minimum spanning tree algorithms using exponentially fewer random bits
ACM Transactions on Algorithms (TALG)
Agent-oriented programming: from prolog to guarded definite clauses
Agent-oriented programming: from prolog to guarded definite clauses
A scaling algorithm for maximum weight matching in bipartite graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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)
| Hi-index | 0.00 |
The (component) merging problem is a new graph problem. Versions of this problem appear as bottlenecks in various graph algorithms. A new data structure solves this problem efficiently, and two special cases of the problem have even more efficient solutions based on other data structures. The performance of the data structures is sped up by introducing a new algorithmic tool called packets.The algorithms that use these solutions to the component merging problem also exploit new properties of two existing data structures. Specifically, &Bgr;-trees can be used simultaneously as a priority queue and a concatenable queue. Similarly, F-heaps support some kinds of split operations with no loss of efficiency.An immediate application of the solution to the simplest version of the merging problem is an &Ogr;(t(m, n)) algorithm for finding minimum spanning trees in undirected graphs without using F-heaps, where t(m, n) = mlog2log2logdn, the graph has n vertices and m edges, and d = max(m/n, 2). Packets also improve the F-heap minimum spanning tree algorithm, giving the fastest algorithm currently known for this problem.The efficient solutions to the merging problem and the new observation about F-heaps lead to an &Ogr;(n(t(m, n) + nlogn)) algorithm for finding a maximum weighted matching in general graphs. This settles an open problem posed by Tarjan [ 15, p. 123], where the weaker bound of O(nm log (n2/m)) was conjectured.