Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
An Efficient Implementation of Edmonds' Algorithm for Maximum Matching on Graphs
Journal of the ACM (JACM)
Some NP-complete geometric problems
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
Combinatorial Algorithms: Theory and Practice
Combinatorial Algorithms: Theory and Practice
A new class of heuristic algorithms for weighted perfect matching
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
Computational experience with an approximation algorithm on large-scale Euclidean matching instances
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
A greedy heuristic for a minimum-weight forest problem
Operations Research Letters
On the existence of weak greedy matching heuristics
Operations Research Letters
| Hi-index | 0.00 |
The problem of finding near optimal perfect matchings of an even number n of vertices is considered. When the distances between the vertices satisfy the triangle inequality it is possible to get within a constant multiplicative factor of the optimal matching in time O(n2 log K) where K is the ratio of the longest to the shortest distance between vertices. Other heuristics are analyzed as well, including one that gets within a logarithmic factor of the optimal matching in time O(n2 log n). Finding an optimal weighted matching requires &thgr;(n3) time by the fastest known algorithm, so these heuristics are quite useful. When the n vertices lie in the unit (Euclidean) square, no heuristic can be guaranteed to produce a matching of cost less than [equation] in the worst case. We analyze various heuristics for this case, including one that always produces a matching costing at most [equation]. In addition, this heuristic also finds a traveling salesman tour of the n vertices costing at most [equation]. A different one of the heuristics analyzed produces asymptotically optimal results. It is also shown that asymptotically optimal traveling salesman tours can be found in O(n log n) time in the unit square.