The Weighted Matching Approach to Maximum Cardinality Matching
نویسنده
چکیده
Several papers have achieved time O( √ nm) for cardinality matching, starting from first principles. This results in a long derivation. We simplify the task by employing well-known concepts for maximum weight matching. We use Edmonds’ algorithm to derive the structure of shortest augmenting paths. We extend this to a complete algorithm for maximum cardinality matching in time O( √ nm).
منابع مشابه
On the inverse maximum perfect matching problem under the bottleneck-type Hamming distance
Given an undirected network G(V,A,c) and a perfect matching M of G, the inverse maximum perfect matching problem consists of modifying minimally the elements of c so that M becomes a maximum perfect matching with respect to the modified vector. In this article, we consider the inverse problem when the modifications are measured by the weighted bottleneck-type Hamming distance. We propose an alg...
متن کاملThe matching interdiction problem in dendrimers
The purpose of the matching interdiction problem in a weighted graph is to find two vertices such that the weight of the maximum matching in the graph without these vertices is minimized. An approximate solution for this problem has been presented. In this paper, we consider dendrimers as graphs such that the weights of edges are the bond lengths. We obtain the maximum matching in some types of...
متن کاملEstimating Weighted Matchings in o(n) Space
We consider the problem of estimating the weight of a maximum weighted matching of a weighted graph G(V, E) whose edges are revealed in a streaming fashion. We develop a reduction from the maximum weighted matching problem to the maximum cardinality matching problem that only doubles the approximation factor of a streaming algorithm developed for the maximum cardinality matching problem. Our re...
متن کامل1 Efficient labelling algorithms for the Maximum Non Crossing Matching Problem
Consider a bipartite graph; letÕs suppose we draw the origin nodes and the destination nodes arranged in two columns, and the edges as straight line segments. A non crossing matching is a subset of edges such that no two of them intersect. Several algorithms for the problem of finding the non crossing matching of maximum cardinality are proposed. Moreover an extension to weighted graphs is cons...
متن کاملFully Dynamic $(1+\epsilon)$-Approximate Matchings
We present the first data structures that maintain near optimal maximum cardinality and maximum weighted matchings on sparse graphs in sublinear time per update. Our main result is a data structure that maintains a (1 + ǫ) approximation of maximum matching under edge insertions/deletions in worst case O( √ mǫ) time per update. This improves the 3/2 approximation given in [Neiman, Solomon, STOC ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Fundam. Inform.
دوره 154 شماره
صفحات -
تاریخ انتشار 2017