Abstract
We show that the problem of constructing a perfect matching in a graph is in the complexity class Random NC; i.e., the problem is solvable in polylog time by a randomized parallel algorithm using a polynomial-bounded number of processors. We also show that several related problems lie in Random NC. These include: (i) Constructing a perfect matching of maximum weight in a graph whose edge weights are given in unary notation; (ii) Constructing a maximum-cardinality matching; (iii) Constructing a matching covering a set of vertices of maximum weight in a graph whose vertex weights are given in binary; (iv) Constructing a maximum s-t flow in a directed graph whose edge weights are given in unary.
Original language | English |
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Pages (from-to) | 35-48 |
Number of pages | 14 |
Journal | Combinatorica |
Volume | 6 |
Issue number | 1 |
DOIs | |
State | Published - Mar 1986 |
Externally published | Yes |
Keywords
- AMS subject classification (1980): 68E10