The document discusses the stable marriage problem and its iterative improvement method. It defines a stable marriage matching as a one-to-one pairing between two disjoint sets where each member of each set is paired with exactly one member of the other set. It notes that a blocking pair occurs when two members who are not currently paired both prefer each other over their current partners. The document states that the stable marriage algorithm terminates in no more than n^2 iterations with a stable marriage output. It lists several applications of the stable marriage problem including student to university matching, doctors to hospitals matching, and student to project guide matching.

1. The Stable Marriage Problem
Iterative Improvement Method
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Dr. P. Subathra
Prof/ IT
KAMARAJ College of Engg. & Tech
(AUTONOMOUS)
Madurai

2. The Stable Marriage Problem
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3. The Stable Marriage Problem
A marriage matching M is a set of n (m, w) pairs
whose members are selected from disjoint n-
element sets Y and X in a one-one fashion, i.e.,
each man m from Y is paired with exactly one
woman w from X and vice versa.
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4. The Stable Marriage Problem
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5. The Stable Marriage Problem
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6. The Stable Marriage Problem
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7. The Stable Marriage Problem
• Blocking Pair
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8. The Stable Marriage Problem
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9. The Stable Marriage Problem
THEOREM
The stable marriage algorithm terminates after no
more than n2 iterations with a stable marriage
output.
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10. The Stable Marriage Problem
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11. The Stable Marriage Problem
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12. The Stable Marriage Problem
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13. The Stable Marriage Problem
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14. The Stable Marriage Problem
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15. The Stable Marriage Problem
APPLICATIONS:
• Student  University
• Student Departments
• Doctors  Hospitals
• Cloud User  Cloud Provider
• Room mates in Hostel
• Student  Project Guide
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