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Lecture 8: Specialized Algorithms for Decision Making
Daniel Frances c
±
2012
Contents
1 Introduction
2
2 The Stable Marriage Problem and the GaleShapely Algorithm
3
3 Checking for Unrequited Love
5
1
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Introduction
We just saw how encryption is based on the existence of problems for which only exponential
algorithms are known. It is interesting to note that a new type of computer is on the
research horizon: quantum computers. Researchers already developed quantum algorithms
for polynomial time factorization which would render RSA to be useless. Thus the search
for unsolved problems needs to go on within the encryption industry and research.
Now let’s turn our attention closer to the OR world where industry and researchers are on
the good guys side, and try to develop better algorithms for solving real life decision making
problems. You are already familiar with the broad classes of problems for which the ﬁeld of
OR has provided algorithms or is still looking:
•
Linear Programming for which we have both exponential (Simplex) and polynomial
(Interior Point) algorithms
•
Integer Programming for which we only have exponential time algorithms
•
Graph Based problems, for which some instances have polynomial time algorithms and
other do not.
•
Dynamic Programming, for which we also ﬁnd combinations
•
Problems that cannot be easily cast into the standard forms and which have their own
specialized algorithms
•
Problems for which Greedy Algorithms provide nearoptimal solutions
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 Spring '12
 Frances

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