opt_prob_1.1

# opt_prob_1.1 - Optimization Problems Greg Stitt ECE...

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Optimization Problems Greg Stitt ECE Department University of Florida

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Introduction Why are we studying optimization problems? Just about every RC-tool related issue is an optimization problem This lecture should provide abstract solutions to many RC tool problems
Time Complexity Time Complexity - Informal definition: Defines how execution time increases as input size increases We are interested in worst case execution time Big O Notation O(n) Execution time increases linearly with input size O(n 2 ) Quadratic growth O(2 n ) Exponential growth

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Problem Classes P A problem is “in P” if it has a polynomial time solution O(n), O(n 2 ), O(n 3 ), etc. Undecidable Provably impossible to solve Example: halting problem NP Does not mean “Not-Polynomial”!!!! A NP problem has a non-deterministic polynomial time solution NP-hard A problem is NP-hard if every problem in NP is reducible to it Basically means that NP-hard problems are at least as hard as the hardest problems in NP NP-complete NP + NP-hard Most interesting problems are NP-complete!!!! Traveling salesman, Subset sum, 0-1 knapsack, graph coloring, vertex cover Place and route, logic minimization, minimum resource scheduling, hw/sw partitioning, etc.
The Big Question Does P = NP? Been studied for a long time Never been proven either true or false Why do we care? Currently, best known solutions for NP-complete problems typically have complexity of O(2 n ), O(n!) Known as intractable – takes more than your lifetime to solve If one NP-complete problem can be solved in polynomial time (is in P), then all NP-complete problems can be solved in polynomial time Remember, many interesting problems are NP-complete If you can find a polynomial time solution to an NP- complete RC problem: I’ll give you an A And, I’ll get a million dollars ( www.claymath.org/millennium/ P _vs_ NP / )

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Problem Classes
Optimization Problems Informal definition Problem of finding the best solution from all possible solutions Typically involves finding best solution for millions, billions, or even

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opt_prob_1.1 - Optimization Problems Greg Stitt ECE...

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