The.Algorithm.Design.Manual.Springer-Verlag.1998
The.Algorithm.Design.Manual.Springer-Verlag.1998 The.Algorithm.Design.Manual.Springer-Verlag.1998
Lecture 22 - techniques for proving hardness which dooms you to lose.'' The sharper the consequences for doing what is undesired, the easier it is to prove if and only if. ● Think strategically at a high level, then build gadgets to enforce tactics. You should be asking these kinds of questions. ``How can I force that either A or B but not both are chosen?'' ``How can I force that A is taken before B?'' ``How can I clean up the things I did not select?'' ● Alternate between looking for an algorithm or a reduction if you get stuck. Sometimes the reason you cannot prove hardness is that there is an efficient algorithm to solve your problem! When you can't prove hardness, it likely pays to change your thinking at least for a little while to keep you honest. Listen To Part 26-8 Now watch me try it! To demonstrate how one goes about proving a problem hard, I accept the challenge of showing how a proof can be built on the fly. I need a volunteer to pick a random problem from the 400+ hard problems in the back of Garey and Johnson. Listen To Part 27-2 Dealing with NP-complete Problems Option 1: Algorithm fast in the Average case Examples are Branch-and-bound for the Traveling Salesman Problem, backtracking algorithms, etc. Option 2: Heuristics Heuristics are rules of thumb; fast methods to find a solution with no requirement that it be the best one. Note that the theory of NP-completeness does not stipulate that it is hard to get close to the answer, only that it is hard to get the optimal answer. file:///E|/LEC/LECTUR16/NODE22.HTM (6 of 7) [19/1/2003 1:35:31]
Lecture 22 - techniques for proving hardness Often, we can prove performance bounds on heuristics, that the resulting answer is within C times that of the optimal one. Next: Lecture 23 - approximation Up: No Title Previous: Lecture 21 - vertex Algorithms Mon Jun 2 09:21:39 EDT 1997 file:///E|/LEC/LECTUR16/NODE22.HTM (7 of 7) [19/1/2003 1:35:31]
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Lecture 22 - techniques for proving hardness<br />
Often, we can prove performance bounds on heuristics, that the resulting answer is within C times that of<br />
the optimal one.<br />
Next: Lecture 23 - approximation Up: No Title Previous: Lecture 21 - vertex<br />
<strong>Algorithm</strong>s<br />
Mon Jun 2 09:21:39 EDT 1997<br />
file:///E|/LEC/LECTUR16/NODE22.HTM (7 of 7) [19/1/2003 1:35:31]
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