Posted by: hmchang | November 14, 2006

Research: Complex Questions w/ Heuristic and Relative Solutions

Prof. Wang gave a very insightful philosophical explanation on NP-completeness today in class. The story starts from solving a high complexity problem- sat Boolean satisfactory problem. People define complexity is a relative way, and furthermore, they apply heuristics to solve problems. As long as one’s solution is better than others, it become a better solution. Initially, there are main heuristic methods that are being solved. Latter there are many tweaking on trade-offs and many of them become noise to the mainstream. Eventually, some big problem will be proposed and then the cycle will be revive again.

Life is also full of complex problems. There is no absolute answers to solve these problems. People apply heuristics for most of the events. There are good ways and there are inferior ways to solve these problem. For example, the stock market is very complex. There is no single rule to guarantee earning money. Nevertheless, some heuristics do apply – to name a few, buy low and sell high. As you gain more experienced, you will learn more heuristics and would be able to solve problem in a better way (say, invest in a higher return rate). Another typical example is inter-personal relationship. It is much harder than any NP-complete problem. Heuristics also apply: treat others in a way you want others to treat you. Other more elegant heuristics also apply. Some of them become how to be ‘polite’, and some of them become billion-dollar class: Carnegie.

The complexity of this world make the world an interesting place but also a competitive place. Since there is no optimum solution to a complex problem, as long as you are better than others in some sense, you can stand out (also mean that you will earn money). For example, one PC design may focus on high performance and the other may focus on energy-saving. These are trade-offs and it is really hard to say which one is superior. Eventually people will buy whichever advertise better. Hence, as long as you are superior than others in some sense, you can survive.

Moreover, under many scenario, we make engineering decision on whether to spend time solving a problem after analyzing its complexity. If a problem is too complex, we may leave it there or simply seek solution. Similarly, in the real life, whatever we decide to do, we would need to analyze the complexity of doing that. If we just whatever without analyzing all the difficulties and complexity (e.g, starting a company), that is considered a brutal move. A brutal move is a consequence of arrogant – ignore the complexity issue. If we understand that solving a problem may need to spend a lot of time and may still lead to failure but anyhow we decided to go ahead and do it, then it would be a choice, not arrogant. I think doing a Ph.D. is such a problem for many people, including me.

Fortunately, at almost every school, we are taught in this relative good solution way. First of all, you don’t need to get full marks in all your homework and exams in order to get an A – you just need to be better than most of your classmates. Furthermore, you don’t need to be knowing everything to pass a Ph.D. qualify exam — you just need to earn higher score than the other half of the examiner. There are more and more these kind of example that guides us to the ‘real world’.

In conclusion, start thinking about how to beat your lab-mate next door.

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