Editing Approximation Algorithms (section)

== <span style="color: #FFFFFF;">Analyzing</span> ==
{| class="wikitable"
|+ Exact vs. Approximation vs. Heuristic
! Feature !! Exact Algorithm !! Approximation Algorithm !! Heuristic (Rule of Thumb)
|-
| Speed || Slow (Exponential) || Fast (Polynomial) || Very Fast
|-
| Accuracy || 100% Correct || "Guaranteed" Close (e.g. 95%) || "Unknown" (Usually good)
|-
| Proof || Provably Perfect || Provably Bound || None (Just Works)
|-
| Use Case || Tiny Data / High Risk || Big Data / Professional Engineering || Games / Simple Logic
|-
| Analogy || A 'High-Precision Scale' || A 'Measuring Tape' || A 'Guess'
|}

'''The Concept of "Hardness of Approximation"''': Analyzing "The Wall." Mathematicians proved that for some problems, even "Approximating" them is "NP-Hard." If you could "Approximate the color of a map" within a certain error, you would automatically "Solve P vs NP." This tells us which problems are "Truly Impossible" and which ones we can "Chew on."
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