# Can all packing/covering problems be rephrased as set packing/covering problems?

Can all packing problems be rephrased as set packing problems?

Can all covering problems be rephrased as set covering problems?

In other words, I was wondering if set packing/covering problems are the most general forms of packing/covering problems?

• Packing/covering problems are larger classes of problems, because the "standard" set packing/covering problems only deal with finite sets (see their definitions). Furthermore you can formulate packing/covering problems using uncomputable stuff; for example: "How many circles of ray $K(x)$ are needed to cover a $x \times x$ square; where $K(x)$ is the Kolmogorov complexity of the binary representation of $x$?" – Vor Oct 29 '12 at 0:01
• I edited out the fourth, less related question. If you are still interested, please ask it separately. – Raphael Feb 23 '15 at 11:36