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Results tagged with reductions
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A reduction is the transformation of one problem into another problem. A example of using a reduction would be to be to show if a problem P is undecidable. This would be achieved by transforming or performing a reduction of a decision problem $P$ into an undecidable problem. If this can be achieved then we have shown that this problem P is undecidable.
3
votes
Many-one reductions vs. Turing reductions to define NPC
Generally, Many-one (Karp) reduction is easier to design because it is a restricted form of reduction that makes one call and the main task involves transforming the input into different encoding. Tur …
- 21.1k
2
votes
Does NP-completeness/hardness have to be constructive?
Agrawal and Biswas presented an NP-complete language for which there is no known Karp or Cook reduction. The proof of completeness follows because its witness relation is universal ( the witness rela …
- 21.1k
4
votes
Slowest many-one reduction?
Allender suggests the answer is no:
There seems to be no pair of natural NP-complete problems A and B known, where a reduction from A to B is known to require more than linear time (even under the …
- 21.1k
1
vote
Subset sum vs. Subset product (strong vs. weak NP hardness)
The literal explanation is that Subset Product problem is NP-complete by a reduction from strongly NP-complete problem such as exact cover by 3-sets. In such "strong" reduction, the input integers are …
- 21.1k
12
votes
Problems that are NP-complete under randomized or P/poly reductions.
To prove their theorem they showed that the promise problem Unique SAT is $NP$-hard under randomized reductions.
[1] Valiant, Leslie; Vazirani, Vijay. …
- 21.1k
22
votes
Accepted
Curious about computer-assisted NP-completeness proofs
As for question 2, there are at least two examples of $NP$-completeness proofs that involve computer-assistant.
Erickson and Ruskey provided a computer-aided proof that Domino Tatami Covering is NP- …
- 21.1k
2
votes
Integer relation detection for Subset Sum or NPP?
Let m be the logarithm of the largest number.
If $m=O(\log n)$ then it is solvable in polynomial time using dynamic programming.
In general, every known algorithm take at least $\Omega(2^{m})$ time. T …
- 21.1k