For the same reason, there exists a polynomial time algorithm for testing whether a given graph has a planar cover, but an explicit description of this algorithm is not known.
32.
This was important for the use of elliptic curves in cryptography, and represented a theoretical breakthrough, as it was the first deterministic polynomial time algorithm for counting points on elliptic curves.
33.
The characterizations of well-covered graphs with girth five or more, and of well-covered graphs that are 3-regular, also lead to efficient polynomial time algorithms to recognize these graphs.
34.
That is, if we assume that Adleman's theorem ), the Karp Lipton theorem is also evidence that the use of randomization does not lead to polynomial time algorithms for NP-complete problems.
35.
Another proof of this theorem based on unique sink orientations was given by, and showed how to use this theorem to derive a polynomial time algorithm for reconstructing the face lattices of simple polytopes from their graphs.
36.
A consequence of this definition is that if we had a polynomial time algorithm ( on a Turing-equivalent abstract machine ) for \ scriptstyle C, we could solve all problems in NP in polynomial time.
37.
Later, Narendra Karmarkar presented a faster algorithm at : Narendra Karmarkar, " A new polynomial time algorithm for linear programming ", Combinatorica, vol 4, no . 4, p . 373 395, 1984.
38.
Similarly, in a unit disk graph ( with a known geometric representation ), there is a polynomial time algorithm for maximum cliques based on applying the algorithm for complements of bipartite graphs to shared neighborhoods of pairs of vertices.
39.
Since it is conjectured that NP-complete problems do not have quasi-polynomial time algorithms, some inapproximability results in the field of approximation algorithms make the assumption that NP-complete problems do not have quasi-polynomial time algorithms.
40.
Since it is conjectured that NP-complete problems do not have quasi-polynomial time algorithms, some inapproximability results in the field of approximation algorithms make the assumption that NP-complete problems do not have quasi-polynomial time algorithms.
