an:06466103
Zbl 1324.05188
Ageev, A. A.; Kel'manov, A. V.; Pyatkin, A. V.
Complexity of the weighted max-cut in Euclidean space
RU EN
Diskretn. Anal. Issled. Oper. 21, No. 4, 3-11 (2014); translation in J. Appl. Ind. Math. 8, No. 4, 453-457 (2014).
00346679
2014
j
05C85 68Q17 05C22
cut; Euclidean space; NP-hard problem
Summary: The max-cut problem is considered in an undirected graph whose vertices are points of a \(q\)-dimensional Euclidean space. The two cases are investigated, where the weights of the edges are equal to (i) the Euclidean distances between the points and (ii) the squares of these distances. It is proved that in both cases the problem is NP-hard in the strong sense. It is also shown that under the assumption \(\mathrm{P} \neq \mathrm{NP}\) there is no fully polynomial time approximation scheme (FPTAS).