# E.Kh. Gimadi. An optimal algorithm for an outerplanar facility location problem with improved time complexity ... С. 74-81.

We consider a network facility location problem with unbounded production levels. This problem is NP-hard in the general case and is known to have an optimal solution with quadratic complexity on a tree network. We study the case of a network representable by an outerplanar graph, i.e., by a graph whose vertices belong to one (outer) face. This problem is known to have an optimal algorithm with time complexity $O(nm^3)$, where $n$ is the number of vertices and $m$ is the number of possible facility locations. Using some properties of outerplanar graphs (binary 2-trees) and the existence of an optimal solution with a family of centrally connected service domains, we obtain recurrence relations for the construction of an optimal algorithm with time complexity that is smaller by a factor of$\sqrt{m}$ than the time complexity of the earlier algorithm.

Keywords: facility location problem, network, outerplanar graph, optimal algorithm, time complexity, connectedness.

The paper was received by the Editorial Office on May 16, 2017.

Eduard Khairutdinovich Gimadi, Dr. Phys.-Math. Sci., Prof., Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk,

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