Local Optimization in the Steiner Problem on the Euclidean Plane
- 28 Downloads
By the local optimal Steiner tree is meant a tree with optimally distributed Steiner points for a given adjacency matrix. The adjacency matrix defines the point of local minimum, and all arrangements (coordinates) of the Steiner points that are admissible for it define the minimum neighborhood. Solution is local optimal if the tree length cannot be reduced by rearranging the Steiner points. An algorithm of local optimization based on the concept of coordinatewise descent was considered.
KeywordsMechanical Engineer Local Minimum System Theory Local Optimization Adjacency Matrix
Unable to display preview. Download preview PDF.
- 1.Lotarev, D.T. and Uzdemir, A.P., Arrangement of the Transport Networks over a Heterogeneous Territory, Avtom. Telemekh., 2002, no.7, pp. 114–124.Google Scholar
- 2.Gordeev, E.N. and Tarastsov, O.G., Steiner Problem. A Review, Diskretn. Mat., 1993, vol.5, no. 2, pp. 3–28.Google Scholar
- 3.Courant, R. and Robbins, H., What is Mathematics?, London: Oxford Univ. Press, 1941. Translated under the title Chto takoe matematika?, Moscow: Prosveshchenie, 1967.Google Scholar
- 4.Nutenko, V. Ya., Ispol'zovanie problemy Shteinera i ee obobshchenii dlya resheniya nekotorykh zadach prostranstvennoi ekonomiki (Using the Steiner Problem and Its Generalizations to Solve Some Problems of Spatial Economics), Moscow: Tsentr. Econom. Mat. Inst., 1968.Google Scholar
- 5.Garey, M.L. and Johnson, D.S., Computers and Intractability: A Guide to the Theory of NP-Completness, San Francisco: Freeman, 1979. Translated under the title Vychislitel'nye machiny i trudnoreshaemye zadachi, Moscow: Mir, 1982.Google Scholar
- 6.Emelichev, V.A., Mel'nikov, O.I., Sarvanov, V.I., et al., Lektsii po teorii grafov (Lectures on the Graph Theory), Moscow: Nauka, 1990.Google Scholar