{"id":10285,"date":"2026-04-06T16:40:48","date_gmt":"2026-04-06T15:40:48","guid":{"rendered":"https:\/\/izvestiyakbncran.ru\/?page_id=10285"},"modified":"2026-06-18T08:16:15","modified_gmt":"2026-06-18T07:16:15","slug":"25-6-5-en","status":"publish","type":"page","link":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-5-en\/","title":{"rendered":"25.6.5 En"},"content":{"rendered":"\n

Computer design method of branched pipeline hydraulic networks with an optimal number of Steiner points<\/strong><\/h1>\n\n\n\n

M.A. Bagov
<\/strong><\/p>\n\n\n\n

\n

<\/p>\n\n\n\n

\n
\n
PDF<\/a><\/div>\n<\/div>\n\n\n\n
<\/div>\n\n\n\n
\n
JATS XML<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n

<\/p>\n<\/div>\n\n\n\n

\n\n\n\n

Abstract<\/strong>.<\/strong> <\/em>A method and algorithm for constructing flow hydraulic networks with an optimal number of Steiner points have been developed. The method consists of sequential removal of Steiner points and subsequent optimization of the coordinates of effective Steiner points. The computer system was created for the design of large distribution pipeline networks for regional and interregional water supply.<\/p>\n\n\n\n

<\/p>\n\n\n\n

Keywords<\/strong>:<\/em><\/strong> stream network, Steiner points, quantity and coordinate optimization<\/p>\n\n\n\n

<\/p>\n\n\n\n

For citation<\/strong>.<\/strong> Bagov M.A. Computer design method of branched pipeline hydraulic networks with an optimal number of Steiner points. News of the Kabardino-Balkarian Scientific Center of RAS. 2023. No. 6(116). Pp. 55\u201364. DOI: 10.35330\/1991-6639-2023-6-116-55-64<\/p>\n\n\n\n

<\/p>\n\n\n\n

R<\/strong>eferences<\/summary>\n
    \n
  1. Kudaev V.Ch. Ranks of extrema and structural optimization of large network systems. News of the Kabardino-Balkarian Scientific Center of RAS<\/em>. 2016. No. 4(72). Pp. 15\u201324. (In Russian)<\/li>\n\n\n\n
  2. Kudaev V.Ch., Bagov M.A. Construction of a Steiner stream network of the 2nd rank of optimality. Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz. Vol. 253. 2021. Pp. 488\u2013499. (In Russian)<\/li>\n\n\n\n
  3. Abazokov M.B., Bagov M.A., Kudaev V.Ch. Computer design of large pipeline networks of high optimality rank. Doklady AMAN [Reports of AMAN]. 2022. Vol. 22. No. 4. Pp. 39\u201356. DOI: https:\/\/doi.org\/10.47928\/1726-9946-2022-22-4-39-56. (In Russian)<\/li>\n\n\n\n
  4. Merenkov A.P., Sennova E.V., Sumarokov S.V. et al. Matematicheskoye modelirovaniye i optimizatsiya sistem teplo-, vodo-, nefte- i gazosnobzheniya [Mathematical modeling and optimization of heat, water, oil and gas supply systems]. Novosibirsk: Nauka, 1992. 407 p. (In Russian)<\/li>\n\n\n\n
  5. Abramov N.N., Pospelova M.M., Somov M.A., Varapaev V.N., Kerimova D.Kh. Raschet vodoprovodnykh setey [Calculation of water supply networks]. Moscow: Stroyizdat, 1983. 278 p. (In Russian)<\/li>\n\n\n\n
  6. Gilbert E.N., Pollak G.O. Minimal Steiner trees. Kiberneticheskiy sbornik [Cybernetic collection]. New series. 1971. Vol. 8. Pp. 19\u201349. (In Russian)<\/li>\n\n\n\n
  7. Gilbert E.N. Minimal Cost Communication Networks. Bell System technological Journal. No. 9. Pp. 48\u201350.<\/li>\n<\/ol>\n<\/details>\n\n\n\n
    Information about the author<\/strong><\/summary>\n
    \n

    Bagov Marat Alievich<\/strong>, Researcher of the Department of Computational Methods, Institute of Applied Mathematics and Automation \u2013 branch of Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences;
    360000, Russia, Nalchik, 89 \u0410 Shortanov street;
    maratniipma@mail.ru, ORCID: https:\/\/orcid.org\/0000-0003-0899-898X<\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n<\/div>\n<\/details>\n","protected":false},"excerpt":{"rendered":"

    Computer design method of branched pipeline hydraulic networks with an optimal number of Steiner points M.A. Bagov Abstract. A method and algorithm for constructing flow hydraulic networks with an optimal number of Steiner points have been developed. The method consists of sequential removal of Steiner points and subsequent optimization of the coordinates of effective Steiner […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"wp-custom-template-home","meta":{"footnotes":""},"class_list":["post-10285","page","type-page","status-publish","hentry"],"yoast_head":"\n25.6.5 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-5-en\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"25.6.5 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\" \/>\n<meta property=\"og:description\" content=\"Computer design method of branched pipeline hydraulic networks with an optimal number of Steiner points M.A. Bagov Abstract. A method and algorithm for constructing flow hydraulic networks with an optimal number of Steiner points have been developed. The method consists of sequential removal of Steiner points and subsequent optimization of the coordinates of effective Steiner […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-5-en\/\" \/>\n<meta property=\"og:site_name\" content=\"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\" \/>\n<meta property=\"article:modified_time\" content=\"2026-06-18T07:16:15+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u041f\u0440\u0438\u043c\u0435\u0440\u043d\u043e\u0435 \u0432\u0440\u0435\u043c\u044f \u0434\u043b\u044f \u0447\u0442\u0435\u043d\u0438\u044f\" \/>\n\t<meta name=\"twitter:data1\" content=\"2 \u043c\u0438\u043d\u0443\u0442\u044b\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/index.php\\\/en\\\/25-6-5-en\\\/\",\"url\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/index.php\\\/en\\\/25-6-5-en\\\/\",\"name\":\"25.6.5 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/#website\"},\"datePublished\":\"2026-04-06T15:40:48+00:00\",\"dateModified\":\"2026-06-18T07:16:15+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/index.php\\\/en\\\/25-6-5-en\\\/#breadcrumb\"},\"inLanguage\":\"ru-RU\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/izvestiyakbncran.ru\\\/index.php\\\/en\\\/25-6-5-en\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/index.php\\\/en\\\/25-6-5-en\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u0413\u043b\u0430\u0432\u043d\u0430\u044f \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0430\",\"item\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"25.6.5 En\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/#website\",\"url\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/\",\"name\":\"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\",\"description\":\"\u041d\u0430\u0443\u0447\u043d\u044b\u0439 \u0436\u0443\u0440\u043d\u0430\u043b\",\"publisher\":{\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"ru-RU\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/#organization\",\"name\":\"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\",\"url\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"ru-RU\",\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/wp-content\\\/uploads\\\/2025\\\/07\\\/oblozhka-zhurnala-na-angl-scaled.jpg\",\"contentUrl\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/wp-content\\\/uploads\\\/2025\\\/07\\\/oblozhka-zhurnala-na-angl-scaled.jpg\",\"width\":1828,\"height\":2560,\"caption\":\"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\"},\"image\":{\"@id\":\"https:\\\/\\\/izvestiyakbncran.ru\\\/#\\\/schema\\\/logo\\\/image\\\/\"}}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"25.6.5 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-5-en\/","og_locale":"ru_RU","og_type":"article","og_title":"25.6.5 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb","og_description":"Computer design method of branched pipeline hydraulic networks with an optimal number of Steiner points M.A. Bagov Abstract. A method and algorithm for constructing flow hydraulic networks with an optimal number of Steiner points have been developed. The method consists of sequential removal of Steiner points and subsequent optimization of the coordinates of effective Steiner […]","og_url":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-5-en\/","og_site_name":"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb","article_modified_time":"2026-06-18T07:16:15+00:00","twitter_card":"summary_large_image","twitter_misc":{"\u041f\u0440\u0438\u043c\u0435\u0440\u043d\u043e\u0435 \u0432\u0440\u0435\u043c\u044f \u0434\u043b\u044f \u0447\u0442\u0435\u043d\u0438\u044f":"2 \u043c\u0438\u043d\u0443\u0442\u044b"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-5-en\/","url":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-5-en\/","name":"25.6.5 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb","isPartOf":{"@id":"https:\/\/izvestiyakbncran.ru\/#website"},"datePublished":"2026-04-06T15:40:48+00:00","dateModified":"2026-06-18T07:16:15+00:00","breadcrumb":{"@id":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-5-en\/#breadcrumb"},"inLanguage":"ru-RU","potentialAction":[{"@type":"ReadAction","target":["https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-5-en\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-5-en\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u0413\u043b\u0430\u0432\u043d\u0430\u044f \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0430","item":"https:\/\/izvestiyakbncran.ru\/"},{"@type":"ListItem","position":2,"name":"25.6.5 En"}]},{"@type":"WebSite","@id":"https:\/\/izvestiyakbncran.ru\/#website","url":"https:\/\/izvestiyakbncran.ru\/","name":"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb","description":"\u041d\u0430\u0443\u0447\u043d\u044b\u0439 \u0436\u0443\u0440\u043d\u0430\u043b","publisher":{"@id":"https:\/\/izvestiyakbncran.ru\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/izvestiyakbncran.ru\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"ru-RU"},{"@type":"Organization","@id":"https:\/\/izvestiyakbncran.ru\/#organization","name":"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb","url":"https:\/\/izvestiyakbncran.ru\/","logo":{"@type":"ImageObject","inLanguage":"ru-RU","@id":"https:\/\/izvestiyakbncran.ru\/#\/schema\/logo\/image\/","url":"https:\/\/izvestiyakbncran.ru\/wp-content\/uploads\/2025\/07\/oblozhka-zhurnala-na-angl-scaled.jpg","contentUrl":"https:\/\/izvestiyakbncran.ru\/wp-content\/uploads\/2025\/07\/oblozhka-zhurnala-na-angl-scaled.jpg","width":1828,"height":2560,"caption":"\u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb"},"image":{"@id":"https:\/\/izvestiyakbncran.ru\/#\/schema\/logo\/image\/"}}]}},"_links":{"self":[{"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/pages\/10285","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/comments?post=10285"}],"version-history":[{"count":9,"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/pages\/10285\/revisions"}],"predecessor-version":[{"id":15082,"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/pages\/10285\/revisions\/15082"}],"wp:attachment":[{"href":"https:\/\/izvestiyakbncran.ru\/index.php\/wp-json\/wp\/v2\/media?parent=10285"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}