A method for optimal grouping of vector objects around centers

Abstract

îïòèìàëüíîé ãðóïïèðîâêè âåêòîðíûõ îáúåêòîâ îòíîñèòåëüíî öåíòðîâ.Àííîòàöèÿ. Ðàññìàòðèâàåòñÿ çàäà÷à ãðóïïèðîâêè âåêòîðíûõ îáúåêòîâ îòíîñèòåëüíî âîçìîaeíûõ öåíòðîâ ñ ó÷åòîì îãðàíè÷åíèé íà ñîñòàâ ãðóïï. Ïðåäëàãàåòñÿ ñïîñîá ïðåäñòàâëåíèÿ ñïåöèôè÷åñêèõ âåêòîðíûõ îãðàíè÷åíèé â âèäå îãðàíè÷åíèé ýêâèâàëåíòíîé çàäà÷è öåëî÷èñëåííîãî ïðîãðàììèðîâàíèÿ è ïîëèíîìèàëüíûå àëãîðèòìû äëÿ íåêîòîðûõ ÷àñòíûõ ñëó÷àåâ. Êëþ÷åâûå ñëîâà: àëãîðèòì, ãðóïïèðîâêà, öåëî÷èñëåííîå ïðîãðàììèðîâàíèå, ïîòîê â ñåòè, ìàòðîèä.Mustan N.G., Ponomarev A.V., Savosin S.V. A method for optimal grouping of vector objects around centers.Abstract. The paper addresses the problem of grouping vector objects around potential centers with respect to restrictions imposed on the group structure. A method for transforming vector restrictions into the restrictions of equivalent integer programming problem is proposed. Polynomial algorithms for some special cases are suggested.