運籌學——圖與網(wǎng)絡(luò)分析ppt課件

1、運 籌 學ABCDEABCDA BcD北京濟南徐州青島南京上海連云港鄭州武漢天津v5v4v3v2v1v7v1v2v3v4e1e2e3e4e5e6e7a9v1v2v3v4v5v6a1a2a8a4a3a5a6a7a10e7qvdVv2)(V2(v1,6)()(min0PwPwP路P0的權(quán)稱為從vs到vt的間隔，記為：d vs，vt 的最短路到的最短路到isjsvvisvvjisvvvvv,.,.,.,ijijjwvPvTvT)(),(min)()(min)(iivTvPwvvvvijisijsjiisvvjisddvvvvvvvjs),(),(,.,.,.,.,min 最短路最短路的最短路到dsj

2、)1(dsj)2(到各點的最短路。即為則該有：，步，對所有的若進行到某一步，如第對（vvvdvvdvvdwvvdvvdwvvdsjskjskjskijistijstsjjspjkpjktpj),(),(),(.,21),.,2 , 1(),(),(,.,2),.,2 , 1(),()1()1()()1(minwdjj1)1(1)()1(1)(1minwddijtiitjddkjkj)1(1)(1dkj)(1025-30-2406400-3047203-10025-3020-3611020-36615020-3361410020-336910020-336910wdjj1) 1 (1)() 1

3、(1)2(1minwddijiij)min()2(1)3(1wddijiijddjj)6(1)5(1vsvtv2v1v4v3(3,3)(5,1)(1,1)(4,3)(1,1)(2,2)(3,0)(2,1)(5,3)0),(),(vvvvijjiffjiij)(),(),(fvvvvvjssjffjssj)(),(),(fvvvvvtjjtffjttj)( fv)( fv)()(),(0)()(),(0tifvtsisifvAffvvcfjiijjiijij.,),(1111111111）的截集，記為（的弧的全體稱為分離指向，則把從且使得，和分成兩部分的點集截集：如果將VVvvVVVVVvVvV

4、VtstsVCAVDV1V1V1V1VV*1*1, fijf cfcfijijijij00),(),(vvvvjiji可行流f 是最大流的充分必要條件是不存在從 到 可行流f 是最大流的充分必要條件是不存在從 到 可行流f 是最大流的充分必要條件是不存在從 f*f*f* ffcijijij*minmin),(min 0 ),(),(),(*vvfvvfvvffjiijjiijjiijij f*f*f*f*f*f*f*必必是是最最大大流流。于于是是）（所所以以，）（）（顯顯然然有有：）于于是是得得截截集集（記記的的增增廣廣鏈鏈，故故因因為為不不存存在在關(guān)關(guān)于于則則令令且且若若則則令令且且若若令令fVVfVVvvVVvvcfVVVVVvfVvfVvVvcfVVvcvVjijiijijtjjiijijijs*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1i*1,)(,),(0