Latex中文论文模板A4双栏，适用课程论文

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Latex中文论文模板A4双栏，适用课程论文

<link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/css/base.min.css" rel="stylesheet"/><link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/css/fancy.min.css" rel="stylesheet"/><link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/88557427/raw.css" rel="stylesheet"/><div id="sidebar" style="display: none"><div id="outline"></div></div><div class="pf w0 h0" data-page-no="1" id="pf1"><div class="pc pc1 w0 h0"><img alt="" class="bi x0 y0 w1 h1" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/88557427/bg1.jpg"/><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">基于<span class="_ _0"> </span><span class="ff2">XXXX<span class="_ _0"> </span></span>优化研究</div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls0 ws0">小明</div><div class="t m0 x3 h3 y3 ff3 fs1 fc0 sc0 ls0 ws0">XX<span class="_ _1"> </span><span class="ff1">大学<span class="_ _1"> </span></span>XX<span class="_ _1"> </span><span class="ff1">学院，学号</span></div><div class="t m0 x4 h4 y4 ff3 fs1 fc0 sc0 ls0 ws0">2023.11.20</div><div class="t m0 x5 h5 y5 ff4 fs2 fc0 sc0 ls0 ws0">摘<span class="_ _2"> </span>要：<span class="_ _3"></span><span class="ff5">君不见，<span class="_ _3"></span>黄河之水天上来，<span class="_ _3"></span>奔流到海不复回。<span class="_ _3"></span>君不见，<span class="_ _3"></span>高堂明镜悲白发，<span class="_ _3"></span>朝如青丝暮成雪。<span class="_ _3"></span>人生得意</span></div><div class="t m0 x5 h5 y6 ff5 fs2 fc0 sc0 ls0 ws0">须尽欢，莫使<span class="_ _4"></span>金樽空对月。<span class="_ _4"></span>天生我材必<span class="_ _4"></span>有用，千金散<span class="_ _4"></span>尽还复来。烹<span class="_ _4"></span>羊宰牛且<span class="_ _4"></span>为乐，会须一<span class="_ _4"></span>饮三百杯。岑<span class="_ _4"></span>夫子，</div><div class="t m0 x5 h5 y7 ff5 fs2 fc0 sc0 ls0 ws0">丹丘生，<span class="_ _3"></span>将进酒，<span class="_ _3"></span>杯莫停。<span class="_ _3"></span>与君歌一曲，<span class="_ _5"></span>请君为我倾耳听。<span class="_ _5"></span>钟鼓馔玉不足贵，<span class="_ _3"></span>但愿长醉不复醒。<span class="_ _3"></span>古来圣贤皆寂</div><div class="t m0 x5 h5 y8 ff5 fs2 fc0 sc0 ls0 ws0">寞，<span class="_ _5"></span>惟有饮者留其名。<span class="_ _3"></span>陈王昔时宴平乐，<span class="_ _3"></span>斗酒十千恣欢谑。<span class="_ _3"></span>主人何为言少钱，<span class="_ _5"></span>径须沽取对君酌。<span class="_ _3"></span>五花马、<span class="_ _3"></span>千金</div><div class="t m0 x5 h5 y9 ff5 fs2 fc0 sc0 ls0 ws0">裘，呼儿将出换美酒，与尔同销万古愁。</div><div class="t m0 x5 h5 ya ff4 fs2 fc0 sc0 ls0 ws0">关键词：<span class="ff5">将进酒，将进酒，将进酒，李白</span></div><div class="t m0 x5 h6 yb ff6 fs3 fc0 sc0 ls0 ws0">1<span class="_ _6"> </span><span class="ff7">引言</span></div><div class="t m0 x5 h3 yc ff6 fs1 fc0 sc0 ls0 ws0">1.1<span class="_ _7"> </span><span class="ff7">研究背景</span></div><div class="t m0 x6 h5 yd ff1 fs2 fc0 sc0 ls0 ws0">君不见，<span class="_ _3"></span>黄河之水天上来，<span class="_ _3"></span>奔流到海不复回。<span class="_ _3"></span>君</div><div class="t m0 x5 h5 ye ff1 fs2 fc0 sc0 ls0 ws0">不见，<span class="_ _3"></span>高堂明镜悲白发，<span class="_ _3"></span>朝如青丝暮成雪。<span class="_ _3"></span>人生得意</div><div class="t m0 x5 h5 yf ff1 fs2 fc0 sc0 ls0 ws0">须尽欢，<span class="_ _3"></span>莫使金樽空对月。<span class="_ _3"></span>天生我材必有用，<span class="_ _3"></span>千金散</div><div class="t m0 x5 h5 y10 ff1 fs2 fc0 sc0 ls0 ws0">尽还复来。<span class="_ _3"></span>烹羊宰牛且为乐，<span class="_ _3"></span>会须一饮三百杯。<span class="_ _3"></span>岑夫</div><div class="t m0 x5 h5 y11 ff1 fs2 fc0 sc0 ls0 ws0">子，<span class="_ _8"></span>丹丘生，<span class="_ _8"></span>将进酒，<span class="_ _8"></span>杯莫停。<span class="_ _8"></span>与君歌一曲，<span class="_ _8"></span>请君为我</div><div class="t m0 x5 h5 y12 ff1 fs2 fc0 sc0 ls0 ws0">倾耳听。<span class="_ _3"></span>钟鼓馔玉不足贵，<span class="_ _3"></span>但愿长醉不复醒。<span class="_ _3"></span>古来圣</div><div class="t m0 x5 h5 y13 ff1 fs2 fc0 sc0 ls0 ws0">贤皆寂寞，<span class="_ _3"></span>惟有饮者留其名。<span class="_ _3"></span>陈王昔时宴平乐，<span class="_ _3"></span>斗酒</div><div class="t m0 x5 h5 y14 ff1 fs2 fc0 sc0 ls0 ws0">十千恣欢谑。<span class="_ _3"></span>主人何为言少钱，<span class="_ _3"></span>径须沽取对君酌。<span class="_ _3"></span>五</div><div class="t m0 x5 h5 y15 ff1 fs2 fc0 sc0 ls0 ws0">花马、千金裘，呼儿将出换美酒，与尔同销万古愁。</div><div class="t m0 x5 h3 y16 ff6 fs1 fc0 sc0 ls0 ws0">1.2<span class="_ _7"> </span><span class="ff7">研究意义</span></div><div class="t m0 x6 h5 y17 ff1 fs2 fc0 sc0 ls0 ws0">君不见，<span class="_ _3"></span>黄河之水天上来，<span class="_ _3"></span>奔流到海不复回。<span class="_ _3"></span>君</div><div class="t m0 x5 h5 y18 ff1 fs2 fc0 sc0 ls0 ws0">不见，<span class="_ _3"></span>高堂明镜悲白发，<span class="_ _3"></span>朝如青丝暮成雪。<span class="_ _3"></span>人生得意</div><div class="t m0 x5 h5 y19 ff1 fs2 fc0 sc0 ls0 ws0">须尽欢，<span class="_ _3"></span>莫使金樽空对月。<span class="_ _3"></span>天生我材必有用，<span class="_ _3"></span>千金散</div><div class="t m0 x5 h5 y1a ff1 fs2 fc0 sc0 ls0 ws0">尽还复来。<span class="_ _3"></span>烹羊宰牛且为乐，<span class="_ _3"></span>会须一饮三百杯。<span class="_ _3"></span>岑夫</div><div class="t m0 x5 h5 y1b ff1 fs2 fc0 sc0 ls0 ws0">子，<span class="_ _8"></span>丹丘生，<span class="_ _8"></span>将进酒，<span class="_ _8"></span>杯莫停。<span class="_ _8"></span>与君歌一曲，<span class="_ _8"></span>请君为我</div><div class="t m0 x5 h5 y1c ff1 fs2 fc0 sc0 ls0 ws0">倾耳听。<span class="_ _3"></span>钟鼓馔玉不足贵，<span class="_ _3"></span>但愿长醉不复醒。<span class="_ _3"></span>古来圣</div><div class="t m0 x5 h5 y1d ff1 fs2 fc0 sc0 ls0 ws0">贤皆寂寞，<span class="_ _3"></span>惟有饮者留其名。<span class="_ _3"></span>陈王昔时宴平乐，<span class="_ _3"></span>斗酒</div><div class="t m0 x5 h5 y1e ff1 fs2 fc0 sc0 ls0 ws0">十千恣欢谑。<span class="_ _3"></span>主人何为言少钱，<span class="_ _3"></span>径须沽取对君酌。<span class="_ _3"></span>五</div><div class="t m0 x5 h5 y1f ff1 fs2 fc0 sc0 ls0 ws0">花马、千金裘，呼儿将出换美酒，与尔同销万古愁。</div><div class="t m0 x7 h5 y20 ff8 fs2 fc0 sc0 ls0 ws0">•<span class="_ _9"> </span><span class="ff1">满足实时性要求</span></div><div class="t m0 x8 h5 y21 ff8 fs2 fc0 sc0 ls0 ws0">•<span class="_ _9"> </span><span class="ff1">满足实时性要求</span></div><div class="t m0 x8 h5 y22 ff8 fs2 fc0 sc0 ls0 ws0">•<span class="_ _9"> </span><span class="ff1">满足实时性要求</span></div><div class="t m0 x9 h3 y23 ff6 fs1 fc0 sc0 ls0 ws0">1.3<span class="_ _7"> </span><span class="ff7">研究目的</span></div><div class="t m0 xa h5 y24 ff1 fs2 fc0 sc0 ls0 ws0">君不见，<span class="_ _3"></span>黄河之水天上来，<span class="_ _3"></span>奔流到海不复回。<span class="_ _3"></span>君</div><div class="t m0 x9 h5 y25 ff1 fs2 fc0 sc0 ls0 ws0">不见，<span class="_ _3"></span>高堂明镜悲白发，<span class="_ _3"></span>朝如青丝暮成雪。<span class="_ _3"></span>人生得意</div><div class="t m0 x9 h5 y26 ff1 fs2 fc0 sc0 ls0 ws0">须尽欢，<span class="_ _3"></span>莫使金樽空对月。<span class="_ _3"></span>天生我材必有用，<span class="_ _3"></span>千金散</div><div class="t m0 x9 h5 y27 ff1 fs2 fc0 sc0 ls0 ws0">尽还复来。<span class="_ _3"></span>烹羊宰牛且为乐，<span class="_ _3"></span>会须一饮三百杯。<span class="_ _3"></span>岑夫</div><div class="t m0 x9 h5 y28 ff1 fs2 fc0 sc0 ls0 ws0">子，<span class="_ _8"></span>丹丘生，<span class="_ _8"></span>将进酒，<span class="_ _8"></span>杯莫停。<span class="_ _8"></span>与君歌一曲，<span class="_ _8"></span>请君为我</div><div class="t m0 x9 h5 y29 ff1 fs2 fc0 sc0 ls0 ws0">倾耳听。<span class="_ _3"></span>钟鼓馔玉不足贵，<span class="_ _3"></span>但愿长醉不复醒。<span class="_ _3"></span>古来圣</div><div class="t m0 x9 h5 y2a ff1 fs2 fc0 sc0 ls0 ws0">贤皆寂寞，<span class="_ _3"></span>惟有饮者留其名。<span class="_ _3"></span>陈王昔时宴平乐，<span class="_ _3"></span>斗酒</div><div class="t m0 x9 h5 y2b ff1 fs2 fc0 sc0 ls0 ws0">十千恣欢谑。<span class="_ _3"></span>主人何为言少钱，<span class="_ _3"></span>径须沽取对君酌。<span class="_ _3"></span>五</div><div class="t m0 x9 h5 y2c ff1 fs2 fc0 sc0 ls0 ws0">花马、千金裘，呼儿将出换美酒，与尔同销万古愁。</div><div class="t m0 x9 h6 y2d ff6 fs3 fc0 sc0 ls0 ws0">2<span class="_ _6"> </span><span class="ff7">关键技术</span></div><div class="t m0 x9 h3 y2e ff6 fs1 fc0 sc0 ls0 ws0">2.1<span class="_ _7"> </span><span class="ff7">系统模型</span></div><div class="t m0 xa h5 y2f ff1 fs2 fc0 sc0 ls0 ws0">君不见，<span class="_ _3"></span>黄河之水天上来，<span class="_ _3"></span>奔流到海不复回。<span class="_ _3"></span>君</div><div class="t m0 x9 h5 y30 ff1 fs2 fc0 sc0 ls0 ws0">不见，<span class="_ _3"></span>高堂明镜悲白发，<span class="_ _3"></span>朝如青丝暮成雪。<span class="_ _3"></span>人生得意</div><div class="t m0 x9 h5 y31 ff1 fs2 fc0 sc0 ls0 ws0">须尽欢，<span class="_ _3"></span>莫使金樽空对月。<span class="_ _3"></span>天生我材必有用，<span class="_ _3"></span>千金散</div><div class="t m0 x9 h5 y32 ff1 fs2 fc0 sc0 ls0 ws0">尽还复来。<span class="_ _3"></span>烹羊宰牛且为乐，<span class="_ _3"></span>会须一饮三百杯。<span class="_ _3"></span>岑夫</div><div class="t m0 x9 h5 y33 ff1 fs2 fc0 sc0 ls0 ws0">子，<span class="_ _8"></span>丹丘生，<span class="_ _8"></span>将进酒，<span class="_ _8"></span>杯莫停。<span class="_ _8"></span>与君歌一曲，<span class="_ _8"></span>请君为我</div><div class="t m0 x9 h5 y34 ff1 fs2 fc0 sc0 ls0 ws0">倾耳听。<span class="_ _3"></span>钟鼓馔玉不足贵，<span class="_ _3"></span>但愿长醉不复醒。<span class="_ _3"></span>古来圣</div><div class="t m0 x9 h5 y20 ff1 fs2 fc0 sc0 ls0 ws0">贤皆寂寞，<span class="_ _3"></span>惟有饮者留其名。<span class="_ _3"></span>陈王昔时宴平乐，<span class="_ _3"></span>斗酒</div><div class="t m0 xb h7 y35 ff9 fs4 fc0 sc0 ls0 ws0">0</div><div class="t m0 xc h8 y36 ff1 fs5 fc0 sc0 ls0 ws0">将进酒李白</div><div class="t m0 xd h9 y37 ff8 fs2 fc0 sc0 ls0 ws0">1</div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div><div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/88557427/bg2.jpg"><div class="t m0 x5 h5 y38 ff1 fs2 fc0 sc0 ls0 ws0">十千恣欢谑。<span class="_ _3"></span>主人何为言少钱，<span class="_ _3"></span>径须沽取对君酌。<span class="_ _3"></span>五</div><div class="t m0 x5 h5 y39 ff1 fs2 fc0 sc0 ls0 ws0">花马、千金裘，呼儿将出换美酒，与尔同销万古愁。</div><div class="t m0 xe h5 y3a ff1 fs2 fc0 sc0 ls0 ws0">图<span class="_ _a"> </span><span class="ff8">1<span class="_ _a"> </span></span>系统模型符号</div><div class="t m0 x6 h5 y3b ff1 fs2 fc0 sc0 ls0 ws0">君不见，<span class="_ _3"></span>黄河之水天上来，<span class="_ _3"></span>奔流到海不复回。<span class="_ _3"></span>君</div><div class="t m0 x5 h5 y3c ff1 fs2 fc0 sc0 ls0 ws0">不见，<span class="_ _3"></span>高堂明镜悲白发，<span class="_ _3"></span>朝如青丝暮成雪。<span class="_ _3"></span>人生得意</div><div class="t m0 x5 h5 y3d ff1 fs2 fc0 sc0 ls0 ws0">须尽欢，<span class="_ _3"></span>莫使金樽空对月。<span class="_ _3"></span>天生我材必有用，<span class="_ _3"></span>千金散</div><div class="t m0 x5 h5 y3e ff1 fs2 fc0 sc0 ls0 ws0">尽还复来。<span class="_ _3"></span>烹羊宰牛且为乐，<span class="_ _3"></span>会须一饮三百杯。<span class="_ _3"></span>岑夫</div><div class="t m0 x5 h5 y3f ff1 fs2 fc0 sc0 ls0 ws0">子，<span class="_ _8"></span>丹丘生，<span class="_ _8"></span>将进酒，<span class="_ _8"></span>杯莫停。<span class="_ _8"></span>与君歌一曲，<span class="_ _8"></span>请君为我</div><div class="t m0 x5 h5 y40 ff1 fs2 fc0 sc0 ls0 ws0">倾耳听。<span class="_ _3"></span>钟鼓馔玉不足贵，<span class="_ _3"></span>但愿长醉不复醒。<span class="_ _3"></span>古来圣</div><div class="t m0 x5 h5 y41 ff1 fs2 fc0 sc0 ls0 ws0">贤皆寂寞，<span class="_ _3"></span>惟有饮者留其名。<span class="_ _3"></span>陈王昔时宴平乐，<span class="_ _3"></span>斗酒</div><div class="t m0 x5 h5 y42 ff1 fs2 fc0 sc0 ls0 ws0">十千恣欢谑。<span class="_ _3"></span>主人何为言少钱，<span class="_ _3"></span>径须沽取对君酌。<span class="_ _3"></span>五</div><div class="t m0 x5 h5 y43 ff1 fs2 fc0 sc0 ls0 ws0">花马、千金裘，呼儿将出换美酒，与尔同销万古愁。</div><div class="t m0 x5 h3 y44 ff6 fs1 fc0 sc0 ls0 ws0">2.2<span class="_ _7"> </span><span class="ff7">问题描述</span></div><div class="t m0 x6 h5 y45 ff1 fs2 fc0 sc0 ls0 ws0">君不见，<span class="_ _3"></span>黄河之水天上来，<span class="_ _3"></span>奔流到海不复回。<span class="_ _3"></span>君</div><div class="t m0 x5 h5 y46 ff1 fs2 fc0 sc0 ls0 ws0">不见，<span class="_ _3"></span>高堂明镜悲白发，<span class="_ _3"></span>朝如青丝暮成雪。<span class="_ _3"></span>人生得意</div><div class="t m0 x5 h5 y47 ff1 fs2 fc0 sc0 ls0 ws0">须尽欢，<span class="_ _3"></span>莫使金樽空对月。<span class="_ _3"></span>天生我材必有用，<span class="_ _3"></span>千金散</div><div class="t m0 x5 h5 y48 ff1 fs2 fc0 sc0 ls0 ws0">尽还复来。<span class="_ _3"></span>烹羊宰牛且为乐，<span class="_ _3"></span>会须一饮三百杯。<span class="_ _3"></span>岑夫</div><div class="t m0 x5 h5 y49 ff1 fs2 fc0 sc0 ls0 ws0">子，<span class="_ _8"></span>丹丘生，<span class="_ _8"></span>将进酒，<span class="_ _8"></span>杯莫停。<span class="_ _8"></span>与君歌一曲，<span class="_ _8"></span>请君为我</div><div class="t m0 x5 h5 y4a ff1 fs2 fc0 sc0 ls0 ws0">倾耳听。<span class="_ _3"></span>钟鼓馔玉不足贵，<span class="_ _3"></span>但愿长醉不复醒。<span class="_ _3"></span>古来圣</div><div class="t m0 x5 h5 y4b ff1 fs2 fc0 sc0 ls0 ws0">贤皆寂寞，<span class="_ _3"></span>惟有饮者留其名。<span class="_ _3"></span>陈王昔时宴平乐，<span class="_ _3"></span>斗酒</div><div class="t m0 x5 h5 y4c ff1 fs2 fc0 sc0 ls0 ws0">十千恣欢谑。<span class="_ _3"></span>主人何为言少钱，<span class="_ _3"></span>径须沽取对君酌。<span class="_ _3"></span>五</div><div class="t m0 x5 h5 y4d ff1 fs2 fc0 sc0 ls0 ws0">花马、千金裘，呼儿将出换美酒，与尔同销万古愁。</div><div class="t m0 x6 h5 y4e ff1 fs2 fc0 sc0 ls0 ws0">根据带宽消耗规则，<span class="_ _b"></span>一条路径的容量在数学上定</div><div class="t m0 x5 h5 y4f ff1 fs2 fc0 sc0 ls0 ws0">义为：</div><div class="t m0 xf h9 y50 ffa fs2 fc0 sc0 ls0 ws0">C<span class="_ _c"></span><span class="ffb">(</span>f</div><div class="t m0 x10 ha y51 ffc fs6 fc0 sc0 ls0 ws0">m</div><div class="t m0 xe h9 y50 ffb fs2 fc0 sc0 ls0 ws0">)<span class="_ _d"> </span>=<span class="_ _e"> </span><span class="ff8">min</span></div><div class="t m0 x11 hb y52 ffd fs6 fc0 sc0 ls0 ws0">(<span class="ffc">i,j<span class="_ _4"></span></span>)<span class="ffe">∈<span class="ffc">E</span></span></div><div class="t m0 x12 h9 y50 ffa fs2 fc0 sc0 ls0 ws0">c<span class="ffb">(</span>i,<span class="_ _f"> </span>j<span class="_ _c"></span><span class="ffb">)</span>α</div><div class="t m0 x13 ha y51 ffc fs6 fc0 sc0 ls0 ws0">m</div><div class="t m0 x14 h9 y50 ffb fs2 fc0 sc0 ls0 ws0">(<span class="ffa">i,<span class="_ _f"> </span>j<span class="_ _c"></span></span>)<span class="ffa">.</span></div><div class="t m0 x6 h5 y53 ff1 fs2 fc0 sc0 ls0 ws0">其中，<span class="ffb">(<span class="ffa">i,<span class="_ _f"> </span>j<span class="_ _c"></span></span>)<span class="_ _10"> </span><span class="fff">∈<span class="_ _10"> </span><span class="ffa">E<span class="_ _9"> </span></span></span></span>为所<span class="_ _4"></span>有数<span class="_ _4"></span>据流<span class="_ _10"> </span><span class="ffa">f</span></div><div class="t m0 x15 ha y54 ffc fs6 fc0 sc0 ls0 ws0">m</div><div class="t m0 x16 h9 y53 ffb fs2 fc0 sc0 ls0 ws0">(<span class="ffa">j<span class="_ _c"></span></span>)<span class="_ _10"> </span><span class="fff">∈<span class="_ _1"> </span><span class="ffa">F</span></span></div><div class="t m0 x17 ha y54 ffc fs6 fc0 sc0 ls0 ws0">L</div><div class="t m0 x18 h5 y53 ff1 fs2 fc0 sc0 ls0 ws0">流</div><div class="t m0 x5 h5 y55 ff1 fs2 fc0 sc0 ls0 ws0">出的流量，<span class="_ _8"></span>令<span class="_ _d"> </span><span class="ffa">C</span></div><div class="t m0 x19 ha y56 ffc fs6 fc0 sc0 ls0 ws0">r</div><div class="t m0 x1a h5 y55 ffb fs2 fc0 sc0 ls0 ws0">(<span class="ffa">i,<span class="_ _f"> </span>j<span class="_ _c"></span></span>)<span class="_ _d"> </span><span class="ff1">表示通过边缘路由的剩余带宽，</span></div><div class="t m0 x5 h5 y57 ff1 fs2 fc0 sc0 ls0 ws0">定义为：</div><div class="t m0 x1b hc y58 ffa fs2 fc0 sc0 ls0 ws0">C</div><div class="t m0 x1c ha y59 ffc fs6 fc0 sc0 ls0 ws0">r</div><div class="t m0 x1d h9 y58 ffb fs2 fc0 sc0 ls0 ws0">(<span class="ffa">i,<span class="_ _f"> </span>j<span class="_ _c"></span></span>)<span class="_ _d"> </span>=<span class="_ _d"> </span><span class="ffa">c</span>(<span class="ffa">i,<span class="_ _f"> </span>j<span class="_ _c"></span></span>)<span class="_ _11"> </span><span class="fff">−</span></div><div class="t m0 x1e hd y5a ff10 fs2 fc0 sc0 ls0 ws0">∑</div><div class="t m0 x1f ha y5b ffc fs6 fc0 sc0 ls0 ws0">f</div><div class="t m0 x1e he y5c ff11 fs4 fc0 sc0 ls0 ws0">m</div><div class="t m0 x20 ha y5b ffe fs6 fc0 sc0 ls0 ws0">∈<span class="ffc">E</span></div><div class="t m0 x21 hc y58 ffa fs2 fc0 sc0 ls0 ws0">q</div><div class="t m0 x22 hf y5d ff12 fs6 fc0 sc0 ls0 ws0">bandwidth</div><div class="t m0 x22 ha y5e ffc fs6 fc0 sc0 ls0 ws0">k</div><div class="t m0 x23 hc y58 ffa fs2 fc0 sc0 ls0 ws0">α</div><div class="t m0 x16 ha y59 ffc fs6 fc0 sc0 ls0 ws0">m</div><div class="t m0 x24 h9 y58 ffb fs2 fc0 sc0 ls0 ws0">(<span class="ffa">i,<span class="_ _f"> </span>j<span class="_ _c"></span></span>)<span class="ffa">.</span></div><div class="t m0 x5 h5 y5f ff13 fs2 fc0 sc0 ls0 ws0">2.2.1<span class="_ _12"> </span><span class="ff7">最大化流量问题</span></div><div class="t m0 x6 h5 y60 ff1 fs2 fc0 sc0 ls0 ws0">君不见，<span class="_ _3"></span>黄河之水天上来，<span class="_ _3"></span>奔流到海不复回。<span class="_ _3"></span>君</div><div class="t m0 x5 h5 y61 ff1 fs2 fc0 sc0 ls0 ws0">不见，<span class="_ _3"></span>高堂明镜悲白发，<span class="_ _3"></span>朝如青丝暮成雪。<span class="_ _3"></span>人生得意</div><div class="t m0 x5 h5 y36 ff1 fs2 fc0 sc0 ls0 ws0">须尽欢，莫使金樽空对月。</div><div class="t m0 x25 h9 y62 ff8 fs2 fc0 sc0 ls0 ws0">P2:<span class="_ _f"> </span>max</div><div class="t m0 x26 hd y63 ff10 fs2 fc0 sc0 ls0 ws0">∑</div><div class="t m0 x27 ha y64 ffc fs6 fc0 sc0 ls0 ws0">f</div><div class="t m0 x28 he y65 ff11 fs4 fc0 sc0 ls0 ws0">m</div><div class="t m0 x29 ha y64 ffe fs6 fc0 sc0 ls0 ws0">∈<span class="ffc">F</span></div><div class="t m0 x2a he y66 ff11 fs4 fc0 sc0 ls0 ws0">L</div><div class="t m0 x2b hd y63 ff10 fs2 fc0 sc0 ls0 ws0">∑</div><div class="t m0 x2c hb y67 ffd fs6 fc0 sc0 ls0 ws0">(<span class="ffc">i,j<span class="_ _4"></span></span>)<span class="ffe">∈<span class="ffc">E</span></span></div><div class="t m0 x2d hc y62 ffa fs2 fc0 sc0 ls0 ws0">f</div><div class="t m0 x2e ha y68 ffc fs6 fc0 sc0 ls0 ws0">m</div><div class="t m0 x2f h9 y62 ffa fs2 fc0 sc0 ls0 ws0">α<span class="ffb">(</span>i,<span class="_ _f"> </span>j<span class="_ _c"></span><span class="ffb">)</span>.</div><div class="t m0 xa h9 y69 ff8 fs2 fc0 sc0 ls0 ws0">s.t.<span class="_ _13"> </span><span class="ffa">C<span class="_ _c"></span><span class="ffb">1<span class="_ _11"> </span><span class="fff">−<span class="_ _14"> </span></span></span>C<span class="_ _c"></span><span class="ffb">4</span></span></div><div class="t m0 x9 h5 y6a ff13 fs2 fc0 sc0 ls0 ws0">2.2.2<span class="_ _12"> </span><span class="ff7">最小化成本问题</span></div><div class="t m0 xa h5 y6b ff1 fs2 fc0 sc0 ls0 ws0">君不见，<span class="_ _3"></span>黄河之水天上来，<span class="_ _3"></span>奔流到海不复回。<span class="_ _3"></span>君</div><div class="t m0 x9 h5 y6c ff1 fs2 fc0 sc0 ls0 ws0">不见，<span class="_ _3"></span>高堂明镜悲白发，<span class="_ _3"></span>朝如青丝暮成雪。<span class="_ _3"></span>人生得意</div><div class="t m0 x9 h5 y6d ff1 fs2 fc0 sc0 ls0 ws0">须尽欢，<span class="_ _3"></span>莫使金樽空对月。<span class="_ _3"></span>天生我材必有用，<span class="_ _3"></span>千金散</div><div class="t m0 x9 h5 y6e ff1 fs2 fc0 sc0 ls0 ws0">尽还复来。<span class="_ _3"></span>烹羊宰牛且为乐，<span class="_ _3"></span>会须一饮三百杯。<span class="_ _3"></span>岑夫</div><div class="t m0 x9 h5 y6f ff1 fs2 fc0 sc0 ls0 ws0">子，<span class="_ _8"></span>丹丘生，<span class="_ _8"></span>将进酒，<span class="_ _8"></span>杯莫停。<span class="_ _8"></span>与君歌一曲，<span class="_ _8"></span>请君为我</div><div class="t m0 x9 h5 y70 ff1 fs2 fc0 sc0 ls0 ws0">倾耳听。<span class="_ _3"></span>钟鼓馔玉不足贵，<span class="_ _3"></span>但愿长醉不复醒。<span class="_ _3"></span>古来圣</div><div class="t m0 x9 h5 y71 ff1 fs2 fc0 sc0 ls0 ws0">贤皆寂寞，<span class="_ _3"></span>惟有饮者留其名。<span class="_ _3"></span>陈王昔时宴平乐，<span class="_ _3"></span>斗酒</div><div class="t m0 x9 h5 y72 ff1 fs2 fc0 sc0 ls0 ws0">十千恣欢谑。<span class="_ _3"></span>主人何为言少钱，<span class="_ _3"></span>径须沽取对君酌。<span class="_ _3"></span>五</div><div class="t m0 x9 h5 y73 ff1 fs2 fc0 sc0 ls0 ws0">花马、千金裘，呼儿将出换美酒，与尔同销万古愁。</div><div class="t m0 x30 h9 y74 ff8 fs2 fc0 sc0 ls0 ws0">P3:<span class="_ _f"> </span>min</div><div class="t m0 x31 hd y75 ff10 fs2 fc0 sc0 ls0 ws0">∑</div><div class="t m0 x32 ha y76 ffc fs6 fc0 sc0 ls0 ws0">f</div><div class="t m0 x33 he y77 ff11 fs4 fc0 sc0 ls0 ws0">m</div><div class="t m0 x34 ha y76 ffe fs6 fc0 sc0 ls0 ws0">∈<span class="ffc">F</span></div><div class="t m0 x26 he y78 ff11 fs4 fc0 sc0 ls0 ws0">L</div><div class="t m0 x35 hd y75 ff10 fs2 fc0 sc0 ls0 ws0">∑</div><div class="t m0 x36 hb y79 ffd fs6 fc0 sc0 ls0 ws0">(<span class="ffc">i,j<span class="_ _4"></span></span>)<span class="ffe">∈<span class="ffc">E</span></span></div><div class="t m0 x37 hc y74 ffa fs2 fc0 sc0 ls0 ws0">f</div><div class="t m0 x38 ha y7a ffc fs6 fc0 sc0 ls0 ws0">m</div><div class="t m0 x39 h9 y74 ffa fs2 fc0 sc0 ls0 ws0">C<span class="_ _c"></span><span class="ffb">(</span>i,<span class="_ _f"> </span>j<span class="_ _c"></span><span class="ffb">)</span>β<span class="_ _4"></span><span class="ffb">(</span>i,<span class="_ _f"> </span>j<span class="_ _c"></span><span class="ffb">)</span>.</div><div class="t m0 xa h9 y7b ff8 fs2 fc0 sc0 ls0 ws0">s.t.<span class="_ _13"> </span><span class="ffa">C<span class="_ _c"></span><span class="ffb">1<span class="_ _11"> </span><span class="fff">−<span class="_ _14"> </span></span></span>C<span class="_ _c"></span><span class="ffb">4</span></span></div><div class="t m0 x9 h3 y7c ff6 fs1 fc0 sc0 ls0 ws0">2.3<span class="_ _7"> </span><span class="ff7">解决方法</span></div><div class="t m0 xa h5 y7d ff1 fs2 fc0 sc0 ls0 ws0">君不见，<span class="_ _3"></span>黄河之水天上来，<span class="_ _3"></span>奔流到海不复回。<span class="_ _3"></span>君</div><div class="t m0 x9 h5 y7e ff1 fs2 fc0 sc0 ls0 ws0">不见，<span class="_ _3"></span>高堂明镜悲白发，<span class="_ _3"></span>朝如青丝暮成雪。<span class="_ _3"></span>人生得意</div><div class="t m0 x9 h5 y7f ff1 fs2 fc0 sc0 ls0 ws0">须尽欢，<span class="_ _3"></span>莫使金樽空对月。<span class="_ _3"></span>天生我材必有用，<span class="_ _3"></span>千金散</div><div class="t m0 x9 h5 y80 ff1 fs2 fc0 sc0 ls0 ws0">尽还复来。<span class="_ _3"></span>烹羊宰牛且为乐，<span class="_ _3"></span>会须一饮三百杯。<span class="_ _3"></span>岑夫</div><div class="t m0 x9 h5 y81 ff1 fs2 fc0 sc0 ls0 ws0">子，<span class="_ _8"></span>丹丘生，<span class="_ _8"></span>将进酒，<span class="_ _8"></span>杯莫停。<span class="_ _8"></span>与君歌一曲，<span class="_ _8"></span>请君为我</div><div class="t m0 x9 h5 y82 ff1 fs2 fc0 sc0 ls0 ws0">倾耳听。<span class="_ _3"></span>钟鼓馔玉不足贵，<span class="_ _3"></span>但愿长醉不复醒。<span class="_ _3"></span>古来圣</div><div class="t m0 x9 h5 y83 ff1 fs2 fc0 sc0 ls0 ws0">贤皆寂寞，<span class="_ _3"></span>惟有饮者留其名。<span class="_ _3"></span>陈王昔时宴平乐，<span class="_ _3"></span>斗酒</div><div class="t m0 x9 h5 y84 ff1 fs2 fc0 sc0 ls0 ws0">十千恣欢谑。<span class="_ _3"></span>主人何为言少钱，<span class="_ _3"></span>径须沽取对君酌。<span class="_ _3"></span>五</div><div class="t m0 x9 h5 y85 ff1 fs2 fc0 sc0 ls0 ws0">花马、千金裘，呼儿将出换美酒，与尔同销万古愁。</div><div class="t m0 x3a h5 y86 ff7 fs2 fc0 sc0 ls0 ws0">算<span class="_ _4"></span>法<span class="_ _13"> </span><span class="ff13">1:<span class="_ _1"> </span><span class="ff1">使<span class="_ _4"></span>用<span class="_ _10"> </span><span class="ff8">PyCUD<span class="_ _15"></span>A<span class="_ _1"> </span><span class="ff1">并<span class="_ _4"></span>行<span class="_ _c"></span>计算<span class="_ _1"> </span></span>k<span class="_ _10"> </span><span class="ff1">条最<span class="_ _c"></span>短</span></span></span></span></div><div class="t m0 x3a h5 y87 ff1 fs2 fc0 sc0 ls0 ws0">路径</div><div class="t m0 x3b h5 y88 ff7 fs2 fc0 sc0 ls0 ws0">输入<span class="ff13">:<span class="_ _13"> </span><span class="ff1">流<span class="_ _a"> </span><span class="ffa">f</span></span></span></div><div class="t m0 x3c ha y89 ffc fs6 fc0 sc0 ls0 ws0">m</div><div class="t m0 x3d h5 y88 ff1 fs2 fc0 sc0 ls0 ws0">，每个流需要满足边的<span class="_ _a"> </span><span class="ff8">QoS<span class="_ _a"> </span></span>要求</div><div class="t m0 x3b h5 y8a ff7 fs2 fc0 sc0 ls0 ws0">输出<span class="ff13">:<span class="_ _13"> </span><span class="ff1">流<span class="_ _a"> </span><span class="ffa">f</span></span></span></div><div class="t m0 x3c ha y8b ffc fs6 fc0 sc0 ls0 ws0">m</div><div class="t m0 x3e h5 y8a ff1 fs2 fc0 sc0 ls0 ws0">的最短路径</div><div class="t m0 x3f h5 y8c ff14 fs7 fc0 sc0 ls0 ws0">1<span class="_ _9"> </span><span class="ff1 fs2">流<span class="_ _a"> </span><span class="ffa">f</span></span></div><div class="t m0 x40 ha y8d ffc fs6 fc0 sc0 ls0 ws0">m</div><div class="t m0 x41 h5 y8c ff1 fs2 fc0 sc0 ls0 ws0">转发至集合<span class="_ _a"> </span><span class="ffa">S</span></div><div class="t m0 x3f h9 y8e ff14 fs7 fc0 sc0 ls0 ws0">2<span class="_ _9"> </span><span class="ffa fs2">P<span class="_ _16"> </span>ointer<span class="_ _17"> </span><span class="fff">←<span class="_ _d"> </span><span class="ffb">1</span></span></span></div><div class="t m0 x3f h9 y8f ff14 fs7 fc0 sc0 ls0 ws0">3<span class="_ _9"> </span><span class="ff13 fs2">while<span class="_ _a"> </span><span class="ffa">P<span class="_ _16"> </span>ointer<span class="_ _17"> </span>><span class="_ _d"> </span><span class="ffb">0<span class="_ _a"> </span></span></span>do</span></div><div class="t m0 x3f h9 y90 ff14 fs7 fc0 sc0 ls0 ws0">4<span class="_ _18"> </span><span class="ffa fs2">P<span class="_ _16"> </span>ointer<span class="_ _17"> </span>><span class="_ _d"> </span><span class="ffb">0</span></span></div><div class="t m0 x3f h5 y91 ff14 fs7 fc0 sc0 ls0 ws0">5<span class="_ _18"> </span><span class="ff1 fs2">更新路径<span class="_ _a"> </span><span class="ffb">(<span class="ffa">S,<span class="_ _f"> </span>E<span class="_ _c"></span>,<span class="_ _16"> </span>D<span class="_ _4"></span>istance<span class="_ _4"></span></span>)</span></span></div><div class="t m0 x3f h10 y92 ff14 fs7 fc0 sc0 ls0 ws0">6<span class="_ _9"> </span><span class="ff13 fs2">end</span></div><div class="t m0 x3f h5 y93 ff14 fs7 fc0 sc0 ls0 ws0">7<span class="_ _9"> </span><span class="ff1 fs2">更新路径<span class="_ _a"> </span><span class="ffb">(<span class="ffa">S,<span class="_ _f"> </span>E<span class="_ _c"></span>,<span class="_ _16"> </span>D<span class="_ _4"></span>istance,<span class="_ _f"> </span>P<span class="_ _16"> </span>r<span class="_ _4"></span>ev<span class="_ _c"></span>ious</span>)</span></span></div><div class="t m0 x3f h5 y94 ff14 fs7 fc0 sc0 ls0 ws0">8<span class="_ _9"> </span><span class="ff1 fs2">计算流量最短路径，转发信息给<span class="_ _a"> </span><span class="ffa">P</span></span></div><div class="t m0 xd h9 y37 ff8 fs2 fc0 sc0 ls0 ws0">2</div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>

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