最小集集合覆盖问题。

aimisiyou

mathe 发表于 2022-10-26 19:54
由于我们很难找到有效的算法从一大批点中选择数十个点包含尽量多的合法曲线，我们可以改为考虑直接选择比较 ...

蚁群算法不行么？

wayne

找到了一篇论文，关于k均匀线性超图的遍历，有个粗略的上限估计，里面的证明不知道对算法 有没有参考价值。
https://www.sciencedirect.com/sc ... i/S0195669813002126

mathe

很有意思，改为选择曲线的切线以及它们的交点可以找出一些不错的解:
https://github.com/emathgroup/se ... /files/ft3.19.outfs
对应代码
https://github.com/emathgroup/se ... les/finitetree3.cpp
其中参数P可以修改为其它素数，而现在发现19产生的解最多样化而且有用。
当然产生的解不一定合法，可以先用
https://github.com/emathgroup/se ... d/files/solve8s.cpp
进行过滤，它依赖于一些宏
https://github.com/emathgroup/se ... ed/files/newdef.cpp

mathe

另外代码中现在开始用A~Za~z代表各个点，但是如果程序出现大于52个点的情况，会有些问题，需要扩展。solve8s.cpp里面还有宏NUM_NODES代表可以处理的最大点数目，同时也需要扩展。
已知结果可以参考https://oeis.org/A172992/b172992.txt，现在还没有能够找到超越这个的结果

mathe

这几个方程大家帮忙看看是否有解
print({T38U36L58}QRTlGOYfLUdkEKdjEWceELQiENTXGINQFLObIbflDUbhJbcdQXbjZabkGMPbDGRcHIegLMWXadgiMOSULNcgKOXaJPWgGHXdFKSgZeilJXhiLahlUZfgMYijQSehPRYaJMNZOTWdDSikIKUcMRdeGTghNOPiNWYhDFHaBFNkBgjlBdfhBSYcBHPQBDTZFJUlFRWZKMQfCSXfCGjkCFTeCHNlCQUWCIJaCKRhBCEb);
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print("C=(1,C_y,0) F_y=0 Q=(0,1,0) R_x=0 R_y=0 T_x=0 U=(1,U_y,0) W=(1,0,0) Z_x=1 Z_y=0 l_x=0 l_y=1 ");
print({T38U36L58}QRTlIOZeMUdkHKUcJPVgEKdiEVcfEMQjENTWLRdfITghNOPjFIWdGKSgYfjlHINQNVZhDFGaJWhjGMObHbelDUbhJbcdQWbiYabkILPbBGNkBgilBdehBSZcBFPQBDTYMahlUYegLZijDIRcFHfgLMVWGRVYKLQeQSfhPRZaJLNYadgjLOSUCSWeCIikCGTfCFNlCQUVCHJaCKRhOTVdDSjkMNcgKOWaGJUlBCEb);
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print("D=(1,D_y,0) G_y=0 J_x=1 J_y=0 M_x=0 M_y=1 U=(1,0,0) a_x=0 b=(1,b_y,0) h=(0,1,0) l_x=0 l_y=0 ");
print({T38U36L58}RcelFKNWEGJjHVZgTVklENdiFRZaRSWkHTafBPVWBEaeBFXbBDOcBKUZBJQkfgijPSZdDNRXOWadHbikLNVcCHLSCJRUCKPkCOefCINaCGWgCFQdGHKQDZjkILflDGISDYdgEIUYFYfkTWYjEPRfKTbdIOQZLPQXacgkMQjlMUWfMRViDEHMKMSeJLMbGMXaKLajGZbeTUciNQbgIWeiELTZGOilJOTXEFglBCMY);
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print("C=(1,C_y,0) G=(1,0,0) I_x=0 I_y=1 O_y=0 W=(0,1,0) e_x=0 g=(1,g_y,0) i_x=0 i_y=0 l_x=1 l_y=0 ");
print({T38U36L58}SbdlFKOVDGJkUWilDOejFSZaHUahfhjkQRZeEOSXBHLQBJSTBKRiBNdhBIOaBGVfBFPeEGIQDRShKUceINPZMPklMTVhMSWjDEHMKMQdJLMcGMXaOPcfIVdjJNUXDFflHWZfQSViCRVWCDadCFXcCENbCKTZCJPiNVaeHcijLOWbEZikILhlEYefDITYFYhiUVYkLPRXabfiGHKPKLakGZcdTUbjDLUZGNjlBCMY);
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K_Y,D_X,G_X,E_Y,C_X,S_X,f_Y]);
print("H_x=0 H_y=0 U_x=0 U_y=1 a=(0,1,0) b=(1,b_y,0) c_y=0 f=(1,f_y,0) h_x=0 i=(1,0,0) j_x=1 j_y=0 ");
print({T38U36L58}ScdiFKNWEGJjEPSfKUbeIOQaGHKQBPVWBEZdBFXbBDOcBKTaBJQlELUaGOikDGIRRSWlKLZjGabdTUckCHLRCJSTCKPlCOdfCINZCGWgCFQeHVagLPQXZcglfgjkPRaeDNSXJOUXEFgiDYegEITYFYflUWYjHUZfNQbgIWdkDajlILfiUVilENekFSZaMQijMTWfMSVkDEHMKMRdJLMbGMXZOWZeHbklLNVcBCMY);
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print("C=(1,0,0) G=(1,G_y,0) O_y=0 W=(1,W_y,0) d_x=1 d_y=0 f_x=0 f_y=0 g=(0,1,0) j_x=0 j_y=1 k_x=0 ");

mathe

另外还有一个，这些都是潜在的可以超越已知最优解的候选结果,就是不知道是否有解，是否实数解
print({T44U44L79:1:12:9:0:19:17:4}FHKUPkloEIMganprRWZdUefqGSTaFLRfTdjpFTYgGIQiNclqPXfpKcejJUVoEabmLQSnThlmIJOfLOPUaghjimoqAJepAGjkAQgoAEPcALMqAFSmOQchIYjoJSgqGPemELXlTZbeLVbjNXdhORYiIVhkMOblLacoEQUjMTViHJXjLYmrNbfkFOjrHLhpBQXmBGbgBHSlBIerBPVqBJYcCJMZCaeiCYpqCFGXCNSUCWkmSVWfKPSYFWaqGUZpXegnITXcQYflEGJNRValIUbdFIlpKRhoEOdnDHZgDGKfDEVeDSboDTnqDPWrABCD);
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print("B_x=1 B_y=0 H_x=0 H_y=1 I=(1,I_y,0) J_x=0 J_y=0 X_x=0 Y=(1,0,0) c_y=0 j=(0,1,0) o=(1,o_y,0) ");