[問題] Merge nodes (graph theory problem)

看板Prob_Solve (計算數學 Problem Solving)作者 (這真是太危險啦)時間17年前 (2007/10/20 01:13), 編輯推噓3(300)
留言3則, 3人參與, 最新討論串1/1
Sorry for type in English. I've recently face a problem when analyzing the data. I have about 8000 vertexs, with distance d(i,j) between them. (i.e. might regard as fully-connected graph) I now, however, want ot merge the vertexs. To downsize my number of vertexs. My goal is to merge every 2 vertexs into 1, so the number of total vertexs become 4000. My optimal criteria is that the Sum( d(i,j) ) between all pairs of merged node is minimal. The very first impression is using Greedy algorithm, which easily failed. Is there any good algorithm to attack this problem? Or it is just NP. Does max flow-min cut relate to this problem. Is the problem similar to the idea of seperating the nodes into two clusters and minimize the distance between the clusters? Thanks a lot! -- -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 128.220.29.227

10/20 21:52, , 1F
看起來跟minimum-weight perfect-matching有點關係~ :)
10/20 21:52, 1F

10/21 09:53, , 2F
感謝樓上 @@ 學到新東西
10/21 09:53, 2F

10/23 03:13, , 3F
thx, eactly mw p-matching is what I need!
10/23 03:13, 3F
文章代碼(AID): #176EMgw6 (Prob_Solve)
文章代碼(AID): #176EMgw6 (Prob_Solve)