Graph Isomorphism🚧
Graph Isomorphism
https://en.wikipedia.org/wiki/Graph_canonization https://en.wikipedia.org/wiki/Graph_isomorphism https://en.wikipedia.org/wiki/Graph_isomorphism_problem#Solved_special_cases
Subgraph Isomorphism
https://en.wikipedia.org/wiki/Subgraph_isomorphism_problem https://en.wikipedia.org/wiki/Maximum_common_subgraph_isomorphism_problem
https://adriann.github.io/Ullman subgraph isomorphism.html Taming Verification Hardness: An Efficient Algorithm for Testing Subgraph Isomorphism
Tree Isomorphism
http://www.cs.upc.edu/~valiente/graph-00-01-c.pdf use radix sort O(nd) = O(#son + #grandson) = O(n + n) = O(n)
為什麼對? https://github.com/juanplopes/icpc/blob/master/uva/12489.cpp
兩棵樹的子圖同構:刪掉G和H的根,變成很多子樹G1...Gp和H1....Hq。建立二分圖:當Gi和Hj同構,建立邊ij。求最大二分匹配。時間複雜度O(V²E)。
UVa 10729 10904 12489 ICPC 2935
Subtree Isomorphism
可以用DP + matching https://code.google.com/codejam/contest/dashboard?c=32005#s=a&a=3 http://www.lsi.upc.edu/~valiente/riga-tre.pdf
Reconstruction Conjecture
https://en.wikipedia.org/wiki/Reconstruction_conjecture
刪掉一點之導出子圖,總共V張,合稱deck。
兩圖同構,顯然deck相同。兩圖deck相同,是否同構?
Graph Enumeration🚧
Subgraph Searching🚧
Subgraph Searching(Subgraph Matching)
https://www.cs.cmu.edu/~jingx/docs/DBreport.pdf
Graph Approximate Isomorphism
https://arxiv.org/abs/1802.08509
Graph Distance(Graph Similarity)(Graph Kernel)
兩張圖的距離。
https://www.zhihu.com/question/57269332 http://www.raetschlab.org/lectures/amsa/5-borgwardt-graph.pdf http://www.stat.purdue.edu/~vishy/talks/Graphs.pdf
Tree Distance(Tree Similarity)
兩棵樹的距離。
Edit Distance Rotation Distance Chain Rotation Distance
Subgraph Counting🚧
Subgraph Counting
《A Survey on Subgraph Counting: Concepts, Algorithms, and Applications to Network Motifs and Graphlets》