Color-coding

Noga Alon, Raphy Yuster, Uri Zwick
1994 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing - STOC '94  
We describe a novel randomized method, the method of color-coding for finding simple paths and cycles of a specified length k, and other small subgraphs, within a given graph G = (V, E). The randomized algorithms obtained using this method can be derandomized using families of perfect hash functions. Using the color-coding method we obtain, among others, the following new results: * • If a graph G = (V, E) contains a subgraph isomorphic to a bounded tree-width graph H = (V H , E H ) where |V H
more » ... , E H ) where |V H | = O(log V ), then such a copy of H can be found in polynomial time. This was not previously known even if H were just a path of length O(log V ). These results improve upon previous results of many authors. The third result resolves in the affirmative a conjecture of Papadimitriou and Yannakakis that the LOG PATH problem is in P. We can even show that the LOG PATH problem is in NC.
doi:10.1145/195058.195179 dblp:conf/stoc/AlonYZ94 fatcat:7escc6ce2nfmtowkqhrauzn3ae