Tight Bounds for Graph Homomorphism and Subgraph Isomorphism
نویسندگان
چکیده
We prove that unless Exponential Time Hypothesis (ETH) fails, deciding if there is a homomorphism from graph G to graph H cannot be done in time |V (H)|o(|V (G)|). We also show an exponential-time reduction from Graph Homomorphism to Subgraph Isomorphism. This rules out (subject to ETH) a possibility of |V (H)|o(|V (H)|)-time algorithm deciding if graph G is a subgraph of H. For both problems our lower bounds asymptotically match the running time of brute-force algorithms trying all possible mappings of one graph into another. Thus, our work closes the gap in the known complexity of these fundamental problems.
منابع مشابه
Tight Bounds for Subgraph Isomorphism and Graph Homomorphism
We prove that unless Exponential Time Hypothesis (ETH) fails, deciding if there is a homomorphism from graph G to graph H cannot be done in time |V (H)|o(|V . Combined with the reduction of Cygan, Pachocki, and Soca la, our result rules out (subject to ETH) a possibility of |V (G)|o(|V -time algorithm deciding if graph H is a subgraph of G. For both problems our lower bounds asymptotically matc...
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