Searching for a k-clique in unknown graphs

Agents that solve problems in unknown graphs are usually required to iteratively explore parts of the graph. In this paper we research the problem of finding a k-clique in an unknown graph while minimizing the number of required exploration actions. Two novel heuristics (KnownDegree and Clique ∗ ) are proposed to reduce the required exploration cost by carefully choosing which part of the environment to explore. We further investigate the problem by adding probabilistic knowledge of the graph and propose an MDP and a Monte Carlo based heuristic (RClique ∗ ) that uses knowledge of edges probabilities to reduce the required exploration cost. The efficiency of the proposed approaches is demonstrated on simulated random and scale free graphs. 1