We consider the adversarial combinatorial multi-armed bandit (CMAB) problem, whose decision set can be exponentially large with respect to the number of given arms. To avoid dealing with such large decision sets directly, we propose an algorithm performed on a zero-suppressed binary decision diagram (ZDD), which is a compressed representation of the decision set. The proposed algorithm achieves either $O(T^{2/3})$ regret with high probability or $O(\sqrt{T})$ expected regret as the any-time guarantee, where $T$ is the number of past rounds. Typically, our algorithm works efficiently for CMAB problems defined on networks. Experimental results show that our algorithm is applicable to various large adversarial CMAB instances including adaptive routing problems on real-world networks.