The immune system can detect and respond against pathogens in time that does not vary with the size of the host animal. We suggest that this is due to the architecture of lymph nodes. Lymph nodes are anatomical structures that facilitate the otherwise serendipitous encounter of immune system cells with pathogens. We develop two complementary mathematical approaches to derive the optimal distribution of lymph nodes that enable a rapid immune response. Our work gives insights into the optimal design and architecture of the immune system and provides valuable inspiration for designing efficient computing systems.