  Architectures for quantum computing based on neutral atoms have risen to
prominence as candidates for both near and long-term applications. These
devices are particularly well suited to solve independent set problems, as the
combinatorial constraints can be naturally encoded in the low-energy Hilbert
space due to the Rydberg blockade mechanism. Here, we approach this connection
with a focus on a particular device architecture and explore the ubiquity and
utility of independent set problems by providing examples of real-world
applications. After a pedagogical introduction of basic graph theory concepts
of relevance, we briefly discuss how to encode independent set problems in
Rydberg Hamiltonians. We then outline the major classes of independent set
problems and include associated example applications with industry and social
relevance. We determine a wide range of sectors that could benefit from
efficient solutions of independent set problems -- from telecommunications and
logistics to finance and strategic planning -- and display some general
strategies for efficient problem encoding and implementation on neutral-atom
platforms.
