Most psychological theories attribute people's failure to achieve their goals exclusively to insufficient motivation or lack of skill. Here, we offer a complementary explanation that emphasizes the inherent complexity of the computational problems that arise from the structure of people's goal systems. Concretely, we hypothesize that people's capacity to achieve their goals can be predicted from combinatorial parameters of the structure of the network connecting their goals to the means available to pursue them. To test this hypothesis, we expressed the relationship between goals and means as a bipartite graph where edges between means and goals indicate which means can be used to achieve which goals. This allowed us to map two computational challenges that arise in goal achievement onto two classic NP-hard problems: Set Cover and Maximum Coverage. The connection between goal pursuit and NP-hard problems led us to predict that people should perform better with goal systems that are tree-like. Three behavioral experiments confirmed this prediction. Our results imply that network parameters that are instrumental to algorithm design could also be useful for understanding when and why people struggle in their goal pursuits.