We study the computational complexity of satisfying proportional representation -- in particular proportional, extended, and fully justified representation (PJR, EJR, and FJR) -- in participatory budgeting and committee elections with additive utilities. First, we give a complete picture of the complexity of the axioms...
Carmel Baharav, Jakob de Raaij, Agnes Totschnig· 2 citations· ⚡1
A graph $G$ is perfect if $\omega(H) = \chi(H)$ for each induced subgraph $H$ of $G$. In 2002, Chudnovsky, Robertson, Seymour, and Thomas famously proved the Strong Perfect Graph Theorem. Motivated by this forbidden induced subgraph characterization of the class of perfect graphs as well as the possible extension of ef...
Cicely Henderson, Hidde Koerts, Taite LaGrange et al.· 0 citations
The results deepen the connection between graph theory and fair division, and offer new tools for studying fairness in structured resource environments, by showing that deciding the existence of an $\mathrm{EF1}_{\mathrm{outer}}$ allocation is NP-complete even for binary additive valuations, thereby resolving an open c...
Nicolas Bousquet, Frank Connor, Agnes Totschnig et al.· 0 citations
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