The paper presents a new algorithm for the SCWRL program, which is widely used for rapid and accurate side-chain conformation prediction. The new algorithm leverages graph theory to solve the combinatorial problem in side-chain prediction by representing side chains as vertices in an undirected graph. Residues with rotamers that have nonzero interaction energies are connected by edges. The graph is partitioned into connected subgraphs, which are then broken down into biconnected components. The combinatorial problem is reduced to finding the minimum energy of these small biconnected components, and the results are combined to identify the global minimum energy conformation. This approach significantly reduces the computational time, allowing the algorithm to complete predictions on a set of 180 proteins with 34,342 side chains in less than 7 minutes. The total χ1 and χ1 + 2 dihedral angle accuracies are 82.6% and 73.7%, respectively, using a simple energy function based on a backbone-dependent rotamer library and a linear repulsive steric energy. The new algorithm enables more demanding applications such as sequence design and ab initio structure prediction, as well as the addition of more complex energy functions and conformational flexibility, leading to increased accuracy.The paper presents a new algorithm for the SCWRL program, which is widely used for rapid and accurate side-chain conformation prediction. The new algorithm leverages graph theory to solve the combinatorial problem in side-chain prediction by representing side chains as vertices in an undirected graph. Residues with rotamers that have nonzero interaction energies are connected by edges. The graph is partitioned into connected subgraphs, which are then broken down into biconnected components. The combinatorial problem is reduced to finding the minimum energy of these small biconnected components, and the results are combined to identify the global minimum energy conformation. This approach significantly reduces the computational time, allowing the algorithm to complete predictions on a set of 180 proteins with 34,342 side chains in less than 7 minutes. The total χ1 and χ1 + 2 dihedral angle accuracies are 82.6% and 73.7%, respectively, using a simple energy function based on a backbone-dependent rotamer library and a linear repulsive steric energy. The new algorithm enables more demanding applications such as sequence design and ab initio structure prediction, as well as the addition of more complex energy functions and conformational flexibility, leading to increased accuracy.