A computing device is provided, including a cluster update accelerator circuit configured to receive signals encoding a combinatorial cost function of a plurality of variables and a connectivity graph for the combinatorial cost function. In an energy sum phase, the cluster update accelerator circuit may determine a respective plurality of accumulated energy change values for the combinatorial cost function based at least in part on the connectivity graph. In an update phase, the cluster update accelerator circuit may determine a respective update indicator bit for each accumulated energy change value. In an encoder phase, based on the plurality of update indicator bits, the cluster update accelerator circuit may select a largest update-indicated cluster of the variables included in the connectivity graph. The cluster update accelerator circuit may output an instruction to update the variables included in the largest update-indicated cluster.