A data structure is described that comprises a balanced binary tree and a binary heap, which may be utilized for combinatorial searching algorithms. For instance, solutions for performing a task, such as a print job or the like, are associated with nodes that are utilized to generate the data structure. Each node is associated with a quality indicator that describes a most optimal solution that may be reached through the node when traversing the binary tree. The binary heap is generated from a subset of the nodes in the tree, wherein each node in the subset has a quality indicator value that is within a predefined range of a best known solution quality. The binary heap is sorted according to a search effort indicator value for each node, where nodes that are more easily reached in the tree are placed higher in the heap to facilitate rapid identification.
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