Within this framework, we introduce a new algorithm, called bucket-tree elimination (BTE), that extends Bucket Elimination (BE) to trees, and show that it can provide a speed-up of n over BE for various reasoning tasks.
For example, one might repeatedly identify one possible node and edge on the periphery of an optimal tree whose elimination reduces the optimal parsimony score, then recurse on the remainder of the data to construct the rest of the tree.
The subtree algorithm [15] minimizes PCIe transmissions by storing an entire branch of the elimination tree in the GPU memory (the elimination tree is a tree data structure describing the workflow of the factorization), and also reduces the total kernel launch time by launching BLAS kernels in batches.
The multi-core parallelization of symbolic decomposition and numerical decomposition are based on the binary elimination tree.
The multithreading technique [17] creates multiple threads for both the CPU and the GPU, to utilize concurrency of the elimination tree.
In [24], the author uses a fill-in minimization technique by analyzing the elimination tree of the global BBD matrix and identifying the coupling nodes such that the fill-in entries are minimized.
Finally, there are methods that integrate classifier training and feature selection, such as decision trees, which essentially perform forward feature selection while growing a tree and backward elimination while pruning the tree (Duda et al, 2001).
The literature describes two high performance concurrent stack algorithms based on combining funnels and elimination trees.
This framework makes our algorithm easier to generalize, and also easier to compare against other methods related to elimination trees.
Unfortunately, the funnels are linearizable but blocking, and the elimination trees are non-blocking but not linearizable.
We analyze the structures of linear equation systems resulting from each of the methods and how different matrix structures lead to different multifrontal solver elimination trees.
