An efficient tree decomposition method for permanents and mixed discriminants
نویسندگان
چکیده
We present an efficient algorithm to compute permanents, mixed discriminants and hyperdeterminants of structured matrices and multidimensional arrays (tensors). We describe the sparsity structure of an array in terms of a graph, and we assume that its treewidth, denoted as ω, is small. Our algorithm requires Õ(n 2) arithmetic operations to compute permanents, and Õ(n + n 3) for mixed discriminants and hyperdeterminants. We finally show that mixed volume computation continues to be hard under bounded treewidth assumptions.
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عنوان ژورنال:
- CoRR
دوره abs/1507.03046 شماره
صفحات -
تاریخ انتشار 2015