We study the complexity of the so called semi-disjoint bilin-ear forms over different semi-rings, in particular the n-dimensional vector convolution and n × n matrix product. We consider a powerful unit-cost computational model over the ring of integers allowing for several addi-tional operations and generation of large integers. We show the following dichotomy for such a powerful model: while almost all arithmetic semi-disjoint bilinear forms have the same asymptotic time complexity as that yielded by naive algorithms, matrix multiplication, the so called distance matrix product, and vector convolution can be solved in a linear number of steps. It follows in particular that in order to obtain a non-trivial lower bounds for these three basic problems one has to assume restrictions on the set of allowed operations and/or the size of used integers.
CITATION STYLE
Lingas, A., Persson, M., & Sledneu, D. (2017). Bounds for semi-disjoint bilinear forms in a unit-cost computational model. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10185 LNCS, pp. 412–424). Springer Verlag. https://doi.org/10.1007/978-3-319-55911-7_30
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