The “Seven Dwarfs” of Symbolic Computation

Abstract

We present the Seven Dwarfs of Symbolic Computation, which are sequential and parallel algorithmic methods that today carry a great majority of all exact and hybrid symbolic compute cycles. SymDwf 1. Exact linear algebra, integer lattices SymDwf 2. Exact polynomial and differential algebra, Gröbner bases SymDwf 3. Inverse symbolic problems, e.g., interpolation and parameterization SymDwf 4. Tarski's algebraic theory of real geometry SymDwf 5. Hybrid symbolic-numeric computation SymDwf 6. Computation of closed form solutions SymDwf 7. Rewrite rule systems and computational group theory We will elaborate on each dwarf and compare with Colella's seven and the Berkeley team's thirteen dwarfs of scientific computing.

Analysis of parallelized libraries and interference effects in concurrent environments

“…Colella has introduced the "Seven Dwarfs" of scientific computing. Kaltofen [7] defines Dwarf as follows: "A dwarf is an algorithmic method that captures a pattern of computation and communication". This pattern is important in the proposed work to provide a basis of knowledge and characterization of types of applications so that when we assess that a certain application can be run in shared environments alongside other applications without degrading the shared resource, one deduces that other applications of the same type (dwarfs) may also compete for the same feature without degrading the resource.…”

Changing computing paradigms towards power efficiency

“…In this regard, the new strategies proposed in [2] represent a first step towards the development of concrete energy-aware metrics. However, to drive the development of future hardware in the correct direction, this effort should be combined with the introduction of new benchmarks based on, for example, the CG method [21] or some of the Dwarfs proposed in [3,4], as replacements of the current power-hungry and FLOP-driven LINPACK benchmark.…”

“…By contrast, by using metrics based on both time-tosolution and energy, as proposed in [2], it is possible to get a much more realistic picture, which can drive and help the design of future energy-efficient machines and algorithms. At the same time, we also need to abandon the (convenient and simple) LINPACK benchmark and make use of a relatively small selected set of benchmarks, characterized by widely different features and thus representative of the majority of the current applications [3,4].…”

Snow White Clouds and the Seven Dwarfs

“…Che et al [11] have proposed parallel benchmarks based on the Dwarf taxonomy, but argue that the Dwarf taxonomy alone may not be sufficient to capture the behaviour in some applications. Furthermore, in a recent study, Kaltofen [12] has identified a need for Dwarves to cover symbolic computation.…”