Lines Matching defs:An
112 However, {\tt isl} currently does not support an integer hull operation
115 expensive to compute given only an implicit representation.
118 and an overapproximation of this hull is sufficient.
119 The ``simple hull'' of a set is such an overapproximation
168 An alternative method for parametric integer programming
213 The dual simplex method starts from an initial sample value that
276 with $b(\vec p)$ the constant term, an affine expression in the
311 an arbitrarily large positive number. Instead of looking for the
336 $\fract {\alpha M } = 0$. It should be noted, though, that an unbounded
338 indicates an incorrect formulation of the problem.
363 produce an error if the problem turns out to be unbounded.
404 Given an equality involving at least one unknown, we pivot
523 to disjunctive normal form can lead to an explosion of the size
533 Currently, {\tt isl} also does not have an internal representation
550 an increase by a factor of $n!$ if all possible orderings end up being
556 on the sign of an affine expression over the elements of the context.
592 When an extra integer division is added to the context,
600 but there are rows with an indeterminate sign, then the context
626 An initial implementation that was never made public would also
629 an extra constraint to the context.
631 is always an integer point and that this point may also satisfy
636 in an accumulation of a large number of cuts.
665 in the set can be rounded up to yield an integer point in the context.
685 The list of witnesses is used to construct an initial approximation
688 Any equality found in this way that expresses an integer division
689 as an \emph{integer} affine combination of other variables is
698 run on an Intel Xeon W3520 @ 2.66GHz.
772 \textcite{Bygde2010licentiate} and an analysis of the results
776 In this section, we present an online detection mechanism that has
874 we can, in the general case, only compute an approximation
884 For computing an approximation of the transitive closure of $R$,
886 and first compute an approximation of $R^k$ for $k \ge 1$ and then project
908 \subsection{Computing an Approximation of $R^k$}
922 to arrive at an image element and ignore the fact that some of these
974 That is, each offset is extended with an extra coordinate that is
1014 Let us now consider how to compute an overapproximation of $P_i'$.
1017 Note that this is just an optimization. The procedure described
1079 To prove that $Q_i$ is indeed an overapproximation of $P_i'$,
1366 Since $K$ is an overapproximation of $R^k$, $T$ will also be an
1379 Since $T$ is known to be an overapproximation, we only need to check
1395 to be an overapproximation, we only need to check whether
1413 an overapproximation of $R^+$, also
1427 an approximation of each strongly connected components separately.
1448 the basic relations and an edge between two basic relations
1450 That is, there is an edge from $R_i$ to $R_j$ iff
1468 That is, whenever the algorithm checks if there is an edge between
1478 still be an overapproximation of the left hand side, but this result
1644 an overapproximation of the power.
1655 In particular, when an entire dependence graph is encoded
1721 However, from an implementation perspective, it is easier
1731 The result of the recursive call will either be exact or an
1733 also exact or an overapproximation.
1796 changed in the second iteration and it does not have an effect
1861 or at least an approximation of this convex hull.
1968 \subsection{An {\tt Omega}-like implementation}
1973 In this section, we describe our implementation of an algorithm
1992 Such an overapproximation can be obtained by computing strides,
2013 If an upper bound is required, it can be calculated in a manner
Indexes created Mon Mar 02 05:31:46 UTC 2026