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CASES

2004

ACM

2004

ACM

Many optimization techniques, including several targeted speciﬁcally at embedded systems, depend on the ability to calculate the number of elements that satisfy certain conditions. If these conditions can be represented by linear constraints, then such problems are equivalent to counting the number of integer points in (possibly) parametric polytopes. It is well known that this parametric count can be represented by a set of Ehrhart polynomials. Previously, interpolation was used to obtain these polynomials, but this technique has several disadvantages. Its worst-case computation time for a single Ehrhart polynomial is exponential in the input size, even for ﬁxed dimensions. The worst-case size of such an Ehrhart polynomial (measured in bits needed to represent the polynomial) is also exponential in the input size. Under certain conditions this technique even fails to produce a solution. Our main contribution is a novel method for calculating Ehrhart polynomials analytically. It e...

Related Content

Added |
30 Jun 2010 |

Updated |
30 Jun 2010 |

Type |
Conference |

Year |
2004 |

Where |
CASES |

Authors |
Sven Verdoolaege, Rachid Seghir, Kristof Beyls, Vincent Loechner, Maurice Bruynooghe |

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