By Ulrich Geske, Hans-Joachim Goltz (auth.), Dietmar Seipel, Michael Hanus, Armin Wolf (eds.)

This quantity constitutes the completely refereed post-conference court cases of the seventeenth overseas convention on functions of Declarative Programming and data administration, INAP 2007, and the twenty first Workshop on good judgment Programming, WLP 2007, held in Würzburg, Germany, in the course of October 4-6, 2007.

The sixteen completely revised complete papers awarded including 1 invited paper have been rigorously reviewed and chosen from a variety of submissions. the themes coated are constraints; databases and information mining; extensions of good judgment programming; and procedure demonstrations.

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Extra resources for Applications of Declarative Programming and Knowledge Management: 17th International Conference, INAP 2007, and 21st Workshop on Logic Programming, WLP 2007, Würzburg, Germany, October 4-6, 2007, Revised Selected Papers

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4(b), ensures that i is not started until all activities in Θ(j, T ) can be finished. Θ(j, T ) Θ(j, T ) j j i lctj ECT(Θ(j, T ) ∪ {i}) (a) The rule is applicable for j and i: ECT(Θ(j, T ) ∪ {i}) > lctj i t t ECT(Θ(j, T )) (b) After the application esti is at least ECT(Θ(j, T )) Fig. 4. An application of the edge-finding rule 44 S. Kuhnert Besides the edge-finding rule, the presented edge-finding algorithm makes use of the following overload rule, that can be checked along the way without much overhead: Rule 2 (Overload).

The knowledge deduced in Lemma 1 is used in the following theorem to prove that the non-decreasing ordering of the tasks with respect to their duration/priority quotients results in a minimal sum of accumulated durations: Theorem 1. Let a PTSP(T ) be given. Further, it is assumed that the tasks in T = {t1 , . . , tn } are ordered such that di dj ≤ holds for 1 ≤ i < j ≤ n. αi αj Then, for an arbitrary permutation σ : {0, 1, . . , n} → {0, 1, . . , n} with σ(0) = 0 it holds n i−1 i=1 n dj ≤ αi · j=0 i−1 ασ(i) · i=1 dσ(j) , j=0 where d0 = min(S1 ∪ .

N} \ {k, k + 1} and θ(k) = σ(k + 1) as well as θ(k + 1) = σ(k). 28 A. Wolf and G. Schrader Proof. It holds that n i−1 αθ(i) · i=1 k−1 j=0 i−1 ασ(i) · dθ(j) = i=1 k−1 dσ(j) + ασ(k+1) · dσ(j) j=0 j=0 k−1 + ασ(k) · n j=0 k−1 i−1 i=1 dσ(j) j=0 i=k+2 ασ(i) · = i−1 ασ(i) · dσ(j) + dσ(k+1) + k dσ(j) + ασ(k+1) · dσ(j) j=0 j=0 + ασ(k) · dσ(k+1) − ασ(k+1) · dσ(k) k−1 + ασ(k) · n j=0 dσ(j) j=0 i=k+2 i−1 n ασ(i) · = i−1 ασ(i) · dσ(j) + i=1 dσ(j) + ασ(k) · dσ(k+1) − ασ(k+1) · dσ(k) j=0 Further, with σ(k + 1) < σ(k) it also holds that ασ(k) · dσ(k+1) ≤ ασ(k+1) · dσ(k) .

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