By Karsten Weihe (auth.), Stefan Näher, Dorothea Wagner (eds.)

This quantity includes the papers accredited for the 4th Workshop on set of rules Engineering (WAE 2000) held in Saarbruc ¨ ken, Germany, in the course of 5–8 September 2000, including the summary of the invited lecture given via Karsten Weihe. The Workshop on set of rules Engineering covers study on all facets of the topic. The aim is to give fresh learn effects and to spot and discover instructions for destiny examine. earlier conferences have been held in Venice (1997), Saarbruc ¨ ken (1998), and London (1999). Papers have been solicited describing unique study in all features of set of rules engineering, together with: – improvement of software program repositories and systems which enable using and experimentation with e?cient discrete algorithms. – Novel makes use of of discrete algorithms in different disciplines and the review of algorithms for reasonable environments. – Methodological matters together with criteria within the context of empirical - seek on algorithms and knowledge constructions. – Methodological concerns concerning the means of changing person requisites into e?cient algorithmic recommendations and implementations. this system committee approved sixteen from a complete of 30 submissions. this system committee assembly used to be performed electronically. the factors for sel- tion have been originality, caliber, and relevance to the topic quarter of the workshop. substantial e?ort was once dedicated to the review of the submissions and to p- viding the authors with suggestions. each one submission used to be reviewed via a minimum of 4 software committee contributors (assisted via subreferees). a different factor of the ACM magazine of Experimental Algorithmics could be dedicated to chosen papers from WAE 2000.

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**Extra info for Algorithm Engineering: 4th International Workshop, WAE 2000 Saarbrücken, Germany, September 5–8, 2000 Proceedings**

**Example text**

Delaunay graphs are known to contain perfect matchings [7]. For the random instances we chose random graphs with n vertices. The number of edges for sparse graphs was chosen as m = αn for small values of α, α ≤ 10. For dense graphs the density is approximately 20%, 40% and 60% of the density of a complete graph. Random weights out of the range [1, . . , 216 ) were assigned to the edges. We checked for perfect matchings with the LEDA cardinality matching implementation. Complete geometric instances were induced by n random points in an n × n square and their Euclidean distances.

Since we enforce case b) or c) for each MergeForest operation, we have the following result. Theorem 3. Let k = log n . EXTERNAL-WEAK-HEAPSORT is an incrementally external sorting algorithm with nk − 2k + 1 comparisons in the best-, worst-, and average case. The number of transposition is bounded by nk − 2k + 1 and the number of assginments is n. 44 Stefan Edelkamp and Patrick Stiegeler PROCEDURE MergeForest(m) x := 1 WHILE (2x + Reverse[x] < m) x := 2x + Reverse[x] IF (Active[x] = 0) x := x DIV 2 IF (depth(x) = depth(m)) temp := x; x := x DIV 2 ELSE temp := m WHILE (x > 0) Merge(temp, x); x := x DIV 2 a[2n - call] := a[temp] Active[temp] := 0 PROCEDURE EXTERNAL-WEAK-HEAPSORT WeakHeapify a[2n-1] := a[0] i := n-1 call := 1 WHILE (i > 1) WHILE (Active[i] = 0 AND i > 1) i := i - 1 call := call + 1 MergeForest(i) Fig.

We ran our algorithm with the greedy heuristic (MST+ ) as well as with the fractional matching heuristic (MST∗ ). The results are given in Tab. 10. Table 10. B4∗ , B4∗var vs. edg instance. 35) The second row states the times that were needed by the heuristics. Observe that both Blossom IV algorithms need more than two days to compute an optimal matching, whereas our algorithm solves the same instance in less than an hour. For our MST algorithm the fractional matching heuristic did not help at all on this instance: to compute a fractional matching took almost as long as computing an optimum matching for the original graph (using the greedy heuristic).