Algorithm Theory - SWAT 2000: 7th Scandinavian Workshop on by Mikkel Thorup, David R. Karger (auth.)

By Mikkel Thorup, David R. Karger (auth.)

This booklet constitutes the refereed complaints of the seventh Scandinavian Workshop on set of rules thought, SWAT 2000, held in Bergen, Norway, in July 2000.
The forty three revised complete papers awarded including three invited contributions have been rigorously reviewed and chosen from a complete of a hundred and five submissions. The papers are geared up in sections on facts constructions, dynamic walls, graph algorithms, on-line algorithms, approximation algorithms, matchings, community layout, computational geometry, strings and set of rules engineering, exterior reminiscence algorithms, optimization, and dispensed and fault-tolerant computing.

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Papadimitriou. “The NP-completeness of the bandwidth minimization problem”. Computing 16 (1976), 263–270. 30. J. Saxe. “Dynamic programming algorithms for recognizing small-bandwidth graphs in polynomial time”. SIAM Journal on Algebraic Methods 1 (1980), 363– 369. 31. J. Turner. “On the probable performance of heuristics for bandwidth minimization”. SIAM J. , 15, (1986), 561–580. 32. W. Unger. “The complexity of the approximation of the bandwidth problem”. In Proc. 39th Annual IEEE Symposium on Foundations of Computer Science, 1998, 82–91.

Blum, J. Spencer. “Coloring Random and Semi-Random k-Colorable Graphs”. Journal of Algorithms 19, 204–234, 1995. 6. H. Bodlaender, M. Fellows, M. Hallet. “Beyond NP-completeness for problems of bounded width: hardness for the W Hierarchy”. Proc. of 26th STOC, 1994, 449– 458. 7. P. Chinn, J. Chvatalova, A. Dewdney, N. Gibbs. “The bandwidth problem for graphs and matrices – a survey”. Journal of Graph Theory, 6 (1982), 223–254. 8. F. Chung, P. Seymour. “Graphs with small bandwidth and cutwidth”. Discrete Mathematics 75 (1989) 113–119.

Let Ti (x) = maxij=1 tj (x). Furthermore, assuming x was inserted at time a and the maximum size of the heap from time a to b is n, Tb (x) ≤ min(b − a, n). The value of Ti (x) is nondecreasing in i. We use ni to denote the current number of nodes in the heap and ηi to denote the maximum value of Tj (x) among all nodes x, among all times j up to the and including i. Note that ηi is also equal to the maximum size the of the heap up to and including time i. In this section the standard tree terminology refers exclusively to the binary representation.

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