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Algorithms for some graph theoretical optimization problems (abstract of thesis). (English) Zbl 1107.05085

Summary: This is a summary of the main results presented in the author’s PhD thesis. This thesis, written in English, was supervised by Frits Spieksma and defended on September 23, 2005 at the Katholieke Universiteit Leuven. A copy of the thesis is available from the authors website (http://www.econ.kuleuven.be/linda.moonen/public/).
The thesis can be roughly split into two parts. The first part is dedicated to the problem of partitioning partially ordered sets into chains of limited size. The second part deals with the structure and the connectivity of the internet.

MSC:

05C85 Graph algorithms (graph-theoretic aspects)
90C10 Integer programming
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
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References:

[1] Courcelle B, Engelfriet J, Rozenberg G (1993) Handle-rewriting hypergraph grammars. J Comput Syst Sci 46:218–270 · Zbl 0825.68446 · doi:10.1016/0022-0000(93)90004-G
[2] Dilworth RP (1950) A decomposition theorem for partially ordered sets. Ann Math 51:161–166 · Zbl 0038.02003 · doi:10.2307/1969503
[3] Moonen LS, Spieksma FCR (2006) Exact algorithms for a loading problem with bounded clique width. INFORMS J Comput (to appear) · Zbl 1241.90088
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