Packing Steiner trees: separation algorithms
Abstract: "In this paper we investigate separation problems for classes of inequalities valid for the polytope associated with the Steiner tree packing problem, a problem that arises, e.g., in VLSI routing. The separation problem for Steiner partition inequalities is NP-hard in general. We show...
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Hauptverfasser: | , , |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Berlin
Konrad-Zuse-Zentrum für Informationstechnik
1993
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Schriftenreihe: | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC
1993,2 |
Schlagworte: | |
Zusammenfassung: | Abstract: "In this paper we investigate separation problems for classes of inequalities valid for the polytope associated with the Steiner tree packing problem, a problem that arises, e.g., in VLSI routing. The separation problem for Steiner partition inequalities is NP-hard in general. We show that it can be solved in polynomial time for those instances that come up in switchbox routing. Our algorithm uses dynamic programming techniques. These techniques are also applied to the much more complicated separation problem for alternating cycle inequalities. In this case we can compute in polynomial time, given some point y, a lower bound for the gap [alpha] - a[superscript T]y over all alternating cycle inequalities a[superscript T]x [> or =] [alpha]. This gives rise to a very effective separation heuristic. A by-product of our algorithm is the solution of a combinatorial optimization problem that is interesting in its own right: Find a shortest path in a graph where the 'length' of a path is its usual length minus the length of its longest edge." |
Beschreibung: | 31 S. graph. Darst. |
Internformat
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100 | 1 | |a Grötschel, Martin |d 1948- |e Verfasser |0 (DE-588)108975282 |4 aut | |
245 | 1 | 0 | |a Packing Steiner trees |b separation algorithms |c Martin Grötschel ; Alexander Martin ; Robert Weismantel |
264 | 1 | |a Berlin |b Konrad-Zuse-Zentrum für Informationstechnik |c 1993 | |
300 | |a 31 S. |b graph. Darst. | ||
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490 | 1 | |a Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |v 1993,2 | |
520 | 3 | |a Abstract: "In this paper we investigate separation problems for classes of inequalities valid for the polytope associated with the Steiner tree packing problem, a problem that arises, e.g., in VLSI routing. The separation problem for Steiner partition inequalities is NP-hard in general. We show that it can be solved in polynomial time for those instances that come up in switchbox routing. Our algorithm uses dynamic programming techniques. These techniques are also applied to the much more complicated separation problem for alternating cycle inequalities. In this case we can compute in polynomial time, given some point y, a lower bound for the gap [alpha] - a[superscript T]y over all alternating cycle inequalities a[superscript T]x [> or =] [alpha]. This gives rise to a very effective separation heuristic. A by-product of our algorithm is the solution of a combinatorial optimization problem that is interesting in its own right: Find a shortest path in a graph where the 'length' of a path is its usual length minus the length of its longest edge." | |
650 | 4 | |a Trees (Graph theory) | |
700 | 1 | |a Martin, Alexander |d 1965- |e Verfasser |0 (DE-588)1013264479 |4 aut | |
700 | 1 | |a Weismantel, Robert |e Verfasser |4 aut | |
830 | 0 | |a Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |v 1993,2 |w (DE-604)BV004801715 |9 1993,2 | |
999 | |a oai:aleph.bib-bvb.de:BVB01-006040735 |
Datensatz im Suchindex
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author | Grötschel, Martin 1948- Martin, Alexander 1965- Weismantel, Robert |
author_GND | (DE-588)108975282 (DE-588)1013264479 |
author_facet | Grötschel, Martin 1948- Martin, Alexander 1965- Weismantel, Robert |
author_role | aut aut aut |
author_sort | Grötschel, Martin 1948- |
author_variant | m g mg a m am r w rw |
building | Verbundindex |
bvnumber | BV009110830 |
ctrlnum | (OCoLC)32525478 (DE-599)BVBBV009110830 |
format | Book |
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id | DE-604.BV009110830 |
illustrated | Illustrated |
indexdate | 2024-07-09T17:31:11Z |
institution | BVB |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006040735 |
oclc_num | 32525478 |
open_access_boolean | |
owner | DE-12 |
owner_facet | DE-12 |
physical | 31 S. graph. Darst. |
publishDate | 1993 |
publishDateSearch | 1993 |
publishDateSort | 1993 |
publisher | Konrad-Zuse-Zentrum für Informationstechnik |
record_format | marc |
series | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |
series2 | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |
spelling | Grötschel, Martin 1948- Verfasser (DE-588)108975282 aut Packing Steiner trees separation algorithms Martin Grötschel ; Alexander Martin ; Robert Weismantel Berlin Konrad-Zuse-Zentrum für Informationstechnik 1993 31 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC 1993,2 Abstract: "In this paper we investigate separation problems for classes of inequalities valid for the polytope associated with the Steiner tree packing problem, a problem that arises, e.g., in VLSI routing. The separation problem for Steiner partition inequalities is NP-hard in general. We show that it can be solved in polynomial time for those instances that come up in switchbox routing. Our algorithm uses dynamic programming techniques. These techniques are also applied to the much more complicated separation problem for alternating cycle inequalities. In this case we can compute in polynomial time, given some point y, a lower bound for the gap [alpha] - a[superscript T]y over all alternating cycle inequalities a[superscript T]x [> or =] [alpha]. This gives rise to a very effective separation heuristic. A by-product of our algorithm is the solution of a combinatorial optimization problem that is interesting in its own right: Find a shortest path in a graph where the 'length' of a path is its usual length minus the length of its longest edge." Trees (Graph theory) Martin, Alexander 1965- Verfasser (DE-588)1013264479 aut Weismantel, Robert Verfasser aut Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC 1993,2 (DE-604)BV004801715 1993,2 |
spellingShingle | Grötschel, Martin 1948- Martin, Alexander 1965- Weismantel, Robert Packing Steiner trees separation algorithms Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC Trees (Graph theory) |
title | Packing Steiner trees separation algorithms |
title_auth | Packing Steiner trees separation algorithms |
title_exact_search | Packing Steiner trees separation algorithms |
title_full | Packing Steiner trees separation algorithms Martin Grötschel ; Alexander Martin ; Robert Weismantel |
title_fullStr | Packing Steiner trees separation algorithms Martin Grötschel ; Alexander Martin ; Robert Weismantel |
title_full_unstemmed | Packing Steiner trees separation algorithms Martin Grötschel ; Alexander Martin ; Robert Weismantel |
title_short | Packing Steiner trees |
title_sort | packing steiner trees separation algorithms |
title_sub | separation algorithms |
topic | Trees (Graph theory) |
topic_facet | Trees (Graph theory) |
volume_link | (DE-604)BV004801715 |
work_keys_str_mv | AT grotschelmartin packingsteinertreesseparationalgorithms AT martinalexander packingsteinertreesseparationalgorithms AT weismantelrobert packingsteinertreesseparationalgorithms |