Packing Steiner trees: polyhedral investigations
Abstract: "Let G = (V, E) be a graph and T [subset] V be a node set. We call an edge set S a Steiner tree with respect to T if S connects all pairs of nodes in T. In this paper we address the following problem, which we call the weighted Steiner tree packing problem. Given a graph G = (V, E) wi...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Konrad-Zuse-Zentrum für Informationstechnik Berlin
1992
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| Schriftenreihe: | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC
1992,8 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "Let G = (V, E) be a graph and T [subset] V be a node set. We call an edge set S a Steiner tree with respect to T if S connects all pairs of nodes in T. In this paper we address the following problem, which we call the weighted Steiner tree packing problem. Given a graph G = (V, E) with edge weights w[subscript e], edge capacities c[subscript e], e [element of] E, and node sets Ts, ..., T[subscript N], find edge sets Ss, ..., S[subscript N] such that each S[subscript k] is a Steiner tree with respect to T[subscript k], at most c[subscript e] of these edge sets use edge e for each e [element of] E, and such that the sum of the weights of the edge sets is minimal. Our motivation for studying this problem arises from the routing problem in VLSI-design, where given sets of points have to be connected by wires We consider the Steiner tree packing problem from a polyhedral point of view and define an appropriate polyhedron, called the Steiner tree packing polyhedron. The goal of this paper is to (partially) describe this polyhedron by means of inequalities. It turns out that, under mild assumptions, each inequality that defines a facet for the (single) Steiner tree polyhedron can be lifted to a facet-defining inequality for the Steiner tree packing polyhedron. The main emphasis of this paper lies on the presentation of so-called joint inequalities that are valid and facet- defining for this polyhedron. Inequalities of this kind involve at least two Steiner trees. The classes of inequalities we have found form the basis of a branch & cut algorithm. This algorithm is described in our companion paper [GMW92]. |
| Beschreibung: | 29 S. graph. Darst. |
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| 520 | 3 | |a Abstract: "Let G = (V, E) be a graph and T [subset] V be a node set. We call an edge set S a Steiner tree with respect to T if S connects all pairs of nodes in T. In this paper we address the following problem, which we call the weighted Steiner tree packing problem. Given a graph G = (V, E) with edge weights w[subscript e], edge capacities c[subscript e], e [element of] E, and node sets Ts, ..., T[subscript N], find edge sets Ss, ..., S[subscript N] such that each S[subscript k] is a Steiner tree with respect to T[subscript k], at most c[subscript e] of these edge sets use edge e for each e [element of] E, and such that the sum of the weights of the edge sets is minimal. Our motivation for studying this problem arises from the routing problem in VLSI-design, where given sets of points have to be connected by wires | |
| 520 | 3 | |a We consider the Steiner tree packing problem from a polyhedral point of view and define an appropriate polyhedron, called the Steiner tree packing polyhedron. The goal of this paper is to (partially) describe this polyhedron by means of inequalities. It turns out that, under mild assumptions, each inequality that defines a facet for the (single) Steiner tree polyhedron can be lifted to a facet-defining inequality for the Steiner tree packing polyhedron. The main emphasis of this paper lies on the presentation of so-called joint inequalities that are valid and facet- defining for this polyhedron. Inequalities of this kind involve at least two Steiner trees. The classes of inequalities we have found form the basis of a branch & cut algorithm. This algorithm is described in our companion paper [GMW92]. | |
| 650 | 4 | |a Steiner systems | |
| 700 | 1 | |a Martin, Alexander |d 1965- |e Verfasser |0 (DE-588)1013264479 |4 aut | |
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| id | DE-604.BV006644650 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:49:46Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004247106 |
| oclc_num | 31508812 |
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| physical | 29 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Konrad-Zuse-Zentrum für Informationstechnik Berlin |
| 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 polyhedral investigations M. Grötschel ; A. Martin ; R. Weismantel Berlin Konrad-Zuse-Zentrum für Informationstechnik Berlin 1992 29 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC 1992,8 Abstract: "Let G = (V, E) be a graph and T [subset] V be a node set. We call an edge set S a Steiner tree with respect to T if S connects all pairs of nodes in T. In this paper we address the following problem, which we call the weighted Steiner tree packing problem. Given a graph G = (V, E) with edge weights w[subscript e], edge capacities c[subscript e], e [element of] E, and node sets Ts, ..., T[subscript N], find edge sets Ss, ..., S[subscript N] such that each S[subscript k] is a Steiner tree with respect to T[subscript k], at most c[subscript e] of these edge sets use edge e for each e [element of] E, and such that the sum of the weights of the edge sets is minimal. Our motivation for studying this problem arises from the routing problem in VLSI-design, where given sets of points have to be connected by wires We consider the Steiner tree packing problem from a polyhedral point of view and define an appropriate polyhedron, called the Steiner tree packing polyhedron. The goal of this paper is to (partially) describe this polyhedron by means of inequalities. It turns out that, under mild assumptions, each inequality that defines a facet for the (single) Steiner tree polyhedron can be lifted to a facet-defining inequality for the Steiner tree packing polyhedron. The main emphasis of this paper lies on the presentation of so-called joint inequalities that are valid and facet- defining for this polyhedron. Inequalities of this kind involve at least two Steiner trees. The classes of inequalities we have found form the basis of a branch & cut algorithm. This algorithm is described in our companion paper [GMW92]. Steiner systems Martin, Alexander 1965- Verfasser (DE-588)1013264479 aut Weismantel, Robert Verfasser aut Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC 1992,8 (DE-604)BV004801715 1992,8 |
| spellingShingle | Grötschel, Martin 1948- Martin, Alexander 1965- Weismantel, Robert Packing Steiner trees polyhedral investigations Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC Steiner systems |
| title | Packing Steiner trees polyhedral investigations |
| title_auth | Packing Steiner trees polyhedral investigations |
| title_exact_search | Packing Steiner trees polyhedral investigations |
| title_full | Packing Steiner trees polyhedral investigations M. Grötschel ; A. Martin ; R. Weismantel |
| title_fullStr | Packing Steiner trees polyhedral investigations M. Grötschel ; A. Martin ; R. Weismantel |
| title_full_unstemmed | Packing Steiner trees polyhedral investigations M. Grötschel ; A. Martin ; R. Weismantel |
| title_short | Packing Steiner trees |
| title_sort | packing steiner trees polyhedral investigations |
| title_sub | polyhedral investigations |
| topic | Steiner systems |
| topic_facet | Steiner systems |
| volume_link | (DE-604)BV004801715 |
| work_keys_str_mv | AT grotschelmartin packingsteinertreespolyhedralinvestigations AT martinalexander packingsteinertreespolyhedralinvestigations AT weismantelrobert packingsteinertreespolyhedralinvestigations |