On linear area embedding of planar graphs:
Planar embedding with minimal area of graphs on an integer grid is one of the major issues in VLSI. Valiant (V) gave an algorithm to construct a planar embedding for trees in linear area; he also proved that there are planar graphs that require quadratic area. We give an algorithm to embed outerplan...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Stanford, Calif.
1981
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| Schriftenreihe: | Stanford University / Computer Science Department: Report STAN-CS
876 |
| Schlagworte: | |
| Zusammenfassung: | Planar embedding with minimal area of graphs on an integer grid is one of the major issues in VLSI. Valiant (V) gave an algorithm to construct a planar embedding for trees in linear area; he also proved that there are planar graphs that require quadratic area. We give an algorithm to embed outerplanar graphs in linear area. We extend this algorithm to work for every planar graph that has the following property: for every vertex there exists a path of length less than K to the exterior face, where K is a constant. Finally, finding a minimal embedding area is shown to be NP-complete for forests, and hence more general types of graphs. (Author). |
| Beschreibung: | 21 S. |
Internformat
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| 100 | 1 | |a Dolev, Danny |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a On linear area embedding of planar graphs |c Danny Dolev ; Howard Trickey* |
| 264 | 1 | |a Stanford, Calif. |c 1981 | |
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| 490 | 1 | |a Stanford University / Computer Science Department: Report STAN-CS |v 876 | |
| 520 | 3 | |a Planar embedding with minimal area of graphs on an integer grid is one of the major issues in VLSI. Valiant (V) gave an algorithm to construct a planar embedding for trees in linear area; he also proved that there are planar graphs that require quadratic area. We give an algorithm to embed outerplanar graphs in linear area. We extend this algorithm to work for every planar graph that has the following property: for every vertex there exists a path of length less than K to the exterior face, where K is a constant. Finally, finding a minimal embedding area is shown to be NP-complete for forests, and hence more general types of graphs. (Author). | |
| 650 | 4 | |a Trees(Mathematics) | |
| 650 | 4 | |a VLSI(Very Large Scale Integration) | |
| 650 | 7 | |a Algorithms |2 dtict | |
| 650 | 7 | |a Electrical and Electronic Equipment |2 scgdst | |
| 650 | 7 | |a Embedding |2 dtict | |
| 650 | 7 | |a Graphs |2 dtict | |
| 650 | 7 | |a Grids(coordinates) |2 dtict | |
| 650 | 7 | |a Integrated circuits |2 dtict | |
| 650 | 7 | |a Linear systems |2 dtict | |
| 650 | 7 | |a Microelectronics |2 dtict | |
| 650 | 7 | |a Planar structures |2 dtict | |
| 650 | 7 | |a Theorems |2 dtict | |
| 650 | 7 | |a Theoretical Mathematics |2 scgdst | |
| 700 | 1 | |a Trickey, Howard |e Verfasser |4 aut | |
| 810 | 2 | |a Computer Science Department: Report STAN-CS |t Stanford University |v 876 |w (DE-604)BV008928280 |9 876 | |
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| id | DE-604.BV009075626 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:30:35Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006012967 |
| oclc_num | 227518863 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | 21 S. |
| publishDate | 1981 |
| publishDateSearch | 1981 |
| publishDateSort | 1981 |
| record_format | marc |
| series2 | Stanford University / Computer Science Department: Report STAN-CS |
| spelling | Dolev, Danny Verfasser aut On linear area embedding of planar graphs Danny Dolev ; Howard Trickey* Stanford, Calif. 1981 21 S. txt rdacontent n rdamedia nc rdacarrier Stanford University / Computer Science Department: Report STAN-CS 876 Planar embedding with minimal area of graphs on an integer grid is one of the major issues in VLSI. Valiant (V) gave an algorithm to construct a planar embedding for trees in linear area; he also proved that there are planar graphs that require quadratic area. We give an algorithm to embed outerplanar graphs in linear area. We extend this algorithm to work for every planar graph that has the following property: for every vertex there exists a path of length less than K to the exterior face, where K is a constant. Finally, finding a minimal embedding area is shown to be NP-complete for forests, and hence more general types of graphs. (Author). Trees(Mathematics) VLSI(Very Large Scale Integration) Algorithms dtict Electrical and Electronic Equipment scgdst Embedding dtict Graphs dtict Grids(coordinates) dtict Integrated circuits dtict Linear systems dtict Microelectronics dtict Planar structures dtict Theorems dtict Theoretical Mathematics scgdst Trickey, Howard Verfasser aut Computer Science Department: Report STAN-CS Stanford University 876 (DE-604)BV008928280 876 |
| spellingShingle | Dolev, Danny Trickey, Howard On linear area embedding of planar graphs Trees(Mathematics) VLSI(Very Large Scale Integration) Algorithms dtict Electrical and Electronic Equipment scgdst Embedding dtict Graphs dtict Grids(coordinates) dtict Integrated circuits dtict Linear systems dtict Microelectronics dtict Planar structures dtict Theorems dtict Theoretical Mathematics scgdst |
| title | On linear area embedding of planar graphs |
| title_auth | On linear area embedding of planar graphs |
| title_exact_search | On linear area embedding of planar graphs |
| title_full | On linear area embedding of planar graphs Danny Dolev ; Howard Trickey* |
| title_fullStr | On linear area embedding of planar graphs Danny Dolev ; Howard Trickey* |
| title_full_unstemmed | On linear area embedding of planar graphs Danny Dolev ; Howard Trickey* |
| title_short | On linear area embedding of planar graphs |
| title_sort | on linear area embedding of planar graphs |
| topic | Trees(Mathematics) VLSI(Very Large Scale Integration) Algorithms dtict Electrical and Electronic Equipment scgdst Embedding dtict Graphs dtict Grids(coordinates) dtict Integrated circuits dtict Linear systems dtict Microelectronics dtict Planar structures dtict Theorems dtict Theoretical Mathematics scgdst |
| topic_facet | Trees(Mathematics) VLSI(Very Large Scale Integration) Algorithms Electrical and Electronic Equipment Embedding Graphs Grids(coordinates) Integrated circuits Linear systems Microelectronics Planar structures Theorems Theoretical Mathematics |
| volume_link | (DE-604)BV008928280 |
| work_keys_str_mv | AT dolevdanny onlinearareaembeddingofplanargraphs AT trickeyhoward onlinearareaembeddingofplanargraphs |