Planar embedding of planar graphs:
Planar embedding with minimal area of graphs on an integer grid is an interesting problem in VLSI (Very Large Scale Integrated) theory. Valiant gave an algorithm to construct a planar embeddding for trees in linear area; he also proved that there are planar graphs that require quadratic area. We fil...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, Mass.
Lab. for Computer Science, Massachusetts Inst. of Technology
1983
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| Schlagworte: | |
| Zusammenfassung: | Planar embedding with minimal area of graphs on an integer grid is an interesting problem in VLSI (Very Large Scale Integrated) theory. Valiant gave an algorithm to construct a planar embeddding for trees in linear area; he also proved that there are planar graphs that require quadratic area. We fill in a spectrum between Valiant's results by showing that an N-node planar graphs has a planar embedding with area 0(NF), where F is a bound on the path length from any node to the exterior face. In particular, an outerplanar graph can be embedded without crossovers in linear area. This bound is tight, up to constant factors: for any N and F, there exist graphs requiring omega(NF) area for planar embedding. Also, finding a minimal embedding area is shown to be Nu-complete for forests, and hence for more general types of graphs. (author). |
| Beschreibung: | 8 S. |
Internformat
MARC
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| 100 | 1 | |a Dolev, Danny |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Planar embedding of planar graphs |c Danny Dolev ; Frank Thomson Leighton ; Howard Trickey |
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| 520 | 3 | |a Planar embedding with minimal area of graphs on an integer grid is an interesting problem in VLSI (Very Large Scale Integrated) theory. Valiant gave an algorithm to construct a planar embeddding for trees in linear area; he also proved that there are planar graphs that require quadratic area. We fill in a spectrum between Valiant's results by showing that an N-node planar graphs has a planar embedding with area 0(NF), where F is a bound on the path length from any node to the exterior face. In particular, an outerplanar graph can be embedded without crossovers in linear area. This bound is tight, up to constant factors: for any N and F, there exist graphs requiring omega(NF) area for planar embedding. Also, finding a minimal embedding area is shown to be Nu-complete for forests, and hence for more general types of graphs. (author). | |
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Datensatz im Suchindex
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| id | DE-604.BV021875881 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:03:35Z |
| indexdate | 2024-07-09T20:46:30Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015091524 |
| oclc_num | 227593154 |
| open_access_boolean | |
| owner | DE-706 |
| owner_facet | DE-706 |
| physical | 8 S. |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Lab. for Computer Science, Massachusetts Inst. of Technology |
| record_format | marc |
| spelling | Dolev, Danny Verfasser aut Planar embedding of planar graphs Danny Dolev ; Frank Thomson Leighton ; Howard Trickey Cambridge, Mass. Lab. for Computer Science, Massachusetts Inst. of Technology 1983 8 S. txt rdacontent n rdamedia nc rdacarrier Planar embedding with minimal area of graphs on an integer grid is an interesting problem in VLSI (Very Large Scale Integrated) theory. Valiant gave an algorithm to construct a planar embeddding for trees in linear area; he also proved that there are planar graphs that require quadratic area. We fill in a spectrum between Valiant's results by showing that an N-node planar graphs has a planar embedding with area 0(NF), where F is a bound on the path length from any node to the exterior face. In particular, an outerplanar graph can be embedded without crossovers in linear area. This bound is tight, up to constant factors: for any N and F, there exist graphs requiring omega(NF) area for planar embedding. Also, finding a minimal embedding area is shown to be Nu-complete for forests, and hence for more general types of graphs. (author). Algorithms dtict Computer graphics dtict Control theory dtict Graphs dtict Planar structures dtict Problem solving dtict Theorems dtict Theoretical Mathematics scgdst Graph (DE-588)4021842-9 gnd rswk-swf Einbettung Mathematik (DE-588)4151233-9 gnd rswk-swf Internetworking (DE-588)4225115-1 gnd rswk-swf Graph (DE-588)4021842-9 s DE-604 Einbettung Mathematik (DE-588)4151233-9 s Internetworking (DE-588)4225115-1 s Leighton, Frank T. Verfasser aut Trickey, Howard Verfasser aut |
| spellingShingle | Dolev, Danny Leighton, Frank T. Trickey, Howard Planar embedding of planar graphs Algorithms dtict Computer graphics dtict Control theory dtict Graphs dtict Planar structures dtict Problem solving dtict Theorems dtict Theoretical Mathematics scgdst Graph (DE-588)4021842-9 gnd Einbettung Mathematik (DE-588)4151233-9 gnd Internetworking (DE-588)4225115-1 gnd |
| subject_GND | (DE-588)4021842-9 (DE-588)4151233-9 (DE-588)4225115-1 |
| title | Planar embedding of planar graphs |
| title_auth | Planar embedding of planar graphs |
| title_exact_search | Planar embedding of planar graphs |
| title_exact_search_txtP | Planar embedding of planar graphs |
| title_full | Planar embedding of planar graphs Danny Dolev ; Frank Thomson Leighton ; Howard Trickey |
| title_fullStr | Planar embedding of planar graphs Danny Dolev ; Frank Thomson Leighton ; Howard Trickey |
| title_full_unstemmed | Planar embedding of planar graphs Danny Dolev ; Frank Thomson Leighton ; Howard Trickey |
| title_short | Planar embedding of planar graphs |
| title_sort | planar embedding of planar graphs |
| topic | Algorithms dtict Computer graphics dtict Control theory dtict Graphs dtict Planar structures dtict Problem solving dtict Theorems dtict Theoretical Mathematics scgdst Graph (DE-588)4021842-9 gnd Einbettung Mathematik (DE-588)4151233-9 gnd Internetworking (DE-588)4225115-1 gnd |
| topic_facet | Algorithms Computer graphics Control theory Graphs Planar structures Problem solving Theorems Theoretical Mathematics Graph Einbettung Mathematik Internetworking |
| work_keys_str_mv | AT dolevdanny planarembeddingofplanargraphs AT leightonfrankt planarembeddingofplanargraphs AT trickeyhoward planarembeddingofplanargraphs |