| dbo:abstract
|
- In computational geometry, a maximum disjoint set (MDS) is a largest set of non-overlapping geometric shapes selected from a given set of candidate shapes. Every set of non-overlapping shapes is an independent set in the intersection graph of the shapes. Therefore, the MDS problem is a special case of the maximum independent set (MIS) problem. Both problems are NP complete, but finding a MDS may be easier than finding a MIS in two respects:
* For the general MIS problem, the best known exact algorithms are exponential. In some geometric intersection graphs, there are sub-exponential algorithms for finding a MDS.
* The general MIS problem is hard to approximate and doesn't even have a constant-factor approximation. In some geometric intersection graphs, there are polynomial-time approximation schemes (PTAS) for finding a MDS. Finding an MDS is important in applications such as automatic label placement, VLSI circuit design, and cellular frequency division multiplexing. The MDS problem can be generalized by assigning a different weight to each shape and searching for a disjoint set with a maximum total weight. In the following text, MDS(C) denotes the maximum disjoint set in a set C. (en)
|
| dbo:thumbnail
| |
| dbo:wikiPageExternalLink
| |
| dbo:wikiPageID
| |
| dbo:wikiPageLength
|
- 31582 (xsd:nonNegativeInteger)
|
| dbo:wikiPageRevisionID
| |
| dbo:wikiPageWikiLink
| |
| dbp:wikiPageUsesTemplate
| |
| dcterms:subject
| |
| gold:hypernym
| |
| rdfs:comment
|
- In computational geometry, a maximum disjoint set (MDS) is a largest set of non-overlapping geometric shapes selected from a given set of candidate shapes. Every set of non-overlapping shapes is an independent set in the intersection graph of the shapes. Therefore, the MDS problem is a special case of the maximum independent set (MIS) problem. Both problems are NP complete, but finding a MDS may be easier than finding a MIS in two respects: Finding an MDS is important in applications such as automatic label placement, VLSI circuit design, and cellular frequency division multiplexing. (en)
|
| rdfs:label
|
- Maximum disjoint set (en)
|
| owl:sameAs
| |
| prov:wasDerivedFrom
| |
| foaf:depiction
| |
| foaf:isPrimaryTopicOf
| |
| is dbo:wikiPageRedirects
of | |
| is dbo:wikiPageWikiLink
of | |
| is foaf:primaryTopic
of | |
