StackOverflow2013

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plurals

PO
primarykey
Id
5912696
data
AcceptedAnswerId
0
AnswerCount
0
ClosedDate
CommentCount
2
CommunityOwnedDate
CreationDate
2011-05-06T14:14:50.153
FavoriteCount
0
LastActivityDate
2011-05-06T14:26:59.960
LastEditDate
2011-05-06T14:26:59.960
LastEditorUserId
288875
OwnerUserId
288875
ParentId
5912253
PostTypeId
2
Score
1
ViewCount
0
LastEditorDisplayName
text
Body
If you think of a graph with club members as vertices and 'like' as edges (i.e. if two members do not hate each other there is an edge between the corresponding vertices), one can reformulate the problem as follows: <blockquote> find the maximum subset of vertices for which there is an edge between all vertices in the subset. </blockquote> In fact, a subset where all vertices have mutual edges is called a <a href="http://en.wikipedia.org/wiki/Clique_%28graph_theory%29" rel="nofollow">Clique</a> or complete subgraph. To find the maximum clique takes exponential time if one can not exploit further features of the graph (see <a href="http://en.wikipedia.org/wiki/Clique_problem#Finding_maximum_cliques_in_arbitrary_graphs" rel="nofollow">this link</a>). This article suggests the <a href="http://en.wikipedia.org/wiki/Bron%E2%80%93Kerbosch_algorithm" rel="nofollow">Bron–Kerbosch algorithm</a>. Drawing the members in the <code>(S,B)</code> plane, one can see that a 'like' edge corresponds to lines going out of a vertex in the direction between 12 and 3 o'clock and between 6 and 9 o'clock. It is easy to construct an example where such edges intersect, so it's unfortunately not a planar graph. And unfortunately, the 'like' relationship is not <a href="http://en.wikipedia.org/wiki/Transitive_relation" rel="nofollow">transitive</a>, i.e. if <code>A</code> likes <code>B</code> and <code>B</code> likes <code>C</code> this does not imply that <code>A</code> also likes <code>C</code> (again, this is easy to see in the <code>(S,B)</code> plane).
Tags
Title
singulars
PostAcceptedAnswerId
1. This table or related slice is empty.
PostParentId
1. POO(N*LogN) algorithm for the following problem
 singulars
 PostTypePostTypeId
 PTQuestion
PostTypePostTypeId
1. PTAnswer
UserLastEditorUserId
1. USAndre Holzner
UserOwnerUserId
1. USAndre Holzner
plurals
PostLinksPostIdRelatedPostId
1. This table or related slice is empty.
PostLinksRelatedPostIdPostId
1. This table or related slice is empty.
PostsAcceptedAnswerId
1. This table or related slice is empty.
PostsParentIdCreationDate
1. This table or related slice is empty.
VotesPostIdCreationDate
1. VO
 singulars
 PostPostId
 PO
 UserUserId
 This table or related slice is empty.
 VoteTypeVoteTypeId
 VTUpMod
CommentsPostId
1. CO*And unfortunately, the 'like' relationship is not transitive* if it was transitive relationship it would be possible to solve the problem in O(N*LogN) time (http://en.wikipedia.org/wiki/Longest_increasing_subsequence#Efficient_algorithms)
 singulars
 PostPostId
 PO
 UserUserId
 USTim
2. COLike is not transitive, but `respect` is.
 singulars
 PostPostId
 PO
 UserUserId
 UShugomg

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