3 ms·
Planarity - a game with planar graphs
- jurjenhaitsma 18y agoThis is pretty choice - reminds me of untangling a circuit layout... Never really looked into it that much, but I'd imagine there must be a mathematical technique that can be applied. My first instinct has always been to put the point with the most connections in the centre, then map out from that.
- eru 18y agoGood luck. The problem may be NP complete in general.
- shrughes 18y agoWell, for the cases on planarity.net, it seems O(n) to me. Or maybe something like O(n log n)
- gjm11 18y agoIt's O(n) in the general case, so certainly also for the special cases on planarity.net.
- eru 18y agoCould you give me a source or the name of the algorithm, that allows this running time?
- eru 18y agoP.S. I found a O(n) running time for planarity testing - but not embedding.
- gjm11 18y agoThe Wikipedia article on planarity testing cites, for instance, this paper: http://jgaa.info/accepted/2004/BoyerMyrvold2004.8.3.pdf http://jgaa.info/accepted/2004/BoyerMyrvold2004.8.3.pdf which describes a not-insanely-complicated algorithm that constructs planar embeddings (or proves they don't exist) in linear time.
- deleted 18y ago[deleted]
- boblol123 18y agoTake the vertex whose vertices cross the biggest number of other vertices and move it. Repeat until nothing crosses. I remember this problem in maths ages ago, there is a way to know if you can't untangle something- look up the water gas electricity problem
- gjm11 18y agoA graph is nonplanar if and only if it has a subgraph that looks like either (1) five vertices all connected to one another or (2) two sets of three vertices, with every vertex in one set connected to every vertex in the other. "Looks like" means: can be turned into by repeatedly replacing -o- (a vertex with two edges coming out of it) with -- (a single edge between the vertex's two old neighbours). See http://en.wikipedia.org/wiki/Planar_graph http://en.wikipedia.org/wiki/Planar_graph for details.
- barrettcolin 18y agoSpooky: there is an almost identical iPhone game called 'The Plateau'. Screens here: http://www.tuaw.com/photos/the-plateau/1270610/ http://www.tuaw.com/photos/the-plateau/1270610/
- smanek 18y agoI remember playing playing Planarity well before the iPhone came out, so 'The Plateau' is just a copy. In fact, the "Way Back Machine" shows Planarity, basically unchanged, in 2005: http://web.archive.org/web/20050731231914/http://www.planarity.net/ http://web.archive.org/web/20050731231914/http://www.planari...
- derwiki 18y agoI think this game won John "One of the Most Interesting People In Cleveland" when he wrote this sophomore year at CWRU. I'm happy to see that his project is still being enjoyed!
- gord 18y agoHighly addictive... Got to 1500 odd, had a sneak peak at level 30 then gracefully bowed out. Used a combination of heuristics - move a vertex to the centroid of its neighbors, and move randomly to reduce edge intersections. eyes burning.
- madair 18y agoIt would be interesting to couple this game with user profiles that include questions related to mysteries and observations in cognitive science. Thinks like left/right handed, formal education, would be interesting too.