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    <p>This is too long for a comment but here's just an idea as to how I'd "play" with this and see if I can come up with something interesting. But one thing is sure: the following can be made to be <em>very</em> fast.</p> <p>Can this be easily translated to some discrete problem? You'd first "align" all your coordinates to a big map (you define how much each square is big and you make every entry map to one such point). You'd then end up with something like this:</p> <pre><code>0000000000000000000000000000 00XX000000000000000000X00000 00X00000000000000X0000000000 0000000000000000000000000000 0000000000000000000000000000 000000X00000000X000000000000 0000000000000000000000000000 000000000000X000000000X00000 00000000000000000000000X0000 0000000000000000000000000000 </code></pre> <p>Then you'd compute each entry and it's number of adjacent neighbours:</p> <pre><code>0000000000000000000000000000 0033000000000000000001000000 0030000000000000010000000000 0000000000000000000000000000 0000000000000000000000000000 0000001000001001000000000000 0000000000000000000000000000 0000000000001010000000200000 0000000000000000000000020000 0000000000000100000000000000 </code></pre> <p>Then you can augment the size of your square, say by two, and hence divide your map:</p> <p>(the map ain't correct, it's jut to give an idea of what I'm thinking about)</p> <pre><code>09001001000000 00000000000000 00100001100000 00000110002000 00000002000000 00000100000000 </code></pre> <p>Then you re-count the adjacent neighbours, etc.</p> <p>To me this would allow to find hotspot depending on your "resolution": you'd simply look for the biggest numbers and that would be your "hotspots".</p> <p>Because in this case:</p> <pre><code>0000X00000 0000XX0000 0000000000 0000000000 0Y0Y000000 0000000000 0Y0Y000000 </code></pre> <p>Either 'X' can be the hottest spot (three interesting point close to each other) or 'Y' (four points close to each other, but they're not as close than for the 'X').</p> <p>Because you said you needed speed, I'd just turn this into a discrete problem and represent my graphs as arrays. I'd then allow for a variable "area" size. </p> <p>Looks like a fun problem to work on :)</p>
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    1. POEfficient algorithm for calculating areas on geographical map with the highest density of spots
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    1. CONice idea for starting, one addition to this - a "point" in your representation could include multiple entries, so it needs to consider this. Replace the 'X's with the number of entries in that coordinate, then refine the calculation.
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