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done quite a bit of work on approximate closest pairs in spaces that are not low-dimensional Euclidean. You might try looking up some of his research. —David...

"in these models, the closest pair of points problem requires Ω(n log n) time, but the closest pair is necessarily an edge of the EMST, so the EMST also...

is slightly less than one. With this choice of edge length the closest pair of points in different hexagons with the same color is greater than 1. Maybe...

Wikipedia page for the Closest Pair of Points problem). At the very least, Quicksort comes earlier (1961). As I see it, the current form of the page is clearly...

"minimal" pair, we can construct another point-line pair that determines a closer distance. This contradicts our assumption that we had the "closest" pair. Therefore...

your organization of the article there's a problem with the subsection "Pairs of solutions". To understand why solutions are paired, the reader needs...

coloring of any subset of a given set of points, the bichromatic closest pair produces one edge of the minimum spanning tree" Clarify that it's the MST of the...

the candidate who is "closest to winning every match" (different methods define "closest" differently). Includes Ranked pairs, Schulze's method, Minimax...

algorithm for creating a Voronoi diagram would seem to be, for each pair of points, to draw a line between them, and then to draw a boundary perpendicular...

Ok, the main problem I see is with the invalid grouping of outcomes, which causes the number of possibilities to be reduced. The following 2 are syntactically...

.. "Traditionally, precision has been paired with recall to overcome such length-related problems." -- All of the papers are online, so you can look...

Vd1=Ve2 as the tangents are equal at each pair of points. The second half is analogous to saying that in a congruence of concentric circles in E2, if we consider...

mentioned". Perhaps you could pair together the first mention and the promotion to collegiate status. Y I think I paired them like that because I was mentioning...

Richard you have changed the problem statement in the lead to: Of two indistinguishable envelopes, each containing money, one contains twice as much as...

applications of dynamic closest pairs" first, but others that are maybe more specific to this method include El Krari et al "An Empirical Study of the Multi-fragment...

given a "certain" pair of doors. He cannot escape: A "certain" pair of doors is given to the host. And in each and every "pair of doors" there necessarily...

the pair of power ballads turn the tempo into moderate pace." What is this trying to say? Six of the tracks are performed at fast tempos, while two of them...

goats). So the problem is already solved, chances and risks are well known, regardless whether you can see one goat within this pair of doors or you still...

incorrect though. The "distribution of the pairs of numbers that might be in the envelopes" is nowhere mentioned in the problem and is irrelevant anyway. It...

second closest pair of first magnitude stars as seen from the Earth, and due to the effects of proper motion, they will become the closest pair around...