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I have a point with spatial and temporal coordinates

x=(lonx,latx,timex)

and I would like to find the nearest neighbour (according to some metric) amongst these other points

y1 = c(lony1,laty1,timey1)
y2 = c(lony2,laty2,timey2)
...
yn = c(lonyn,latyn,timeyn)

Is there any nearest-neighbour algorithm that I can use?

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The solution is to calculate the time when you can reach your neighbour's place and compare that time with its time. The only parameter is the speed.

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Yes.

Any metric index will work if you provide the metric.

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