I solved this problem( 0.015 sec) but My algo is heuristic.
Why this problem is geometric? Or how can we use geometry in this task to reduce the search?

I think there might be as well a mistake in tags.
To me, this problem reminds of http://acm.timus.ru/problem.aspx?space=1&num=1326 with minor differences:
1) cities = bottle taps
2) N <= 30 instead of N <= 20;
3) city's "group" is a list of cities hit when bombing this one.