[-] Question 4
by dekelr - Monday, 27 April 2009 13:30:48
Just to make sure I understand the definitions -
If X = {0, 2, 5, 10, 12},
a minimal coverage will be: [0,5], [10,12]?
[-] Re: Question 4
by kantora - Monday, 27 April 2009 18:17:33
NO!!! the size of an interval is 1 and not 5 or 2 like in your example
in this example a possible minimal coverage will be
[-0.5 , 0.5] , [1.7 , 2.7] , [4.3 , 5.3] , [9.9 , 10.9] , [11 , 12]
[-] Re: Question 4
by eladbend - Tuesday, 28 April 2009 09:37:18
הקבוצה הנתונה
X
נתונה ממויינת מראש ?
Re: Question 4
by kantora - Tuesday, 28 April 2009 15:11:50
Yes
[-] Re: Question 4
by eial - Friday, 1 May 2009 12:18:38
is it possible that the coverage I'll take will match the number? for example if I have the number 3 in the set, then can I take the cover [2,3]?
if the answer to the question is no, what is the maximal digits after the dot that we must take in account?

edit: by minimal, do you mean that the number of groups will be minimal? e.g. for the given example in the beginning of the post, the answer is 5?
Re: Question 4
by kantora - Sunday, 3 May 2009 16:33:11
Yes, it is possible
[-] Re: Question 4
by guyrap - Saturday, 2 May 2009 14:48:09

Can the unit-intervals exceed the largest point in X, i.e. if Xn = 9.5, can [9.5 - 10.5] be included in the solution?

Can the unit-intervals overlap each other? i.e. if 0.5, 1 and 1.6 are my points, can [0.5-1.5], [0.6-1.6] be a legal solution?

Minimal - in terms of area covered, or in terms of units used? i.e. if 1 and 2.1 are my points, [1..2] and [1.1 .. 2.1] cover both points with minimal area covered (since they overlap), and [0..1], [1.1..2.1] also cover both points but more than the minimal possible area.

Re: Question 4
by ivryg - Saturday, 2 May 2009 17:16:57

The way I see it, the last unit-interval can exceed the largest-value point, as long as the number of intervals is minimal (and correct me if I'm wrong). Same thing about overlaping intervals.
Look at the example in the 2nd reply above, which explains this well.

[-] Re: Question 4
by kantora - Sunday, 3 May 2009 16:36:59
1) Yes
2) Yes
3) minimal in number of intervals used(units)
[-] Re: Question 4
by naorp - Tuesday, 5 May 2009 14:54:12
didn't quit understand the meaning of minimal intervals used.. i.e: if for example the points i have are[0,0.5,1] what can be a possible solution?
Re: Question 4
by kantora - Tuesday, 5 May 2009 19:13:32
Here you have only one solution that is [0,1] (minimal number of intervals)