Re: Finding overlapping time periods - suggestions please

I have once been asked to suggest the solution for the same problem, and I have suggested a solution which was out of this world, but completely in line with my education of a mathematician. The project was scrapped and I didn't have an opportunity to apply the solution.
To start describing the solution, let me remind you that overlapping areas of space would be discovered by using spatial option. To apply the spatial option, you need to define distance function. Temporal difference does satisfy the necessary conditions for a distance function, as far as mathematics is concerned. In mathematics, there is a structure called "metric space", which is, basically, a set with a distance function. Distance function d ("metric") on set S is a function d:S x S->R which satisfies the following two conditions:

1. d(x,y)>=0 for all x,y from S.
2. d(x,z)<=d(x,y)+d(y,z) for every x,y,z from S. (Cauchy inequality).

Points in time, with the difference in seconds do satisfy the above conditions, which means that you can define geometry and use spatial option. Next lesson will be about Cauchy sequences, complete metric spaces, continuous functions, contractions and Banach theorem. If Cary got away with queuing theory, why wouldn't I get away with some abstract calculus and general topology?
As I've said earlier, I've never actually had an opportunity to actually apply this solution, but it still looks quite elegant to me, despite it's apparent oddity.

On 10/31/2003 01:24:37 PM, babette.turnerunderwood_at_hrdc-drhc.gc.ca wrote:
> I was wondering if anyone had the need to find overlapping time periods and how to identify them efficiently.
>
> Here is the scenario:
>
> Elapsed minutes refer to the actual "clock" time either spent on a given task. Thus an activity that started at 9:00 am and finished at 11:00 am on the same day is said to have 120 elapsed minutes.
> If one task overlaps another (either completely or partially with another task), then the tasks are said to be "multitasked". In that case the system will store the portion of the elapsed time that was multitasked as "elapsed multitask minutes" and the portion of the time that was not overlapped as "elapsed single minutes". In addition, for the portion of time that two or more activities were simultaneously taking place; their time will be divided by the number of simultaneous activities and stored as "prorated multi minutes". The sum of Elapsed Single Minutes and Prorated Minutes will equal the actual clock time that a vehicle was active.
> The following example should help to illustrate these concepts. In the table below a list of fictitious activities for a vehicle are shown in addition to how the time is allocated to the various measures:
> Activity Start Time End Time Elapsed Minutes Elapsed Multitask Minutes Elapsed Single Minutes Prorated Multi Minutes Prorated Minutes
> 1 10:00 12:00 120 60 60 25 85
> 3 11:00 13:00 120 120 0 55 55
> 4 11:30 13:30 120 90 30 40 70
> 7 13:30 16:00 150 0 150 0 150
> Totals 510 270 240 120 360
> The vehicle was active from 10:00 to 16:00, a total of 6 hours (360 minutes) which is equal to the total of Prorated Minutes.
> The vehicle performed 8 ½ hours (510 minutes) of work during that 6-hour time span. This can be arrived at by adding the total of Elapsed Multitask Minutes (270) + the total of Elapsed Single Minutes (240).
>
>

Mladen Gogala
Oracle DBA

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