On 23 March 2017 at 16:26, Amit Khandekar <
amitdkhan.pg@gmail.com> wrote:
> On 23 March 2017 at 05:55, Robert Haas <
robertmhaas@gmail.com> wrote:
>> On Wed, Mar 22, 2017 at 4:49 AM, Amit Khandekar <
amitdkhan.pg@gmail.com> wrote:
>>> Attached is the updated patch that handles the changes for all the
>>> comments except the cost changes part. Details about the specific
>>> changes are after the cost-related points discussed below.
>>>
>>> For non-partial paths, I was checking following 3 options :
>>>
>>> Option 1. Just take the sum of total non-partial child costs and
>>> divide it by number of workers. It seems to be getting close to the
>>> actual cost.
>>
>> If the costs for all children are about equal, then that works fine.
>> But when they are very unequal, then it's highly misleading.
>>
>>> Option 2. Calculate exact cost by an algorithm which I mentioned
>>> before, which is pasted below for reference :
>>> Persubpath cost : 20 16 10 8 3 1, with 3 workers.
>>> After 10 time units (this is minimum of first 3 i.e. 20, 16, 10), the
>>> times remaining are :
>>> 10 6 0 8 3 1
>>> After 6 units (minimum of 10, 06, 08), the times remaining are :
>>> 4 0 0 2 3 1
>>> After 2 units (minimum of 4, 2, 3), the times remaining are :
>>> 2 0 0 0 1 1
>>> After 1 units (minimum of 2, 1, 1), the times remaining are :
>>> 1 0 0 0 0 0
>>> After 1 units (minimum of 1, 0 , 0), the times remaining are :
>>> 0 0 0 0 0 0
>>> Now add up above time chunks : 10 + 6 + 2 + 1 + 1 = 20
>>
>
>> This gives the same answer as what I was proposing
>
> Ah I see.
>
>> but I believe it's more complicated to compute.
> Yes a bit, particularly because in my algorithm, I would have to do
> 'n' subtractions each time, in case of 'n' workers. But it looked more
> natural because it follows exactly the way we manually calculate.
>
>> The way my proposal would work in this
>> case is that we would start with an array C[3] (since there are three
>> workers], with all entries 0. Logically C[i] represents the amount of
>> work to be performed by worker i. We add each path in turn to the
>> worker whose array entry is currently smallest; in the case of a tie,
>> just pick the first such entry.
>>
>> So in your example we do this:
>>
>> C[0] += 20;
>> C[1] += 16;
>> C[2] += 10;
>> /* C[2] is smaller than C[0] or C[1] at this point, so we add the next
>> path to C[2] */
>> C[2] += 8;
>> /* after the previous line, C[1] is now the smallest, so add to that
>> entry next */
>> C[1] += 3;
>> /* now we've got C[0] = 20, C[1] = 19, C[2] = 18, so add to C[2] */
>> C[2] += 1;
>> /* final result: C[0] = 20, C[1] = 19, C[2] = 19 */
>>
>> Now we just take the highest entry that appears in any array, which in
>> this case is C[0], as the total cost.
>
> Wow. The way your final result exactly tallies with my algorithm
> result is very interesting. This looks like some maths or computer
> science theory that I am not aware.
>
> I am currently coding the algorithm using your method.
