The discussion

https://libguides.usc.edu/writingguide/discussion

Now that I'm at the end of the road, this thing about discussing the results come up... I've no idea how to do that as I've not been able to reproduce complicated algorithms from other papers to compare an discuss it with... so i'm drawing blank here...

So "The discussion"- demonstrates your ability to think critically on an issue-develop creative solutions to problems based on a logical synthesis of the problem- formulate a deeper more profound understanding of the research problem under consideration

(Okay so, basically, I'm reinstating the problem statement in terms of the findings...)

Present the underlying meaning of your research, note possible implications in other areas of study, and explore possible improvements that can be made in order to further develop the concerns of your research.

(Okay, so i can write about that... there are tonnes of future work that needs to be done 'nywayz.

Highlight the importance of your study and how it may be able to contribute to and/or help fill existing gaps in the field. If appropriate, the discussion section is also where you state how the findings from your study revealed and helped fill gaps in the literature that had not been previously exposed or adequately described, and

Engage the reader in thinking critically about issues based upon an evidence-based interpretation of findings; it is not governed strictly by objective reporting of information.

(that might be a little tricky!)   The rest of the article is pretty informative too... give a lot of pointers!!)

Just had a thought... it's difficult to be highly critical of your own work, so I'm just gonna take all those critical reviewer comments and put them in my paper 😁 best idea I've had so far!!

And they've given me lot's of things to discuss about to... like all those things that are not in the paper... the good bits, etc...

Notes on Pareto optimal Cloud Bursting

Pareto-Optimal Cloud Bursting

 Farahabady, YLee, and  Zomaya

October 2014

focus of cloud bursting is on performance to cost ratio.
BoT applications are chosen- horizontally scalability

degree of performance is not strongly correlated with cost.

2 conflicting objectives:
1. minimizing cost(c)
2.  maximizing performance by minimizing makespan (t)

Schedule -
not possible to achieve best values for both criteria simultaneously.
sigma-bar - is said to be dominated by a schedule sigma if both the cost and time metrics are worser than or equal to the latter.

sigma star - a schedule that is not dominated by other schedule.  It is called pareto-optimal schedule.

Pareto frontier - set of all feasible pareto-optimal points.

Each user possesses a utility function, U (c,t) - represents value of a particular schedule from the user's interest.

**Actual user preferences are difficult to obtain...
** complex utility function makes the scheduling problem intractable.

Main contribution : allows users to recognize the best performance to cost ratio
the framework presented is also capable of effectively dealing with uncertainties in application or resource performance.

Problem formulated as binary integer programming problem.

- k different resource types with speeds (s1,.... sk) and cost(c1,..., ck)
- no. of resources that can be leased by the public cloud - Lk
- no of homogeneous resources that are available in the private cloud is Lv

BoT Application model
 - application B, consists of n tasks all available at scheduling time t=0
   (execution of the task is dependent on the clock spee,hence it is CPU intensive.
- the running time of task j is denoted by Pj

** preemption is not considered

If task j is assigned to run on resource i,
processing time = Pj / si
cost of execution  = (ci X Pj) / si

- |B|R - represents the amount of time taken by a BoT application to complete in a reference machine.

Objective function

 min z = theta Cost + (1 - theta) Time : theta is between 0 and 1

value of theta - helps user make better realization of the optimization goal.

• theta = 1 :  generates a solution that all tasks run in resources of the most cost effective type, i.e. with the highest values of si / ci

eg. speed is 1000 MIPS, cost is $2.00 per hour
1000/2 = 500

speed is 500 MIPS, cost is $1.00 per hour
500/2 = 250

• theta = 0 : leads to a load balance solution among available resources.

                 each resource of type i receives a load proportional to the value of si / sum of the total number of resources X the speed


Let E denote a set of pareto points denoted by the user
Let Tbest and Tworst be the best and worst makespan achievable for the execution of a given BoT application.

Writing pseudocode

I had no idea writing pseudo code will be so difficult.  I'm still not sure whether it's more appropriate to write an algorithm or pseudocode.

https://link.springer.com/content/pdf/bbm%3A978-1-4471-5173-9%2F1.pdf

So there's this link from Springer on how to write a pseudo code, I think that's a good start.  There was a review some few years back that I'm mixing up various conventions when writing a pseudo code.
Then I tried to follow some conventions and it was just too complicated.

Let's see if I'm able to write with this convention.

Also I feel an algorithm is better

Notes on Algorithms and Complexity

From a 1993 handbook on OR and MS

Sequencing and Scheduling.

Definition:optimal allocation of scarce resources to activities over time.

Algorithms and Complexity

Complexity Theory : provides a mathematical framework where mathematical problems can be classified as "easy" or "hard"

NP Complete problem :  hardest problem in NP, meaning in that if it is solvable, then each problem in NP would be solvable.
so P=NP
NP-completeness - strong evidence that a polynomial time algorithm does not exist.

A problem is NP-complete if every problem is NP and it reduces to NP-complete

Optimization problem is NP Hard - if the associated decision problem is NP-complete.

optimization problem is NP Hard - meaning it is impossible to always find an optimal solution quickly.
possible to have some approximation algorithms.

Arbitrary precedence constraints, release dates, deadlines

if release dates are specified, makes the problem strongly NP Hard.

when jobs have to meet deadlines : shown to be NP- Hard by Lawler

Many have developed elimination criteria. i.e., of it meets certain criteria for tasks, then schedule, etc.
if elimination criteria are met then the problem can be approximated to polynomial time.

The rest of the chapter examines each type of scheduling problem ones with uniform processors, heterogeneous processor, job-shop.

There is a reference to Ibarra and Kim from which I'd somewhat understood the scheduling problem.