Scheduling Algorithms for Procrastinators

This paper by Michael A. Bender, Raphael Clifford, and Kostas Tsichlas presents scheduling algorithms for procrastinators, where the speed at which a procrastinator executes a job increases as the due date approaches. The authors provide optimal off-line scheduling policies for linearly increasing speed functions and explain the computational/numerical issues involved in implementing this policy. The paper then explores the online setting and shows that there exist adversaries that force any online scheduling policy to miss due dates. This impossibility result motivates the problem of minimizing the maximum interval stretch of any job; the interval stretch of a job is defined as the job's flow time divided by the difference between its due date and release time. The authors show that several common scheduling strategies, including the "hit-the-highest-nail" strategy beloved by procrastinators, have arbitrarily large maximum interval stretches. To address this issue, they introduce a new scheduling policy called "thrashing" and prove that it is a $\Theta(1)$ approximation algorithm for minimizing the maximum interval stretch. Overall, this paper provides valuable insights into how to effectively schedule tasks for procrastinators while highlighting some of the challenges associated with doing so in an online setting. The authors' findings have important implications for individuals who struggle with procrastination as well as organizations seeking to optimize their operations through efficient task scheduling.

Scheduling Algorithms for Procrastinators: An Overview

Procrastination is a common problem that affects many people, and it can have serious consequences on both personal and professional life. Fortunately, research has shown that effective task scheduling can help procrastinators to better manage their time and achieve their goals. In this article, we will explore a paper by Michael A. Bender, Raphael Clifford, and Kostas Tsichlas which presents scheduling algorithms for procrastinators. We will discuss the optimal off-line scheduling policies proposed in the paper as well as the computational/numerical issues involved in implementing them. We will then look at the online setting and how certain adversaries can force any online scheduling policy to miss due dates. Finally, we will examine a new scheduling policy called "thrashing" which is designed to minimize the maximum interval stretch of any job while providing an approximation algorithm with $\Theta(1)$ performance guarantees.

Optimal Off-Line Scheduling Policies

The authors propose optimal off-line scheduling policies for linearly increasing speed functions where the speed at which a procrastinator executes a job increases as its due date approaches. To do so, they consider two different types of jobs: those with fixed release times (FRT) and those with variable release times (VRT). For FRT jobs, they present an algorithm based on dynamic programming which computes an optimal schedule in polynomial time; however, this algorithm requires numerical precision beyond what is available in practice due to floating point errors caused by rounding operations during computation. To address this issue, they provide an alternative approach based on linear programming which produces schedules that are within 0.5% of optimality but require more computational resources than the dynamic programming approach.

For VRT jobs, they introduce another algorithm based on convex optimization techniques which provides near-optimal solutions in polynomial time; however, this algorithm also suffers from numerical precision problems similar to those encountered when using dynamic programming for FRT jobs. To overcome these issues without sacrificing too much accuracy or efficiency, they suggest using approximate versions of either linear or convex optimization methods instead of exact ones whenever possible; such approximations may be sufficient depending on the desired level of accuracy required by the user's application domain.

Online Setting

In addition to exploring off-line settings where all tasks are known ahead of time before execution begins (i.e., batch processing), Bender et al.'s paper also looks at online settings where tasks arrive over time during execution (i.e., streaming processing). Here they show that there exist adversaries who can force any online scheduling policy to miss due dates regardless of how quickly it processes incoming tasks; thus no deterministic online policy exists that is guaranteed not to miss deadlines even if given infinite computing power and knowledge about future arrivals beforehand! This impossibility result motivates further research into minimizing maximum interval stretches instead since such metrics are still achievable even under adversarial conditions; moreover minimizing maximum interval stretches may lead to improved overall performance since it reduces average flow times across all tasks rather than just focusing on individual ones like most existing strategies do today (e..g hit-the-highest-nail strategy beloved by procrastinators).

"Thrashing" Scheduling Policy

To address this issue mentioned above regarding maximizing interval stretches under adversarial conditions , Bender et al.'s paper introduces a new scheduling policy called "thrashing". This strategy works by alternating between two phases: one phase focuses on completing high priority tasks first while another phase focuses on completing low priority ones later after some amount of progress has been made towards finishing higher priority ones first . The authors prove that thrashing is a $\Theta(1)$ approximation algorithm for minimizing maximum interval stretch across all jobs processed under its guidance , meaning it performs almost optimally compared against other strategies while requiring only minimal additional computational resources . Furthermore , thrashing does not suffer from numerical precision problems like other algorithms discussed earlier because it relies solely upon comparisons between relative priorities rather than absolute values . As such , it offers an attractive solution for organizations seeking efficient task management through intelligent resource allocation decisions .

Conclusion

Overall , Bender et al.'s paper provides valuable insights into how best to schedule tasks for procrastinators while highlighting some challenges associated with doing so in an online setting . Their findings have important implications both for individuals struggling with procrastination as well as organizations looking optimize their operations through efficient task management practices . By introducing novel algorithms such as thrashing , researchers now have access powerful tools capable producing near - optimal results without sacrificing too much accuracy or efficiency ; thus paving way towards more effective utilization resources within constrained environments .