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Revoke vs. Restart in Unweighted Throughput Scheduling

Changdao He

TL;DR

The paper addresses unweighted throughput scheduling on a single machine under the preemption-revoke model, where a running job can be aborted but progress is lost and cannot be resumed. It establishes a strong negative result: no deterministic online algorithm can achieve a constant competitive ratio. The authors construct an adversarial sequence starting from a 3-job instance and iteratively nest it to produce, for every $k\ge 3$, instances where $\textsf{ALG}\le 1$ while $\textsf{OPT}\ge k$, yielding a ratio of at most $1/k$ (which approaches zero as $k$ grows). This highlights a sharp contrast with the preemption-restart model, where a $1/2$-competitive deterministic algorithm exists, and motivates exploring input restrictions or randomized strategies to obtain nontrivial guarantees. The work provides a rigorous framework for understanding the fundamental limitations of deterministic online scheduling under irrevocable revocation and outlines avenues for future research in restricted settings and probabilistic approaches.

Abstract

We study the unweighted throughput scheduling problem on a single machine in the preemption-revoke model, where a running job may be aborted at any time, but all progress is permanently lost and the job cannot be restarted. Each job $J_i=(r_i,p_i,s_i)$ is defined by a release time $r_i$, a processing time $p_i$, and a slack $s_i$, and must start no later than $r_i+s_i$ to be feasible. We prove that no deterministic online algorithm can achieve a constant competitive ratio. The lower bound is established via an adversarial construction: starting from a three-job instance where $\textsf{ALG}$ completes at most one job while $\textsf{OPT}$ completes all three, we iteratively nest such constructions. By induction, for every $k\ge 3$, there exists an instance where $\textsf{ALG}$ completes at most one job, while $\textsf{OPT}$ completes at least $k$ jobs. Thus, the competitive ratio can be forced to $1/k$, and hence made arbitrarily close to zero. Our result stands in sharp contrast to the preemption-restart model, where Hoogeveen, Potts, and Woeginger (2000) gave a deterministic $1/2$-competitive algorithm.

Revoke vs. Restart in Unweighted Throughput Scheduling

TL;DR

The paper addresses unweighted throughput scheduling on a single machine under the preemption-revoke model, where a running job can be aborted but progress is lost and cannot be resumed. It establishes a strong negative result: no deterministic online algorithm can achieve a constant competitive ratio. The authors construct an adversarial sequence starting from a 3-job instance and iteratively nest it to produce, for every , instances where while , yielding a ratio of at most (which approaches zero as grows). This highlights a sharp contrast with the preemption-restart model, where a -competitive deterministic algorithm exists, and motivates exploring input restrictions or randomized strategies to obtain nontrivial guarantees. The work provides a rigorous framework for understanding the fundamental limitations of deterministic online scheduling under irrevocable revocation and outlines avenues for future research in restricted settings and probabilistic approaches.

Abstract

We study the unweighted throughput scheduling problem on a single machine in the preemption-revoke model, where a running job may be aborted at any time, but all progress is permanently lost and the job cannot be restarted. Each job is defined by a release time , a processing time , and a slack , and must start no later than to be feasible. We prove that no deterministic online algorithm can achieve a constant competitive ratio. The lower bound is established via an adversarial construction: starting from a three-job instance where completes at most one job while completes all three, we iteratively nest such constructions. By induction, for every , there exists an instance where completes at most one job, while completes at least jobs. Thus, the competitive ratio can be forced to , and hence made arbitrarily close to zero. Our result stands in sharp contrast to the preemption-restart model, where Hoogeveen, Potts, and Woeginger (2000) gave a deterministic -competitive algorithm.
Paper Structure (11 sections, 3 theorems, 7 equations, 6 figures, 1 table)

This paper contains 11 sections, 3 theorems, 7 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Our Contribution
  4. Preliminaries
  5. Problem Definition
  6. The Preemption-Revoke Model
  7. Notation and Convention on Competitive Ratios
  8. Notation Summary
  9. A Warm-Up Lower Bound
  10. No Constant Competitive Ratio
  11. Conclusions and Discussion

Key Result

Theorem 1

For the unweighted throughput problem on one machine in the preemption-revoke model, no deterministic online algorithm is $>1/3$-competitive. In particular, for any deterministic online algorithm $\textsf{ALG}$ there is an input on which $\textsf{ALG}$ completes at most one job while $\textsf{OPT}$

Figures (6)

  • Figure 1: Intervals $[r, d)$ and $[x, y)$ illustrating the side-gap condition.
  • Figure 2: $J_2$ is released immediately after $a_1$.
  • Figure 3: $J_3$ is released immediately after $a_2$.
  • Figure 4: $J_4$ is released immediately after $r_2+s_2$.
  • Figure 5: $J_{k+1}$ is released immediately after $a_k$.
  • ...and 1 more figures

Theorems & Definitions (6)

  • Theorem 1
  • Lemma 1
  • proof
  • proof : Proof of Theorem \ref{['thm:one-third']}
  • Theorem 2
  • proof