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Improved Algorithms for Unrelated Crowd Worker Scheduling in Mobile Social Networks

Chi-Yeh Chen

Abstract

This paper addresses the scheduling problem for unrelated crowd workers in mobile social networks, where the required service time for each task varies among the assigned crowd workers. The goal is to minimize the total weighted completion time of all tasks. First, in an environment with identical crowd workers, we improve the approximation ratio of the Largest-Ratio-First (LRF) scheduling algorithm and provide an updated competitive ratio for its online version. Next, for the unrelated crowd workers environment, we introduce a randomized approximation algorithm that achieves an expected approximation ratio of 1.45. This result improves upon the 1.5-approximation ratio reported in our previous work. We also present a derandomization method for this algorithm. Furthermore, to improve computational efficiency, we propose an algorithm that leverages the property that the optimal schedule on a single crowd worker arranges tasks in non-increasing order by their Smith ratios. Experimental results demonstrate that our proposed method outperforms three variants of the LRF algorithm.

Improved Algorithms for Unrelated Crowd Worker Scheduling in Mobile Social Networks

Abstract

This paper addresses the scheduling problem for unrelated crowd workers in mobile social networks, where the required service time for each task varies among the assigned crowd workers. The goal is to minimize the total weighted completion time of all tasks. First, in an environment with identical crowd workers, we improve the approximation ratio of the Largest-Ratio-First (LRF) scheduling algorithm and provide an updated competitive ratio for its online version. Next, for the unrelated crowd workers environment, we introduce a randomized approximation algorithm that achieves an expected approximation ratio of 1.45. This result improves upon the 1.5-approximation ratio reported in our previous work. We also present a derandomization method for this algorithm. Furthermore, to improve computational efficiency, we propose an algorithm that leverages the property that the optimal schedule on a single crowd worker arranges tasks in non-increasing order by their Smith ratios. Experimental results demonstrate that our proposed method outperforms three variants of the LRF algorithm.

Paper Structure

This paper contains 16 sections, 7 theorems, 53 equations, 10 figures, 1 table, 5 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Our Contributions
  4. Organization
  5. Notation and Preliminaries
  6. Largest-Ratio-First Based Task Scheduling
  7. Online Task Scheduling
  8. Randomized Approximation Algorithm with Time-indexed Approach
  9. Deterministic Algorithm with Time-indexed Approach
  10. Efficient Deterministic Algorithm with Time-indexed Approach
  11. Results and Discussion
  12. Synthetic Datasets and Settings
  13. Real Datasets and Settings
  14. Algorithms
  15. Results
  16. ...and 1 more sections

Key Result

Lemma 3.2

Let $WCT_{OPT}$ represent the minimum total weighted completion time from the optimal solution. We have where

Figures (10)

  • Figure 1: Performance comparison of algorithms with varying numbers of tasks per crowd worker ($n/m$).
  • Figure 2: Box plot of WCTR for the four algorithms.
  • Figure 3: Performance comparison of algorithms with varying numbers of crowd workers.
  • Figure 4: Performance comparison of algorithms with different means of the base service time $\alpha$.
  • Figure 5: Performance comparison of algorithms with various standard deviations of the base service time $\alpha$.
  • ...and 5 more figures

Theorems & Definitions (14)

  • Definition 1
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof
  • Theorem 3.4
  • proof
  • Theorem 3.5
  • Theorem 3.6
  • proof
  • ...and 4 more