Unifying Scheduling Algorithms for Group Completion Time

2025-01-29

AI Summary

This paper addresses the minimization of the weighted sum of group completion times in team task scheduling, unifying both online (non-clairvoyant) and offline (full-information) settings. It introduces, for the first time, the “group completion time” abstraction framework, which subsumes diverse scheduling and graph coloring problems under a common optimization paradigm. For the online setting, the authors design a progressively optimal algorithm achieving an $O(log g)$ competitive ratio, where $g$ denotes the number of groups. For the offline setting, they develop a generic meta-framework integrating LP relaxation, randomized rounding, and group scheduling theory, yielding significant improvements in approximation ratios: related-machine non-preemptive scheduling improves from 13.5 to 10.874; unrelated-machine preemptive scheduling achieves $2+varepsilon$; and graph coloring on perfect graphs is improved to 5.437. These results advance the state of the art across multiple classical combinatorial optimization problems.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose new abstract problems that unify a collection of scheduling and graph coloring problems with general min-sum objectives. Specifically, we consider the weighted sum of completion times over groups of entities (jobs, vertices, or edges), which generalizes two important objectives in scheduling: makespan and sum of weighted completion times. We study these problems in both online and offline settings. In the non-clairvoyant online setting, we give a novel $O(log g)$-competitive algorithm, where $g$ is the size of the largest group. This is the first non-trivial competitive bound for many problems with group completion time objective, and it is an exponential improvement over previous results for non-clairvoyant coflow scheduling. Notably, this bound is asymptotically best-possible. For offline scheduling, we provide powerful meta-frameworks that lead to new or stronger approximation algorithms for our new abstract problems and for previously well-studied special cases. In particular, we improve the approximation ratio from $13.5$ to $10.874$ for non-preemptive related machine scheduling and from $4+varepsilon$ to $2+varepsilon$ for preemptive unrelated machine scheduling (MOR 2012), and we improve the approximation ratio for sum coloring problems from $10.874$ to $5.437$ for perfect graphs and from $11.273$ to $10.874$ for interval graphs (TALG 2008).

Problem

• Task Scheduling
• Optimization
• Real-time Allocation

Innovation

• Real-time Task Allocation
• Optimal Solution Approximation
• Coloring Problems on Perfect and Interval Graphs