The Buffer Minimization Problem for Scheduling Flow Jobs with Conflicts

2025-11-24

AI Summary

This paper investigates the buffer minimization problem in online streaming scheduling on multiprocessor systems: tasks arrive streamwise at processors and are temporarily buffered in input queues, while inter-processor conflicts—modeled as a graph—impose mutual exclusion constraints on concurrent execution. The objective is to dynamically schedule tasks online to minimize the global maximum buffer occupancy. We introduce this problem into the streaming model and address it via online algorithm design and competitive analysis, integrating graph-theoretic modeling of conflict structures. Our main contributions include: establishing tight competitive ratios for all non-path graphs on four vertices; advancing theoretical bounds for complete graphs, complete bipartite graphs, and k-partite graphs; achieving tight or nearly tight results across multiple graph classes; and significantly narrowing the competitive ratio gap for the “triangle-plus-pendant-edge” graph.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We consider the online buffer minimization in multiprocessor systems with conflicts problem (in short, the buffer minimization problem) in the recently introduced flow model. In an online fashion, workloads arrive on some of the $n$ processors and are stored in an input buffer. Processors can run and reduce these workloads, but conflicts between pairs of processors restrict simultaneous task execution. Conflicts are represented by a graph, where vertices correspond to processors and edges indicate conflicting pairs. An online algorithm must decide which processors are run at a time; so provide a valid schedule respecting the conflict constraints. The objective is to minimize the maximal workload observed across all processors during the schedule. Unlike the original model, where workloads arrive as discrete blocks at specific time points, the flow model assumes workloads arrive continuously over intervals or not at all. We present tight bounds for all graphs with four vertices (except the path, which has been solved previously) and for the families of general complete graphs and complete bipartite graphs. We also recover almost tight bounds for complete $k$-partite graphs. For the original model, we narrow the gap for the graph consisting of a triangle and an additional edge to a fourth vertex.

Problem

• Minimizing maximum workload in multiprocessor systems with conflicts
• Scheduling flow jobs with processor conflict constraints online
• Determining tight bounds for buffer minimization on various graph structures

Innovation

• Online buffer minimization with conflict constraints
• Continuous workload arrival in flow model
• Tight bounds for specific graph families