On the Complexity of Conditional DAG Scheduling in Multiprocessor Systems

Abstract

As parallel processing became ubiquitous in modern computing systems, parallel task models have been proposed to describe the structure of parallel applications. The workflow scheduling problem has been studied extensively over past years, focusing on multiprocessor systems and distributed environments (e.g. grids, clusters). In workflow scheduling, applications are modeled as directed acyclic graphs (DAGs). DAGs have also been introduced in the real-time scheduling community to model the execution of multi-threaded programs on a multi-core architecture. The DAG model assumes, in most cases, a fixed DAG structure capturing only straight-line code. Only recently, more general models have been proposed. In particular, the conditional DAG model allows the presence of control structures such as conditional (if-then-else) constructs. While first algorithmic results have been presented for the conditional DAG model, the complexity of schedulability analysis remains wide open.We perform a thorough analysis on the worst-case makespan (latest completion time) of a conditional DAG task under list scheduling (a.k.a. fixed-priority scheduling). We show several hardness results concerning the complexity of the optimization problem on multiple processors, even if the conditional DAG has a well-nested structure. For general conditional DAG tasks, the problem is intractable even on a single processor. Complementing these negative results, we show that certain practice-relevant DAG structures are very well tractable.

Response-Time Analysis and Optimization for Probabilistic Conditional Parallel DAG Tasks

“…A plethora of research concerning the real-time schedulability of this model has been conducted by e.g., [3], [10], [25]. Most recently, the computational complexity of the scheduling of conditional DAG with real-time constraints has been investigated by Marchetti et al [24]. However, due to the worst-case parameters and the worst-case conditional structure that has to be considered during real-time verification of the scheduling algorithms, resource over-provisioning is inevitable.…”

DAG-based Scheduling with Resource Sharing for Multi-task Applications in a Polyglot GPU Runtime

“…Expressing a multi-task computation as a DAG that can be used to estimate an effective scheduling and to optimize execution is a concept that has already been explored with a great degree of success: well-known work that covers GPU computations includes Nvidia's CUDA Graphs [7] and Google's Tensorflow [8]; academic research has also shown interest in domains such as distributed and heterogeneous computing [9]- [11], and presented valuable theoretical results [12], [13]. CUDA Graphs are a programming model…”