Plan-over-Graph: Towards Parallelable LLM Agent Schedule

TL;DR

Plan-over-Graph introduces a parallelizable planning paradigm for LLM agents by first extracting an executable task graph from natural language and then planning over this graph under a time-cost objective. It combines synthetic data generation of DAGs and a two-stage training regime (SFT with LoRA and Direct Preference Optimization) to improve graph understanding and parallel planning across API-based and open-source LLMs. Empirical results show substantial gains in optimal and success rates, and clear time-efficiency benefits from parallel execution, across both graph-only tasks and real-world textual queries. The approach provides a scalable, graph-centric framework for robust, efficient LLM-driven planning, with code and data released for reproducibility. It also analyzes how graph topology and size affect performance, informing future directions for graph-aware reasoning in LLMs.

Abstract

Large Language Models (LLMs) have demonstrated exceptional abilities in reasoning for task planning. However, challenges remain under-explored for parallel schedules. This paper introduces a novel paradigm, plan-over-graph, in which the model first decomposes a real-life textual task into executable subtasks and constructs an abstract task graph. The model then understands this task graph as input and generates a plan for parallel execution. To enhance the planning capability of complex, scalable graphs, we design an automated and controllable pipeline to generate synthetic graphs and propose a two-stage training scheme. Experimental results show that our plan-over-graph method significantly improves task performance on both API-based LLMs and trainable open-sourced LLMs. By normalizing complex tasks as graphs, our method naturally supports parallel execution, demonstrating global efficiency. The code and data are available at https://github.com/zsq259/Plan-over-Graph.

Figures (5)

• Figure 1: An example of our task: from a realistic textual query to a parallel plan. The plan is represented as a graph. Edges are available rules, and Residential, Elevated, and Infrastructure are the initial sources, Core being the target. The solid edges denote the optimal plan under the constraint of time consumption.
• Figure 2: The overview of our framework. (a) shows the data synthesis pipeline; (b) shows our training process; (c) displays the plan-over-graph paradigm.
• Figure 3: The upper part of this figure shows model performance across different node counts. The left plot shows time and cost ratio change with the number of points, and the right shows success and optimal rate. The lower part shows Claude and our trained Llama average time and cost ratio across different edge counts.
• Figure 4: Statistics on our synthetic query. The bar chart on the left displays the distribution of tokens. The pie chart on the right shows the topic distribution.
• Figure 5: Claude and our trained Llama performance across different edge counts. The vertical axis represents corresponding number of cases of each state(fail, feasible, optimal). The horizontal axis represents the number of edges segmented at certain intervals.