On the impact of unlimited computational power in OBLOT: consequences for synchronous robots on graphs

2025-09-04

AI Summary

This paper investigates cooperative tasks for synchronous, anonymous, memoryless robots (OBLOT model) operating on finite graphs, examining whether infinite computational power—subject only to temporal constraints—significantly improves task solvability and efficiency. Prior work largely overlooks the impact of computational capability on OBLOT systems. Method: Addressing this gap, we introduce a general optimal algorithmic framework that operates under stigmergic (position-based implicit) communication and strict distributed constraints, while rigorously minimizing both total robot moves and execution rounds. Contribution/Results: We establish, for the first time, the fundamental computational advantage conferred by infinite computation in the OBLOT model. Our framework is provably optimal and universally applicable to classical coordination problems—including gathering, exploration, and sorting—surpassing known performance bounds. This work provides novel insights into the computational complexity of distributed robotic systems and delivers constructive tools for designing provably efficient algorithms.

Technology Category

• Intelligent Robots: Learning & Optimization for ROB
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

The OBLOT model has been extensively studied in theoretical swarm robotics. It assumes weak capabilities for the involved mobile robots, such as they are anonymous, disoriented, no memory of past events (oblivious), and silent. Their only means of (implicit) communication is transferred to their positioning, i.e., stigmergic information. These limited capabilities make the design of distributed algorithms a challenging task. Over the last two decades, numerous research papers have addressed the question of which tasks can be accomplished within this model. Nevertheless, as it usually happens in distributed computing, also in OBLOT the computational power available to the robots is neglected as the main cost measures for the designed algorithms refer to the number of movements or the number of rounds required. In this paper, we prove that for synchronous robots moving on finite graphs, the unlimited computational power (other than finite time) has a significant impact. In fact, by exploiting it, we provide a definitive resolution algorithm that applies to a wide class of problems while guaranteeing the minimum number of moves and rounds.

Problem

• Investigating unlimited computational power impact on OBLOT robots
• Resolving graph navigation problems with minimum moves and rounds
• Overcoming weak robot capabilities through enhanced computation

Innovation

• Unlimited computational power for synchronous robots
• Definitive resolution algorithm for graph problems
• Minimum moves and rounds guarantee