title: "Freeze-Tag Thesis" date: "2026-09-07" description: "My B.Sc. thesis — Bounding the Freeze-Tag Problem in Various Metric Spaces — as an interactive website."
Freeze-Tag Thesis
Bounding the Freeze-Tag Problem in Various Metric Spaces — my B.Sc. thesis at the University of Tehran, presented as an interactive website.
Visit the interactive thesis: freezetag.sahroush.ir
Background
The freeze-tag problem is a multi-robot scheduling problem: starting from a single awake robot at the origin, awake robots travel to wake frozen robots as fast as possible. The question is how long an optimal schedule takes, as a function of the number of robots and the metric space they live in.
The work
The thesis builds on my co-authored research on the Geometric Freeze-Tag Problem (AAMAS 2025, journal version JAAMAS 2026):
- New upper bounds for the problem in (ℝ³, l₁) and (ℝ³, l₂) norms.
- Interactive visualizations of the problem space, the wake-up schedules, and the algorithms behind the bounds.
- Interactive simulators for experimenting with schedules in different metric spaces.
The website renders all of this in the browser: the problem, the algorithms, and the proofs behind the upper bounds.
Links
- Interactive thesis website: freezetag.sahroush.ir
- Conference paper: "Geometric Freeze-Tag Problem", AAMAS 2025
- Journal version: Autonomous Agents and Multi-Agent Systems (JAAMAS), 2026