Stabilization Time in Minority Processes
Abstract
We analyze the stabilization time of minority processes in graphs. A minority process is a dynamically changing coloring, where each node repeatedly changes its color to the color which is least frequent in its neighborhood. First, we present a simple $\Omega(n^2)$ stabilization time lower bound in the sequential adversarial model. Our main contribution is a graph construction which proves a ${\Omega}(n^{2-\epsilon})$ stabilization time lower bound for any $\epsilon>0$. This lower bound holds even if the order of nodes is chosen benevolently, not only in the sequential model, but also in any reasonable concurrent model of the process.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2019
- DOI:
- 10.48550/arXiv.1907.02131
- arXiv:
- arXiv:1907.02131
- Bibcode:
- 2019arXiv190702131A
- Keywords:
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- Computer Science - Discrete Mathematics