A Further Study on Weak Byzantine Gathering of Mobile Agents

The gathering of mobile agents in the presence of Byzantine faults is first studied by Dieudonné et al.. Authors provide a polynomial time algorithm handling any number of weak Byzantine agents in the presence of at least one good agent considering start-up delays, i.e., the good agents may not wake up at the same time. Hirose et al. come up with an algorithm considering start-up delays that use a strong team of at least 4f2 + 8f + 4 many good agents but runs much faster than that of Dieudonné et al.. Later Hirose et al. provide another polynomial time algorithm for gathering in the presence of at least 8f + 8 good agents. However, this algorithm does not work in the presence of start-up delays, also simultaneous termination of good agents is not possible. We, in this work, provide an algorithm considering start-up delays of the good agents reducing the number of good agents w.r.t. Hirose et al. from 4f2 + 8f + 4 to f2 + 4f + 9. Also, our algorithm guarantees simultaneous termination of the good agents.