$p$ $(0<p \leq 1)$ that no randomized algorithm exists that solves, with probability $p$, the gathering problem with (termination) detection. For this reason, we consider the relaxed gathering problem, called the gathering problem without detection, which does not require termination detection. We propose a randomized algorithm that solves, with any given constant probability $p$ $(0<p<1)$ , the gathering problem without detection. Finally, we prove that no randomized algorithm exists that solves, with probability 1, the gathering problem without detection." /> $p$ $(0<p \leq 1)$ that no randomized algorithm exists that solves, with probability $p$, the gathering problem with (termination) detection. For this reason, we consider the relaxed gathering problem, called the gathering problem without detection, which does not require termination detection. We propose a randomized algorithm that solves, with any given constant probability $p$ $(0<p<1)$ , the gathering problem without detection. Finally, we prove that no randomized algorithm exists that solves, with probability 1, the gathering problem without detection." /> $p$ $(0<p \leq 1)$ that no randomized algorithm exists that solves, with probability $p$, the gathering problem with (termination) detection. For this reason, we consider the relaxed gathering problem, called the gathering problem without detection, which does not require termination detection. We propose a randomized algorithm that solves, with any given constant probability $p$ $(0<p<1)$ , the gathering problem without detection. Finally, we prove that no randomized algorithm exists that solves, with probability 1, the gathering problem without detection." /> Randomized Gathering of Mobile Agents in Anonymous Unidirectional Ring Networks
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Issue No.05 - May (2014 vol.25)
pp: 1289-1296
Toshimitsu Masuzawa , Grad. Sch. of Inf. Sci. & Technol., Osaka Univ., Suita, Japan
ABSTRACT
We consider the gathering problem of multiple (mobile) agents in anonymous unidirectional ring networks under the constraint that each agent knows neither the number of nodes nor the number of agents. For this problem, we fully characterize the relation between probabilistic solvability and termination detection. First, we prove for any (small) constant p(0 <; p ≤ 1) that no randomized algorithm exists that solves, with probability p, the gathering problem with (termination) detection. For this reason, we consider the relaxed gathering problem, called the gathering problem without detection, which does not require termination detection. We propose a randomized algorithm that solves, with any given constant probability p(0 <; p <; 1), the gathering problem without detection. Finally, we prove that no randomized algorithm exists that solves, with probability 1, the gathering problem without detection.
INDEX TERMS
Mobile agents, Algorithm design and analysis, Synchronization, Upper bound, Probabilistic logic, Robot kinematics,ring networks, Mobile agents, gathering problem, randomized algorithm
CITATION
Toshimitsu Masuzawa, "Randomized Gathering of Mobile Agents in Anonymous Unidirectional Ring Networks", IEEE Transactions on Parallel & Distributed Systems, vol.25, no. 5, pp. 1289-1296, May 2014, doi:10.1109/TPDS.2013.259