The gathering over meeting nodes problem asks the robots to gather at one of the pre-defined meeting nodes. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting nodes. Robots are identical, autonomous, anonymous and oblivious. They operate under an asynchronous scheduler. They do not have any agreement on a global coordinate system. All the initial configurations for which the problem is deterministically unsolvable have been characterized. A deterministic distributed algorithm has been proposed to solve the problem for the remaining configurations. The efficiency of the proposed algorithm is studied in terms of the number of moves required for gathering. A lower bound concerning the total number of moves required to solve the gathering problem has been derived.
For a given positive integer k, the k-circle formation problem asks a set of autonomous, asynchronous robots to form disjoint circles having k robots each at distinct locations, centered at a set of fixed points in the Euclidean plane. The robots are identical, anonymous, oblivious, and they operate in Look–Compute–Move cycles. This paper studies the k-circle formation problem and its relationship with the k-epf problem, a generalized version of the embedded pattern formation problem, which asks exactly k robots to reach and remain at each fixed point. First, the k-circle formation problem is studied in a setting where the robots have an agreement on the common direction and orientation of one of the axes. We have characterized all the configurations and the values of k, for which the k-circle formation problem is deterministically unsolvable in this setting. For the remaining configurations and the values of k, a deterministic distributed algorithm has been proposed, in order to solve the problem. It has been proved that for the initial configurations with distinct robot positions, if the k-circle formation problem is deterministically solvable then the k-epf problem is also deterministically solvable. It has been shown that by modifying the proposed algorithm, the k-epf problem can be solved deterministically.
The gathering over meeting nodes problem asks the robots to gather at one of the pre-defined meeting nodes. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid, which has a subset of nodes marked as meeting nodes. Robots are identical, autonomous, anonymous and oblivious. They operate under an asynchronous scheduler. They do not have any agreement on a global coordinate system. All the initial configurations for which the problem is deterministically unsolvable have been characterized. A deterministic distributed algorithm has been proposed to solve the problem for the remaining configurations. The efficiency of the proposed algorithm is studied in terms of the number of moves required for gathering. A lower bound concerning the total number of moves required to solve the gathering problem has been derived.
The gathering over meeting nodes problem requires the robots to gather at one of the pre-defined meeting nodes. This paper investigates the problem with respect to the objective function that minimizes the total number of moves made by all the robots. In other words, the sum of the distances traveled by all the robots is minimized while accomplishing the gathering task. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting nodes. The robots do not agree on a global coordinate system and operate under an asynchronous scheduler. A deterministic distributed algorithm has been proposed to solve the problem for all those solvable configurations, and the initial configurations for which the problem is unsolvable have been characterized. The proposed gathering algorithm is optimal with respect to the total number of moves performed by all the robots in order to finalize the gathering.
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