SUMMARY:The planning and 3D reconstruction in craniofacial defects based on anatomical principles of symmetry and passive adaptation has evolved radically the past few years. This article recounts the possibility to develop personalized and extensive craniofacial implants. We present a case of a patient with a 10-year trauma sequel evolution; the patient lost the right frontal bone, supraorbital wall and part of the temporal fossa. From the computerized tomography, and by using Materialise software (3-Matic and Mimics). Subsequently, the printing was performed using the virtual planning with a laser printer in titanium where the piece was elaborated with the determined specifications in the planning; surgery was performed without complications in which the implant was placed via a coronal approach, which did not require any type of adaptation. After a two-year follow-up we observed a correct position, symmetry, absence of infection or any other alteration. It is concluded that the planning and 3D printing are suitable to perform craniofacial reconstructions with a low morbidity, shorter surgical time, and with an adequate facial symmetry and aesthetic return.
The Freeze-Tag Problem (FTP) is a scheduling-like problem motivated by robot swarm activation. The input consists of the locations of a set of mobile robots in some metric space. One robot is initially active, while the others are initially frozen. Active robots can move at unit speed, and upon reaching the location of a frozen robot, the latter is activated. The goal is to activate all the robots within the minimum time, i.e., minimizing the time the last frozen robot is activated, the so-called makespan of the schedule. Arkin et al. proved that FTP is strongly NP-hard even if we restrict the problem to metric spaces arising from the metric closure of an edge-weighted star graph, where a frozen robot is placed on each leaf, and the active robot is placed at the center of this star [Arkin et al. 2002]. In this work, we continue to explore the complexity of FTP and show that it keeps its hardness even if further restricted to binary unweighted rooted trees with frozen robots only at leaves and the active robot on its root. Additionally, we prove that a generalized version, whose domain includes ternary weighted trees, remains hard, even if we require that every non-root node has precisely one frozen robot.
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