The crossing resolution of a non-planar drawing of a graph is the value of the minimum angle formed by any pair of crossing edges. Recent experiments suggest that the larger the crossing resolution is, the easier it is to read and interpret a drawing of a graph. However, maximizing the crossing resolution turns out to be an NP-hard problem in general, and only heuristic algorithms are known that are mainly based on appropriately adjusting force-directed algorithms. In this paper, we propose a new heuristic algorithm for the crossing resolution maximization problem and we experimentally compare it against the known approaches from the literature. Our experimental evaluation indicates that the new heuristic produces drawings with better crossing resolution, but this comes at the cost of slightly higher edge-length ratio, especially when the input graph is large.

Understanding forest functioning is limited by the scalability of monitoring solutions and difficulty of access. Manual sensor placement can reach most locations but lacks scalability. Micro‐aerial vehicles (MAVs) allow for scalable sensor delivery, but current solutions are limited to attaching sensors to the trunk or large branches with spines or adhesives. The thinner branches of the outer canopy remain inaccessible, despite being of particular interest due to the important physiological processes occurring in the foliage. Herein, a MAV‐deployable bistable helically coiling origami gripper is developed. The unfurled state allows for transport with a MAV, and when pushed against a branch triggers the second helically coiled state, which permits secure attachment to branches. Origami manufacturing keeps the weight of the gripper below 5 g, despite holding up to 280 g, and gripping diameters from 8 mm to 38 mm inclined up to 30°. The holding force, activation force, and resistance to tilt and rotation offsets are experimentally characterized. The deployment and retrieval of the gripper and sensor are demonstrated outside, where sensor data are collected from previously inaccessible branches in the outer canopy. Enabling robust sensor attachment in the outer canopy marks a step toward scalable environmental monitoring of forest ecosystems.

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The crossing resolution of a non-planar drawing of a graph is the value of the minimum angle formed by any pair of crossing edges. Recent experiments have shown that the larger the crossing resolution is, the easier it is to read and interpret a drawing of a graph. However, maximizing the crossing resolution turns out to be an NP-hard problem in general and only heuristic algorithms are known that are mainly based on appropriately adjusting force-directed algorithms. In this paper, we propose a new heuristic algorithm for the crossing resolution maximization problem and we experimentally compare it against the known approaches from the literature. Our experimental evaluation indicates that the new heuristic produces drawings with better crossing resolution, but this comes at the cost of slightly higher aspect ratio, especially when the input graph is large.