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Some biological experiments show that the tubular structures of Physarum polycephalum are often analogous to those of Steiner trees. Therefore, the emerging Physarum-inspired Algorithms (PAs) have the potential of computing Steiner trees. In this paper, we propose two PAs to solve the Steiner Tree Problem in Graphs (STPG). We apply some widely-used artificial and real-world VLSI design instances to evaluate the performance of our PAs. The experimental results show that: 1) for instances with hundreds of vertices, our first PA can find feasible solutions with an average error of 0.19%, while the Genetic Algorithm (GA), the Discrete Particle Swarm Optimization (DPSO) algorithm and a widely-used Steiner tree approximation algorithm: the Shortest Path Heuristic (SPH) algorithm can only find feasible solutions with an average error above 4.96%; and 2) for larger instances with up to tens of thousands of vertices, where our first PA, GA and DPSO are too slow to be used, our second PA can find feasible solutions with an average error of 3.69%, while SPH can only find feasible solutions with an average error of 6.42%. These experimental results indicate that PAs can compute Steiner trees, and it may be preferable to apply our PAs to solve STPG in some cases.

It is challenging to design large and low-cost communication networks. In this paper, we formulate this challenge as the prize-collecting Steiner Tree Problem (PCSTP). The objective is to minimize the costs of transmission routes and the disconnected monetary or informational profits. Initially, we note that the PCSTP is MAX SNP-hard. Then, we propose some post-processing techniques to improve suboptimal solutions to PCSTP. Based on these techniques, we propose two fast heuristic algorithms: the first one is a quasilinear time heuristic algorithm that is faster and consumes less memory than other algorithms; and the second one is an improvement of a stateof-the-art polynomial time heuristic algorithm that can find high-quality solutions at a speed that is only inferior to the first one. We demonstrate the competitiveness of our heuristic algorithms by comparing them with the state-of-the-art ones on the largest existing benchmark instances (169 800 vertices and 338 551 edges). Moreover, we generate new instances that are even larger (1 000 000 vertices and 10 000 000 edges) to further demonstrate their advantages in large networks. The state-ofthe-art algorithms are too slow to find high-quality solutions for instances of this size, whereas our new heuristic algorithms can do this in around 6 to 45s on a personal computer. Ultimately, we apply our post-processing techniques to update the bestknown solution for a notoriously difficult benchmark instance to show that they can improve near-optimal solutions to PCSTP. In conclusion, we demonstrate the usefulness of our heuristic algorithms and post-processing techniques for designing large and low-cost communication networks.

The Steiner tree problems are well-known NP-hard problems that have diverse applications. Duin et al. (2004) have intuitively proposed the widely-used transformation from the classical group Steiner tree problem to the classical Steiner tree problem in graphs. This transformation has not been rigorously proven so far. Specifically, the large M value that is used in this transformation has not been specified. In this paper, we address this issue by rigorously prove this transformation for a specific large M value.

Star sensor's image plane can have three kinds of displacement after a long time working in space, and the displacements are the principal point drift, incline displacement and rotation displacement. These displacements can severely decrease star sensor's measuring accuracy, therefore it's necessary to analyze and calibrate them. The previous researches have only considered the principal point drift of image plane, which is three-degree-of-freedom. In contrast, the image plane displacements under the rest three degrees of freedom, that are the incline displacement and the rotation displacement, have been modeled in this paper. These two kinds of displacement's influences on star sensor's accuracy have been analyzed. And the necessity to calibrate them has been pointed out. At last, the Extended Kalman Filter has been used to on-orbit calibrate the six-degree-of-freedom image plane displacement. And the simulation results reveal that the on-orbit calibration algorithm can effectively calibrate the image plane displacement of star sensor. The measuring accuracy of star sensor has been increased to 0.23'' after the calibration. Therefore the new six-degree-of-freedom image plane displacement model has made up the deficiency of the conventional displacement model and enhance the performance of star sensor greatly.

The popular Physarum-inspired Algorithms (PAs) have the potential to solve challenging network optimization problems. However, the existing researches on PAs are still immature and far from being fully recognized. A major reason is that these researches have not been well organized so far. In this paper, we aim to address this issue. First, we introduce Physarum and its intelligence from the biological perspective. Then, we summarize and group four types of Physarum-inspired networking models. After that, we analyze the network optimization problems and applications that have been challenged by PAs based on these models. Ultimately, we discuss the existing researches on PAs and identify two fundamental questions: 1) What are the characteristics of Physarum networks? 2) Why can Physarum solve some network optimization problems? Answering these two questions is essential to the future development of Physarum-inspired network optimization., Comment: Physarum polycephalum; nature-inspired algorithm; data analytics