We present a connection between two dynamical systems arising in entirely different contexts: the Iteratively Reweighted Least Squares (IRLS) algorithm used in compressed sensing and sparse recovery to find a minimum \(\ell _1\)-norm solution in an affine space, and the dynamics of a slime mold (Physarum polycephalum) that finds the shortest path in a maze. We elucidate this connection by presenting a new dynamical system – Meta-Algorithm – and showing that the IRLS algorithms and the slime mold dynamics can both be obtained by specializing it to disjoint sets of variables. Subsequently, and building on work on slime mold dynamics for finding shortest paths, we prove convergence and obtain complexity bounds for the Meta-Algorithm that can be viewed as a “damped” version of the IRLS algorithm. A consequence of this latter result is a slime mold dynamics to solve the undirected transshipment problem that computes a \((1+\varepsilon )-\)approximate solution in time polynomial in the size of the input graph, maximum edge cost, and \(\frac{1}{\varepsilon }\) – a problem that was left open by the work of (Bonifaci V et al. [10] Physarum can compute shortest paths. Kyoto, Japan, pp. 233–240).

我们提出了在完全不同的上下文中出现的两个动力学系统之间的联系：迭代加权最小二乘（IRLS）算法，用于压缩感知和稀疏恢复，以在仿射空间中找到最小\（\ ell _1 \）-范数解；以及粘液霉菌（多头Phys）的动力学）在迷宫中找到最短路径。我们通过介绍一个新的动力学系统-元算法来阐明这种联系，并表明可以通过将IRLS算法和粘液模型动力学专门用于不相交的变量集来获得IRLS算法和粘液动力学。随后，在泥模动力学的基础上寻找最短路径，我们证明了收敛性，并获得了元算法的复杂性界限，可以将其视为IRLS算法的“阻尼”版本。后一个结果的结果是粘液动力学，以解决无方向性转运问题，该问题会按时间多项式在输入图的大小，最大边缘成本和\上计算\（（（1+ \ varepsilon）-\）近似解。 （\ frac {1} {\ varepsilon} \） –（Bonifaci V等人[10] Physarum可以计算最短路径。日本京都，第233-240页）的工作遗留了一个问题。