利用竞争动力学在网络中寻找大型独立集
Finding Large Independent Sets in Networks Using Competitive Dynamics
AI总结：
本文研究生物物种在网络中的竞争共存动力学，发现其可恢复最大独立集问题的近最优解，并基于分岔级联与Katz中心性的联系提出一种生物启发的离散近似算法。
摘要：
许多决策算法从单个生物系统的内部运作中获得灵感。然而，生物物种之间的集体行为是否也能为计算任务提供解决方案，目前仍不清楚。通过研究在网络上通过简单规则相互作用的物种共存现象，我们证明了底层动力系统能够恢复最大独立集问题的近最优解——这是图论中一个基本且计算困难的问题。此外，我们观察到，当系统中的竞争压力逐渐增大时，这些解的最优性会得到改善。我们通过证明以下现象来解释这一结果：随着竞争压力上升，动力系统中出现的分岔点级联自然会导致网络中基于Katz中心性的节点移除。通过形式化这一联系，我们提出了一种受生物学启发的离散算法，用于近似求解图上的最大独立集问题。我们的结果表明，复杂系统可能集体具备执行非平凡计算的能力，其意义涵盖生物学、经济学及其他领域。
英文摘要：
Many decision-making algorithms draw inspiration from the inner workings of individual biological systems. However, it remains unclear whether collective behavior among biological species can also lead to solutions for computational tasks. By studying the coexistence of species that interact through simple rules on a network, we demonstrate that the underlying dynamical system can recover near-optimal solutions to the maximum independent set problem -- a fundamental, computationally hard problem in graph theory. Furthermore, we observe that the optimality of these solutions is improved when the competitive pressure in the system is gradually increased. We explain this phenomenon by showing that the cascade of bifurcation points, which occurs with rising competitive pressure in our dynamical system, naturally gives rise to Katz centrality-based node removal in the network. By formalizing this connection, we propose a biologically inspired discrete algorithm for approximating the maximum independent set problem on a graph. Our results indicate that complex systems may collectively possess the capacity to perform non-trivial computations, with implications spanning biology, economics, and other fields.
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