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I am looking for some insights/discussion on the following problem:

General description:

There is a system, agents within the system and a master agent that can control the system and its enclosed agents to some extent. The system belongs to a certain Region of Interest (ROI) - assume 2-D, which is finite/bounded. The agents consist of two kinds of nodes: big and small. Small nodes 'attach' to the big nodes and big nodes talk to other big nodes. The attachment or detachment is based on a function of the distance between the nodes. (ex.: if dist < a, attachment occurs; if dist > b, detachment occurs).

System dynamics:

All nodes are 'mobile' in the sense that their positions can be changed within the ROI. Over time, big nodes and small nodes enter or leave the ROI - this is not under the control of the master agent and can be modeled as a random process (ex. Poisson). The master agent can control the positions of the nodes (big and small) within the ROI but cannot control their decision to enter/leave the ROI.

Goal:

The goal of the master agent is to find a position for each node in the ROI such that:

  1. all big nodes are connected to each other; and
  2. all small nodes are attached to at least one big node.

I'd like to hear some practical solution approaches to the above problem or simply a discussion on the possibilities.

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    Could you elaborate your setup, please? There are a lot of crucial details that are absent here. For example, what are conditions for (dis)connecting nodes? What is the reason behind movements of nodes? What can be controlled in this process? If you are interested in some topological aspects of such networks (like connectivity), you might want to take a look at Robert Ghrist's papers on similar topics. – 2017-02-28

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