miniz | Single C source file zlib-replacement library | Compression library

I'm trying to set up a shiny server on the free tier AWS EC2 to test my app but I can't get all the packages compiled and installed.

e.g. duckdb

in the terminal connected to my instance I paste:

TL;DR: Short problem description:

I am looking for an efficient algorithm that optimizes how N agents, located in 2D space, can be placed into M shelters by minimizing the distance the agents need to travel.

Each shelter can only hold 1 agent. If N > M (more agents than available shelters), then some agents will not get placed into shelters (all agents are the same).

(Optional simplification: while agents can be freely located in 2D space, shelters are always arranged on a square grid. No agent is located outside of the convex hull of shelters.)

This is all you need to know. However, if you think that this problem has no efficient solution then here is ...

a more specific (and to me most relevant) version of the problem:

There are exactly 9 shelters, arranged on a square grid (with distance d). All N agents are located around the central shelter (in a box of size d*d centered around central shelter). However, in this case, the central shelter is always empty but all other shelters may or may not be available (empty) at the beginning.

For this case, I need an algorithm that solves the problem of arbitrary many agents N (typically N < 9) and arbitrary shelters being available (either all 9, or in the extreme case only the central shelter).

The algorithm should be efficient, since I need to solve many of these problems quickly.

Example:

Here is an example with N=3 agents (black dots) and M=5 available shelters (green dots). The red dots show non-available shelters. ]1 I use letters for shelters and numbers for agents.

What I did so far:

I am sure that this problem has a specific name and has been solved/studied already, but I cannot find its name or any solutions. I need to solve many of those problems fast and I always want the optimal solution (if thats not possible, an almost optimal solution is also sufficient). Here is what I tried/thought of so far:

1. Brute force: I know that the optimal solution to the problem can be found with brute force by checking all possible options, calculating the total travel distance for each and picking the option with smallest total travel distance. This may involve many computations if M and N are large.
2. A fast but very non-optimal solution works as follows: for each agent i, calculate the distance to central node E. Starting from the agent i with smallest distance to E, assign i to its closest shelter (in this case: E). Then assign the next agent to its closest shelter, considering that E is now not available anymore, etc, until all agents are assigned or stop if no more free shelters are available. This works, is fast, but of course produces non-optimal results (in the example image: 2->E, 1->B, 3->F, while the optimal solution should be 3->E, 2->F, 1->B)
3. Another idea I'm working on is to first find the agents that are under the most "pressure", i.e. all of their good options are far away. Starting with the agent under highest pressure, assign it to the closest shelter. Continue for all other agents. However, I am not sure how to properly define "pressure" for this problem, as it likely should be a combination of the distances to the first few shelters. Also, I am not sure that this will lead to the optimal solution, but may result in an almost optimal solution.
4. I am trying to think of this problem as some sort of weighted permutation, that is, I need to select N shelters and map them to the N agents, but each mapping comes at a cost. I need to minize the total cost, but I have no idea how to do this.
5. Also, I am thinking of some sort of Simulated Annealing, or some form of push-and-pull algorithm where each shelter is attracting agents, or agents are attracted to shelters based on their distance. While this may sound interesting, I would expect that this is computationally not efficient.

I am happy for any input, especially if this problem already has a proper name and solutions. I am also happy for a simple and fast-to-compute algorithm that achieves an almost optimal solution.

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