How do I partition/split a graph evenly?

Question

I'm currently trying to parallelize an astar algorithm and I'm trying to split the graph based on the number of processes. The structure of the graph is similar to a grid and Here is my attempt

if __name__ == "__main__":
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
size = comm.Get_size()
file_path = "grid_graph.txt"
graph = None
assigned_nodes = []

if rank == 0:
    graph = load_graph(file_path)


graph = comm.bcast(graph, root=0)
total_nodes = len(graph)
num_processes = comm.Get_size()


base_num_nodes = total_nodes // num_processes
remaining_nodes = total_nodes % num_processes


start_index = rank * base_num_nodes
end_index = (rank + 1) * base_num_nodes

if rank < remaining_nodes:
    start_index += rank
    end_index += rank + 1
else:
    start_index += remaining_nodes
    end_index += remaining_nodes

assigned_nodes = list(graph.keys())[start_index:end_index]

all_assigned_nodes = comm.gather(assigned_nodes, root=0)

if rank == 0:
    for process_rank, nodes in enumerate(all_assigned_nodes):
        print("Process", process_rank, "assigned nodes:", nodes)
print("Process", rank, "assigned nodes:", assigned_nodes)
start = Node((0, 0))
goal = Node((2, 2))

try:
    start_time = time.time()
    path = astar(start, goal, graph)
    print("Process", rank, "Path found:", path)
    print("Process", rank, "Total cost:", total_cost(path, graph))
    print("Process", rank, "Execution time:", time.time() - start_time, "seconds")
except ValueError:
    print("Process", rank, "No path found")

the problem here is that some of the nodes in the subgraphs have no neighbors. How do I partition the graph so that all the nodes in the graph are connected or at least there is a searchable path?

Please show, for a small simple graph, the input and output that demonstrates the problem. Also, please clarify "based on the number of processes." What are these "processes"? — ravenspoint, Jul 08 '23 at 12:43
" nodes in the subgraphs have no neighbors." Perhaps your question should be: "How to split a connected graph so every node has at least one neighbor ( no component is smaller than 2)" — ravenspoint, Jul 08 '23 at 12:46
Your indentation is clearly wrong, but what’s less clear is how this ought to be indented. Don’t make us guess; please [edit] to fix this. (On the desktop version of this site, paste your program, select it, and type ctrl-K to properly format it as code.) — tripleee, Jul 08 '23 at 13:05

score 0 · Answer 1 · answered Jul 08 '23 at 12:49

0

IF

your real question is: "How to split a connected graph so every node as at least one neighbor ( no component is smaller than 2)"

THEN

Do not consider for removal any link that connects a node of degree 1.

answered Jul 08 '23 at 12:49

ravenspoint

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score 0 · Answer 2 · answered Jul 09 '23 at 06:26

If you are interested to the details of the algorithms for graph partitioning, then search for the Louvain algorithm or the Kernighan-Lin algorithm. There are more advanced algorithms, but these two will get you started. You need to be aware that this is a rather complex topic though.

If, instead, you only need to use one graph partitioning algorithm, then search for a graph partitioning library. They are many, including Métis, ParMetis, Zoltan, KaHIP (Karlsruhe High Quality Hypergraph Partitioning, includes many different algorithms), PARTY and Mongoose.

How do I partition/split a graph evenly?

2 Answers2