Path-Value Density (PVD) Ranking

The problem

It is difficult to determine which route is the most efficient when you have to balance the importance of a destination against the effort required to get there. People often struggle to see which path offers the most value for the least amount of work.

What it does

It calculates a score for different paths by weighing the importance of the points reached against the amount of steps taken. It then ranks these paths to show which ones provide the most value.

Why it matters

It provides a clear way to identify the most efficient routes by balancing goals with effort.

Validation

It was run inside an isolated container with no network access. This is the exact command and the real output it produced — captured process output, not written by a model.

$ python3 pvd_ranking.py
Path-Value Density (PVD) Rankings:
B-D: 1.10
A-B: 0.90
A-B-D: 0.70
A-C-D: 0.26

A screenshot of that run.

A clean run proves this does what is shown above, in a CPU-only sandbox. It is a small research demo — not a production tool, and nothing here was published anywhere.

The code

All of it — 63 lines, one file, standard library only.

# pvd_ranking.py

graph = {
    'A': {'B': 2, 'C': 3},
    'B': {'D': 1},
    'C': {'D': 4},
    'D': {}
}

node_importance = {
    'A': 1.0,
    'B': 0.8,
    'C': 0.5,
    'D': 0.3
}

paths_to_evaluate = [
    ['A', 'B', 'D'],
    ['A', 'C', 'D'],
    ['A', 'B'],
    ['B', 'D']
]

def calculate_pvd(path):
    total_importance = 0
    total_effort = 0
    valid = True

    for i, node in enumerate(path):
        if node not in node_importance:
            valid = False
            break
        total_importance += node_importance[node]

        if i < len(path) - 1:
            next_node = path[i+1]
            if next_node not in graph[node]:
                valid = False
                break
            total_effort += graph[node][next_node]

    if not valid:
        return float('-inf')  # Invalid paths get lowest score

    if total_effort == 0:
        return float('inf')  # Handle division by zero

    return total_importance / total_effort

def main():
    scores = {}
    for path in paths_to_evaluate:
        path_name = '-'.join(path)
        scores[path_name] = calculate_pvd(path)

    ranked_paths = sorted(scores.items(), key=lambda x: x[1], reverse=True)

    print('Path-Value Density (PVD) Rankings:')
    for path_name, score in ranked_paths:
        print(f'{path_name}: {score:.2f}')

if __name__ == '__main__':
    main()