👀 Views: 5 💬 Answers: 1 📅 Created: 2025-06-03

dijkstra graph algorithm performance Python

I've been working on this all day and I'm relatively new to this, so bear with me. I'm working on a project where I need to implement Dijkstra's algorithm to find the shortest paths in a large, sparse graph represented using an adjacency list. I noticed that my current implementation is running slower than expected, especially when dealing with graphs that have tens of thousands of nodes but very few edges. I'm using Python 3.9 and the `heapq` library for maintaining the priority queue, but I suspect I might not be using it optimally. Here's a simplified version of my current implementation: ```python import heapq from collections import defaultdict class Graph: def __init__(self): self.graph = defaultdict(list) def add_edge(self, u, v, weight): self.graph[u].append((v, weight)) self.graph[v].append((u, weight)) # For undirected graph def dijkstra(self, start): heap = [] distances = {node: float('infinity') for node in self.graph} distances[start] = 0 heapq.heappush(heap, (0, start)) while heap: current_distance, current_node = heapq.heappop(heap) if current_distance > distances[current_node]: continue for neighbor, weight in self.graph[current_node]: distance = current_distance + weight if distance < distances[neighbor]: distances[neighbor] = distance heapq.heappush(heap, (distance, neighbor)) return distances ``` The algorithm works, but I noticed that for some nodes, the distances are calculated multiple times before reaching the final shortest path, which seems inefficient. When I run it on larger datasets, I get timeouts as the graph size increases. I also see warning messages about 'heap size limit exceeded' when the graph is especially sparse with many nodes but fewer edges. I've read that using a different data structure like a Fibonacci heap could help improve the performance, but I'm not sure how to implement that in Python. Is it worth the effort for a sparse graph, or are there optimizations I can apply to my current implementation with `heapq`? Any insights or suggestions would be appreciated! My development environment is Linux. I'm on Ubuntu 22.04 using the latest version of Python. Any ideas what could be causing this?