Graph Cost

Overview

Graph Cost

graph weighted graph graph metric cost function edge weight path cost scalar numeric

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🔥 Minimum Spanning Tree → MST is defined by minimizing the total edge weights; its greedy algorithms (Kruskal, Prim) and correctness proofs rely on cost orderings and cut/cycle comparisons derived from the graph's weight model.

🔥 Shortest Path → Shortest path algorithms minimize cumulative edge weights; the cost model defines path weight and dictates algorithm choice (e.g., non-negative costs -> Dijkstra, negative edges -> Bellman-Ford).

🔥 Maximum Spanning Tree → A maximum spanning tree is defined by maximizing the sum of edge costs; it requires a well-defined edge-weight (cost) function and comparisons over those costs. Algorithm choices (e.g., Kruskal/Prim variants) operate by ordering edges by cost and rely on properties of the cost model (ties, negative weights, density).

🌟 Greedy Algorithms →

🌟 Single-Pair Shortest Path →

🌟 All-Pairs Shortest Path →

🌟 Single-Source Shortest Path →

⚡️ Prim Algorithm →

⚡️ Kruskal Algorithm →

⚡️ Dijkstra Algorithm →

Network Flow →