Minimum spanning tree
A minimum spanning tree is a spanning tree of a connected, weighted, undirected graph having the smallest possible total edge weight.
Optimization Algorithms: AI techniques for design, planning, and control problems
An algorithm that finds a minimum-weight tree connecting every node of a connected weighted graph.
- How it is used
- Frames minimum spanning trees as an informed-search solution for connecting networks while minimizing total edge cost.
- How deep it goes
- Defines spanning trees, compares three algorithms, works through Kruskal, and demonstrates Python implementation without formal proofs.
- Examples
- Uses the muddy city road-repair problem, toy graph figures, a NetworkX graph, and a University of Toronto street network.
- What you can do after
- Apply it via NetworkX and OSMnx to compute, visualize, and inspect minimum spanning trees for toy or street-network graphs.
Classic Computer Science Problems in Swift: Essential techniques for practicing programmers
A minimum spanning tree is a spanning tree of a weighted graph whose total edge weight is minimal among all spanning trees of that graph.
- How it is used
- Frames minimum-cost network design as connecting every node without cycles.
- How deep it goes
- Defines trees, cycles, connected graphs, and spanning trees, then implements Prim's algorithm with a priority queue.
- Examples
- Uses a 15-city distance graph, printed adjacency lists, selected MST edges, and a total weight of 5,372.
- What you can do after
- Apply it via Swift by constructing a weighted graph and calling mst(start:) to obtain selected edges.
Related concepts
- spanning treekind of · A spanning tree is a tree subgraph of a connected graph that contains every vertex.
- treekind of · A tree is a connected, acyclic structure of nodes, commonly organized hierarchically through parent-child relationships and optionally around a designated root.
- Jarnik's algorithmproduced by · Jarnik’s algorithm, also called Prim’s algorithm, is a greedy algorithm that constructs a minimum spanning tree by repeatedly adding the lowest-weight edge connecting the current tree to an outside vertex.
- Kruskal's algorithmproduced by · Kruskal’s algorithm is a greedy algorithm that constructs a minimum spanning tree by adding edges in nondecreasing weight order when they connect separate components.
- Traveling Salesman problemcontrasts with · The Traveling Salesman problem is a combinatorial optimization problem that seeks a minimum-cost tour visiting each specified location exactly once and returning to the starting location.
- informed searchaddressed by · Informed search is a search strategy that uses problem-specific knowledge or heuristic estimates to prioritize promising states or paths.
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