How to Use
Select graph:
- cw: Cutwidth value
- Layout: Best ordering
- Cut: Max edges crossing
Relationships
bandwidth(G) ≤ cutwidth(G). pathwidth(G) ≤ cutwidth(G). cutwidth(G) ≤ pathwidth(G) · Δ(G). For trees: cutwidth = pathwidth + 1. Tight connections between layout parameters.
VLSI Applications
Cutwidth = maximum wire congestion in a linear VLSI layout. Minimizing cutwidth reduces wire density, heat, crosstalk. Critical for PCB design: component placement on a line with minimum routing congestion.
Step-by-Step Instructions
- 1Select graph.
- 2Try orderings.
- 3Count edge cuts.
- 4Find minimum max.
- 5Apply layout.
Graph Cutwidth Calculator — Frequently Asked Questions
How does cutwidth differ from bandwidth?+
Bandwidth: max stretch of any single edge. Cutwidth: max number of edges crossing any cut. Bandwidth minimizes longest wire; cutwidth minimizes densest cross-section. bandwidth ≤ cutwidth always.
What's the cutwidth of a tree?+
For trees: cw(T) = pw(T) + 1 where pw is pathwidth. Trees have nice recursive structure: cutwidth can be computed in polynomial time via dynamic programming. General graphs: NP-hard.
What's topological bandwidth?+
Allow subdivisions: add vertices on edges, then minimize bandwidth. Topological bandwidth ≤ cutwidth. Measures a 'smoothed' version of layout complexity.
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