A hexagonal routing grid changes which directions an autorouter can use: instead of only horizontal and vertical moves, the model permits tracks running horizontally and at +60° and −60°. That can be a useful alternative in particular routing problems, but historical channel-routing results do not prove that it improves a modern PCB autorouter. The practical answer is to implement it as a controlled routing option and measure it against the existing router on the same boards and design rules.
What a hexagonal routing grid changes
A grid is a graph: its points are routing locations, and its edges are the legal moves between them. In the hexagonal model described by the cited channel-routing papers, tracks follow three orientations—horizontal, +60°, and −60°—rather than being limited to orthogonal directions. The change is therefore not simply a different way to draw a grid; it changes the paths the algorithm is allowed to consider.
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Whether those extra directions help depends on the board geometry, routing constraints, and the rest of the algorithm. The available studies do not establish a contemporary benchmark comparison between hexagonal and orthogonal PCB autorouting.
What the hexagonal channel-routing papers establish
Three-layer channel routing
Tan and Song’s 1995 paper reports a channel width of w ≤ 2d + 1 for density d in its three-layer model. This is a bound for the paper’s channel-routing problem, not a general PCB routing guarantee. See the 1995 paper abstract.
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Multiterminal channel routing
Tan and Song’s 1999 paper reports a channel width of d + 3 for problem density d. It also says the resulting layout can be wired using four layers without overlaps among layers. These findings describe that paper’s multiterminal channel-routing model. They should not be read as directly competing with the 1995 bound without comparing the models’ assumptions and constraints. See the 1999 paper abstract.
Neither result demonstrates that a hexagonal grid shortens routes, reduces congestion, or improves completion rates on present-day PCB designs. Channel width in a defined model is not the same outcome as performance across real boards with manufacturing rules, obstacles, vias, and multiple routing layers.
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Related PCB routing results are not hexagonal-grid results
A 1995 study of diagonal multilayer routing for multiterminal printed circuit boards reported route-length reductions of up to 20% and total route-time reductions of up to 30% in its comparisons. Those are historical abstract claims for that study’s diagonal-routing method; they are not measurements of the exact three-direction hexagonal proposal. See “An efficient multi-layer diagonal router for multi-terminal printed circuit boards”.
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Grid geometry is also only one part of router design. A 1989 high-density printed-wiring-board study described nonuniform grids and a hierarchy of global routing, detailed routing, and design-rule checking. Its abstract reports reducing grid-point count by a factor of 1/20 compared with the conventional method it describes. That is a result about its nonuniform-grid approach, not evidence for hexagonal topology. See Takagi, Mori, and Odawara’s paper.
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How to test whether hexagonal moves help a PCB autorouter
First define the routing graph precisely. Specify the legal move vectors and how those moves map to board coordinates; then ensure the representation can enforce the board’s actual trace-width, clearance, obstacle, and layer rules. The router must also define how transitions between layers work and how vias are counted and constrained. Without those details, a comparison may test a different rule set rather than grid geometry.
Compare the hexagonal option with the current router on the same board set, using identical constraints and stopping conditions. Keep net ordering, routing costs, and rip-up/reroute policy fixed for the main comparison. Then use ablations—controlled variants that change one factor at a time—to distinguish the effect of movement directions from changes to those other algorithm choices.
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Report at least these outcomes:
- Completion rate and the number of connections left unrouted.
- Total wire length and via count.
- Congestion, runtime, and design-rule violations.
- Whether each result satisfies the same board-specific constraints.
Length alone is not enough: a router might find shorter paths while leaving more connections unrouted, adding vias, taking longer, or violating rules. A useful result therefore reports the full set of outcomes rather than treating one metric as proof of overall improvement.
Why constraints and routing strategy still matter
A 2025 IEEE paper abstract describes variable-rule PCB escape routing that combines congestion-avoiding initialization, rip-up and reroute, and length-aware detailed routing. It does not compare hexagonal and orthogonal movement. Its relevance is that modern routing evaluation involves more than choosing a grid direction: rules, congestion management, rerouting, and detailed-route quality all affect the result. See the 2025 paper abstract.
Accordingly, a fair hexagonal-grid experiment should preserve the same board rules and routing strategy in both versions, while separately testing any proposed changes to the strategy. The existing evidence supports hexagonal movement as a research-backed alternative for specific routing models; whether it improves a modern PCB autorouter remains an empirical question.
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