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A hexagonal grid changes which moves an autorouter can make: instead of routing only horizontally and vertically, it can use tracks at 0° and ±60°. That geometry is a research-backed alternative in specific channel-routing models, but the cited results do not establish that it improves a modern PCB autorouter. Whether it reduces wire length or congestion on a real board must be measured against the existing router under identical constraints.
What a hexagonal routing grid changes
A routing grid defines the legal locations and directions available to the search algorithm. In the cited hexagonal channel-routing models, tracks run horizontally and at +60° and −60° (Tan and Song, 1999; Tan and Song, 1995). Compared with a grid limited to horizontal and vertical moves, this offers additional directions for connecting terminals.
The potential benefit is geometric flexibility: a path may fit a channel or avoid a conflict using angled tracks. But extra legal moves do not by themselves guarantee shorter routes, fewer vias, less congestion, or faster routing. Those outcomes depend on the board, design rules, routing costs, and search strategy.
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Hexagonal channel-routing results
Tan and Song’s 1999 multiterminal channel-routing 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 (paper abstract). A 1995 paper on three-layer channel routing reports a width bound of w ≤ 2d + 1 for density d (paper abstract).
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These are results for different channel-routing models and layer assumptions. Their bounds should not be read as a direct head-to-head comparison, nor as proof that a hexagonal grid improves PCB autorouting.
Related PCB routing results
A 1995 study of a diagonal multilayer router for multiterminal printed circuit boards reports route length reductions of up to 20% and total route-time reductions of up to 30% in its comparisons (paper abstract). This is relevant evidence that diagonal routing has been explored for PCB routing, but it is not a test of the exact hexagonal-grid proposal described here. The figures are historical claims from that study’s comparisons, not expected gains for another router.
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Other work shows why grid geometry should be assessed alongside the rest of the routing method. A 1989 high-density printed wiring board router paper describes nonuniform grids and a hierarchy of global routing, detailed routing, and design-rule checking; its abstract reports reducing grid points to 1/20 of those in the conventional method it describes (paper abstract). That result concerns nonuniform grids, not hexagonal topology.
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Why a hexagonal grid may help—or may not
Potential advantages
- More directional choices: Angled moves can offer paths unavailable on an orthogonal grid, potentially helping in channels where the added orientations fit the geometry.
- A different representation of routing space: A grid’s topology can affect the paths the algorithm considers and the conflicts it encounters. This makes geometry a worthwhile variable to test, not a guaranteed performance improvement.
Costs and constraints to account for
- Board rules still govern legality: The router must preserve trace width, clearance, and other board-specific constraints regardless of grid geometry.
- Layer transitions need explicit treatment: The graph must define how moves between layers and vias work; a planar change in move directions does not settle those choices.
- Search behavior can confound results: Net ordering, cost functions, rip-up and reroute policies, and detailed-routing behavior can all affect outcomes independently of the grid.
How to evaluate a hexagonal-grid router
Compare the proposed router with the current one using the same board set, connectivity requirements, and design rules. Define the grid graph and its legal moves before running the test, and represent layer transitions and vias explicitly. A recent 2025 IEEE paper abstract on variable-rule PCB escape routing describes congestion-avoiding initialization, rip-up and reroute, and length-aware detailed routing—concerns that illustrate why a useful evaluation must include more than path geometry. It does not report a hexagonal-versus-orthogonal comparison (paper abstract).
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- Hold the problem constant. Use the same boards, nets, rule constraints, and stopping criteria for both routers.
- Define the movement graph. Specify the legal horizontal and ±60° moves, grid spacing, layer connections, and via representation. Ensure the design-rule checks apply to the resulting geometry.
- Measure multiple outcomes. Record completion rate, unrouted connections, wire length, via count, congestion, runtime, and design-rule violations. A shorter route is not an improvement if it leaves more connections unrouted or violates rules.
- Isolate the geometry effect. Keep net ordering, cost functions, rip-up/reroute policy, and detailed-routing method fixed, then run ablations that vary those factors separately. This helps distinguish gains from movement directions from gains caused by other algorithm changes.
- Report the test conditions. State the board set, rules, router settings, and measurement method with the results so that any claimed improvement is interpretable.
What conclusion is justified today?
Hexagonal movement is a legitimate alternative for routing models that use horizontal and ±60° tracks, and the cited channel-routing papers establish bounds within their stated models. Related diagonal PCB work offers historical evidence worth considering, but it does not answer whether a contemporary PCB autorouter will improve with a hexagonal grid. The cited material does not establish a contemporary open benchmark comparing hexagonal and orthogonal PCB autorouting; the practical answer therefore depends on a controlled, rule-compliant evaluation on the boards the router is meant to handle.
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