Researchers at the Georgia Institute of Technology described a heuristic for the Traveling Salesman Problem that orders points according to a spacefilling curve, producing tours that are typically about 25% longer than optimal but can be generated quickly.

A spacefilling curve is a continuous mapping that fills a higher‑dimensional space, and the Sierpinski curve is constructed by repeatedly copying and shrinking a pattern. Points that are close in the plane remain close in the curve’s sequence, which supports the heuristic.

The algorithm constructs a tour of n points in O(n log n) time and can update the solution by adding or removing points in O(log n) time. It does not require explicit distance calculations between points, and it is parallelizable, unlike the comparable Nearest Neighbor method.

The heuristic has been applied to several practical problems. It was used to design routing for Meals‑on‑Wheels in Fulton County, Georgia, to schedule blood deliveries for the American Red Cross in the Atlanta metropolitan area, and to plan targeting for a space‑based laser under the Strategic Defense Initiative, as reported by scientists from TRW Systems. The method also reduced drawing time for large road maps when employed with a pen‑plotter, according to work by M. Iri and colleagues at the University of Tokyo.

The approach has been incorporated into commercial GIS and logistics tools, including the ARC/Info Geographic Information System and the Baan CAPS Logistics Toolkit.

In a comparison with an optimal TSP solver developed by D. Applegate, R. Bixby, V. Chvatal, and W. Cook, the spacefilling curve solution for a 15,112‑city instance in Germany was about 34% longer than the optimal tour while being computed in less than a second on a standard laptop. The optimal computation required 22.6 years of processor time on a network of 110 processors. At a travel rate of 600 km per day, the longer route would take roughly 147 days versus 110 days for the optimal solution.

The researchers also extended the method to robust multidimensional searching, continuous indexing of hierarchical globe subdivisions, vertex‑labeling algorithms for the Hilbert curve, and a Hamiltonian cycle in the vertex‑adjacency dual of a triangulated irregular network, as detailed in publications from 1994 to 2004. Perouz Taslakian provided an illustration of these concepts.

The study demonstrates a trade‑off between solution quality and computation speed, offering rapid route generation at the cost of increased travel distance.