Kurt Anstreicher, professor of management sciences in the Henry B. Tippie College of Business, working with Nathan Brixius, who earned his doctoral degree in computer science from the UI College of Liberal Arts and Sciences in 2000, discovered how to link 34 computer components together on a 9-by-4 grid using the shortest-possible wiring scheme. The problem, formally know as "ste36a" and based on the design of a UNIVAC computer, was posed by researcher Leon Steinberg in 1961. The solution to the problem was scheduled to be presented at a Friday, Oct. 12 mathematics workshop held in Berlin, Germany.
Anstreicher says that because there are only 36 possible locations for components, with a total of 2,625 connections between them, the wiring problem may not seem very difficult. However, the number of possible solutions is about "5E40," or the number represented by the number 5 followed by 40 zeros. The algorithm that solved the problem considered about 1.8 billion sub-problems and required about 18 days running on a single 800-megahertz personal computer.
"This may sound like a lot, but it is in fact much less time than anyone would ever have thought possible," Anstreicher says. In the summer of 2000 Anstreicher, Brixius, and colleagues from Argonne National Lab used an average of 650 computers for a week to solve the "nug30" problem, posed in 1968. "People who work on such problems thought that the wiring problem would be harder to solve than nug30, but it turned out to be much easier," says Anstreicher. "We learned techniques in the course of solving nug30 that were very effective in speeding up the solution of Steinberg's problem."
Like the nug30 problem, the wiring problem is a "quadratic assignment problem," or QAP. Such problems arise in the field of location theory, and are known to be extremely difficult to solve. Other applications of QAPs include designing computer chips, and arranging departments within a hospital so as to minimize the total distance that patients must travel between them.
Brixius, a Cedar Falls native who works for Microsoft Corporation in Redmond, Wash., says the knowledge he gains from such projects helps him in his work developing project management and scheduling software. "Microsoft is not in the business of solving 40-year-old wiring problems, but there are underlying similarities between ste36a and many scheduling problems," says Brixius. "The techniques we used to solve Steinberg's problem can be adapted to help solve problems I encounter in my day-to-day work."
Looking to the future, Anstreicher says, "Problems like nug30 and ste36a were, until very recently, considered intractable. With continued improvements in algorithms and hardware, solving them could be commonplace in the not-too-distant future." Adds Brixius, "I am hopeful that our work will inspire further research that leads to even better methods for taking on difficult problems in this area."