The Steinberg Wiring Problem

In a paper Leon Steinberg described a backboard wiring problem that has resisted solution for years The problem concerns the placement of computer components so as to minimize the total amount of wiring required to connect them In the particular instance considered by Steinberg components with a total of interconnections are to be placed on a backboard with open positions The geometry of the backboard is illustrated in Figure To formulate the wiring problem mathematically it is convenient to add dummy components with no connections to any others so that the numbers of components and locations are both n Letting aik be the number of wires that connect components i and k bjl be the distance between locations j and l on the backboard and doubling the objective the problem can be written in the form