Order-Picking in a Rectangular Warehouse: A Solvable Case of the Traveling Salesman Problem

in press. 17 H and L chain preparations in 1 M propionic acid were mixed in the ratio of 3: 1 based on O.D. and then dialyzed against cold water followed by borate buffer. 18 This arc was not apparent in the plate of the original y-globulin nor in any of the other plates. It did not appear when the horse anti-rabbit globulin was absorbed with normal rabbit 72-globulin prior to diffusion. Since it appears to fuse with the more prominent arc, the protein responsible for it presumably contains only some of the antigenic determinants on the rest of the reconstituted molecules. Given an nxn matrix D of nonnegative numbers di,, the traveling salesman problem for D is the problem of finding a cyclic permutation r of 1,..., n, called a tour, n for which C(r), defined to be E diTn, is a minimum. The bottleneck traveling i = 1 salesman problem for D is the problem of finding a tour r for which MC(T), defined to be Max { dij, is a minimum.1 1 <i <n The purpose of this note is to announce a solution to the traveling salesman problem and the bottleneck traveling salesman problem for a special class of matrices. The solution of the bottleneck traveling salesman problem provides also a solution to the problem of characterizing those directed graphs, of a certain well-defined class, which possess Hamiltonian circuits. Proofs will be given in outline