\input zb-basic \input zb-ioport \iteman{io-port 04131978} \itemau{Kindervater, G.A.P.; Lenstra, J.K.; Savelsbergh, M.W.P.} \itemti{Parallel local search for the time-constrained traveling salesman problem.} \itemso{Twenty-five years of operations research in the Netherlands, Pap. Dedicated to Gijs de Leve, CWI Tracts 70, 61-75 (1989).} \itemab [For the entire collection see Zbl 0682.00019.] The problem considered is the so called time-constrained travelling salesman problem where each city has to be visited within a given time interval. Due to the presence of time windows there are feasible and unfeasible tours. This complexifies the standard local search strategy in which a given cycle is improved by changing k edges up to proving its k- optimality. A search strategy is proposed which finds a k-optimal tour in a PRAM model in O(log n) time using O(n/log n) processors. \itemrv{N.I.Yanev} \itemcc{} \itemut{parallel processing; time-constrained travelling salesman; time windows; k-optimality} \itemli{} \end