Session: Discrete and Combinatorial Optimization I (06/07, 11:15-13:15, Room 10A)

On Asymptotic Complexity of the Optimum Golomb Ruler Problem: From Established Stochastic Methods to Self-Avoiding Walks



This paper proposes a model to experimentally predict the asymptotic runtime complexity of any gr solver that returns the best- known-value (BKV) Golomb ruler defined by the paired list L = length, M = order}. A subset of this list includes {(6,4), (11,5), (17,6), (25,7), (34,8), (44,9),..., (680,30)}. Given the number of processors $N$ and the runtime limit t_lmt, we observe at least N_u >= 100 processors reaching the target BKV with the first-passage-time < t_lmt and say that each such observation is uncensored. In other words, the mean runtime value we measure is based strictly on at least 100 uncensored observations from the experiment. Experiments in this paper focus on a stochastic gr-solver that implements a variation of a self- avoiding walk. In the total number of steps, the solver asymptotic walkLength complexity is 409.2*1.0762^L. When measuring the number of CPU seconds on a loaded grid of 100 processors, the solver asymptotic runtime complexity is 0.000206*1.08711^L. This solver significantly outperforms the alternative stochastic gr-solvers reported to date.