Journal of the ACM (JACM)
Evolution of Non-Deterministic Incremental Algorithms as a New Approach for Search in State Spaces
Proceedings of the 6th International Conference on Genetic Algorithms
More Effective Genetic Search For The Sorting Network Problem
GECCO '02 Proceedings of the Genetic and Evolutionary Computation Conference
Sorting networks and their applications
AFIPS '68 (Spring) Proceedings of the April 30--May 2, 1968, spring joint computer conference
Secure multi-party computation made simple
Discrete Applied Mathematics - Special issue: Coding and cryptography
A graph-based Lamarckian-Baldwinian hybrid for the sorting network problem
IEEE Transactions on Evolutionary Computation
| Hi-index | 0.00 |
A sorting network is a mathematical model of an oblivious sorting algorithm - that is, a sorting algorithm in which all comparisons take place in a fixed order at predetermined positions in the list. The search for sorting networks of optimal size is an old problem. Asymptotically optimal networks of size O(n log n) are known, where n is the number of inputs, but the hidden constants are enormous. Genetic algorithms have been used to tackle this problem in a number of studies since the early 1990s, often focusing on the historically interesting case of 16 inputs. In this special case, the best known bound of 60 comparisons has been attained, but often through the use of a particular, highly structured, initial sequence of comparisons that narrows the search space by filtering out all but a small core of input sequences. We make explicit the concept of a filter - a fixed sequence of comparisons to be extended to a sorting network through a stochastic process - and present a new construction for any perfect square number of inputs. In the case of 9 inputs, we extend the filter to a sorting network of size 25, attaining the best known bound. For 16 and 25 inputs, we present a simple GA variant that extends the filter to produce small sorting networks with highly regular structure.