A generalization of the 0-1 principle for sorting

The traditional zero-one principle for sorting networks states that ”if a network with n input lines sorts all 2n binary sequences into nondecreasing order, then it will sort any arbitrary sequence of n numbers into nondecreasing order.” We generalize this to the situation when a network sorts almost all binary sequences and relate it to the behavior of the sorting network on arbitrary inputs. We also present an application to mesh sorting. ∗This research has been supported in part by the NSF Grants CCR-9912395 and ITR-0326155. †257 ITE Building, Dept. of CSE, Univ. of Connecticut, Storrs, CT 06269 Email: [email protected] ‡Department of Computer Science and Engineering, IIT Delhi, New Delhi 1100116, India. Email:[email protected]. Part of the research done when the author was visiting University of Connecticut and supported by NSF Grant ITR-0326155 .