Oddeven

Oddeven, often written as odd-even, is a term used to describe a parity-based distinction between odd and even numbers and to refer to policies and technologies that apply this dichotomy in different contexts.

In mathematics, odd numbers are integers that are not divisible by 2, while even numbers are divisible by 2. Examples include 3 (odd) and 8 (even). Parity has several simple rules: the sum of two even numbers is even, the sum of two odd numbers is even, and the sum of an even and an odd number is odd. The product is even if at least one factor is even. Parity is a basic concept in number theory and modular arithmetic, often used to simplify reasoning about divisibility and symmetry.

In computing and algorithms, the term appears in methods such as the odd-even transposition sort (also called odd-even sort). This parallel sorting algorithm repeatedly compares and swaps adjacent pairs in alternating phases: in one phase pairs (0,1), (2,3), etc., and in the next phase pairs (1,2), (3,4), etc. It is simple and easy to implement in parallel hardware, though not the most efficient for large datasets compared to more advanced sorting algorithms.

In urban planning and policy, oddeven refers to odd-even car restrictions designed to reduce traffic congestion and air pollution. On designated days, vehicles with odd-numbered license plates may be allowed to circulate, or conversely on even days for even-numbered plates. Exemptions often apply to emergency vehicles, motorbikes, or certain essential services. Proponents cite decreased traffic volumes and improved air quality, while critics point to limited long-term impact, equity concerns, and the potential shift of congestion rather than its elimination. Implementations have occurred in cities such as Beijing and Delhi, among others, at varying intensities and durations.