This paper by K. E. Batcher from Goodyear Aerospace Corporation discusses the design and applications of sorting networks, which are essential for achieving high throughput rates in modern computing systems. The primary challenge in such systems is the efficient connection of various components, such as I/O devices, memories, and processing units. Traditional methods like high-speed buses and cross-bar switches have limitations in terms of hardware complexity and fan-in/fan-out requirements. The paper introduces sorting networks, which can order $2^p$ words in $(\frac{1}{2})p(p+1)$ steps. These networks can also function as multiple-input, multiple-output switching networks, offering advantages over traditional crossbars in terms of hardware efficiency and constant fan-in/fan-out requirements. This makes sorting networks suitable for connecting large-scale computing systems with thousands of input and output lines. The basic element of sorting networks is the comparison element, which compares two numbers and outputs their minimum and maximum. The paper details the implementation of these elements and their use in constructing larger networks. It also explores the use of sorting networks in various applications, including switching networks, multi-access memories, multi-access content-addressable memories, and multiprocessors. The paper provides detailed constructions for odd-even merging networks and bitonic sorters, which are used to merge ascendingly ordered lists into a single ordered list. These networks can be built using standard modules and can handle input lists of various lengths. The paper also discusses the use of re-clocking delays to achieve parallel data transmission and the potential for large-scale integration. Finally, the paper outlines the applications of sorting networks in solving communication problems associated with large-scale computing systems, such as conflict resolution in switching networks, multi-access memories, and multiprocessors. The fast sorting capability of these networks can significantly enhance the performance of these systems.This paper by K. E. Batcher from Goodyear Aerospace Corporation discusses the design and applications of sorting networks, which are essential for achieving high throughput rates in modern computing systems. The primary challenge in such systems is the efficient connection of various components, such as I/O devices, memories, and processing units. Traditional methods like high-speed buses and cross-bar switches have limitations in terms of hardware complexity and fan-in/fan-out requirements. The paper introduces sorting networks, which can order $2^p$ words in $(\frac{1}{2})p(p+1)$ steps. These networks can also function as multiple-input, multiple-output switching networks, offering advantages over traditional crossbars in terms of hardware efficiency and constant fan-in/fan-out requirements. This makes sorting networks suitable for connecting large-scale computing systems with thousands of input and output lines. The basic element of sorting networks is the comparison element, which compares two numbers and outputs their minimum and maximum. The paper details the implementation of these elements and their use in constructing larger networks. It also explores the use of sorting networks in various applications, including switching networks, multi-access memories, multi-access content-addressable memories, and multiprocessors. The paper provides detailed constructions for odd-even merging networks and bitonic sorters, which are used to merge ascendingly ordered lists into a single ordered list. These networks can be built using standard modules and can handle input lists of various lengths. The paper also discusses the use of re-clocking delays to achieve parallel data transmission and the potential for large-scale integration. Finally, the paper outlines the applications of sorting networks in solving communication problems associated with large-scale computing systems, such as conflict resolution in switching networks, multi-access memories, and multiprocessors. The fast sorting capability of these networks can significantly enhance the performance of these systems.