 a nonblocking minimal spanning switch is a device that can connect n inputs to n outputs in any combination. the most familiar use of switches of this type is in a telephone exchange. the term "non-blocking" means that if it is not defective, it can always make the connection. the term "minimal" means that it has the fewest possible components, and therefore the minimal expense. historically, in telephone switches, connections between callers were arranged with large, expensive banks of electromechanical relays, strowger switches. the basic mathematical property of strowger switches is that for each input to the switch, there is exactly one output. much of the mathematical switching circuit theory attempts to use this property to reduce the total number of switches needed to connect a combination of inputs to a combination of outputs. in the 1940s and 1950s, engineers in bell laboratories began an extended series of mathematical investigations into methods for reducing the size and expense of the "switched fabric" needed to implement a telephone exchange. one early, successful mathematical analysis was performed by charles clos (), and a switched fabric constructed of smaller switches is called a clos network. == background: switching topologies == ===the crossbar switch=== the crossbar switch has the property of being able to connect n inputs to n outputs in any one-to-one combination, so it can connect any caller to any non-busy receiver, a property given the technical term "nonblocking". being nonblocking it could always complete a call (to a non-busy receiver), which would maximize service availability. however, the crossbar switch does so at the expense of using n2 (n squared) simple spst switches. for large n (and the practical requirements of a phone switch are considered large) this growth was too expensive. further, large crossbar switches had physical problems. not only did the switch require too much space, but the metal bars containing the switch contacts would become so long that they would sag and become unreliable. engineers also noticed that at any time, each bar of a crossbar switch was only making a single connection. the other contacts on the two bars were unused. this seemed to imply that most of the switching fabric of a crossbar switch was wasted. the obvious way to emulate a crossbar swi
Graph_algorithms Telephone_exchanges