Connecting apparatus and system

A router comprising:

• a connecting apparatus;
• N interconnection units;
• M line processing units;
• and
• X switch processing units,
• wherein each of the N interconnection units are connected to at least one switch processing unit of the X switch processing units,
• wherein at least one of the X switch processing units is directly connected to each interconnection unit of the N interconnection units,
• wherein each of the M line processing units is directly attached to exactly one respective interconnection unit of the N interconnection units such that each of the M line processing units is directly attached to a different exactly one interconnection unit of the N interconnection units than other line processing units of the M line processing units,
• wherein M is a positive integer indicating the number of line processing units and is greater than one, N is a positive integer indicating the number of interconnection units and is greater than one, and X is a positive integer indicating the number of switch processing units, X being greater than or equal to N;
• wherein each of the N interconnection units comprises exactly M first connectors directly connected to M corresponding second connectors included in the X switch processing units in a one-to-one ratio;
• and
• wherein each of the N interconnection units further comprises X third connectors directly connected to X corresponding fourth connectors included in a respective exactly one corresponding line processing unit.

A connecting apparatus comprising:

• M interconnection units;
• X line processing units;
• and
• N switch processing units,
• wherein each of the M interconnection units is connected to at least one X line processing unit of the X line processing units,
• wherein at least one of the X line processing units is directly connected to each interconnection unit of the M interconnection units,
• wherein each of the N switch processing units is connected to exactly one respective interconnection unit of the M interconnection units such that each of the N switch processing units is connected to a different exactly one interconnection unit of the M interconnection units than other switch processing units of the N switch processing units, and
• wherein M is a positive integer indicating the number of interconnection units and is greater than one, X is a positive integer indicating the number of line processing units, N is a positive integer indicating the number of switch processing units and is greater than one, and X is greater than or equal to M.