To elucidate on silverlake's writeup a bit, the critical path is the "spine" of any given project. It takes its name from Critical Path Management - a complex school of "scientific" project management developed during the second world war on the Manhattan Project and the methodological foundation for all contemporary project management.

In some ways, it's nothing more than a list of the order in which job stages must be completed, but since large scale projects often have a great deal of work happening in parallel it's more a listing of bottlenecks in production. As the various side sub-projects flow together, the "big river" that they follow to the sea is the critical path.

The best way to graphically examine the critical path is with a PERT chart, or "Program Evaluation and Review Technique". Most any project management software package, like the creatively named Microsoft Project will automatically create a PERT chart from other project info, like a Gannt chart (which is essentially a fancy outline and time estimate). In a PERT chart, the individual job stages appear as boxes (nodes), with their interrelationship illustrated by lines (vertices). Using connectivity and adjacency logic, the software picks out the critical path and highlights it. Add up how long the it takes to complete the critical path, and you have the shortest possible time in which to complete the project, as you have collapsed out the processes that can be pursued in parallel.

I must say that if you has told me in high school that I would wind up a project manager at an advertising agency, I might have punched you out. However, the word "critical path" is a real show stopper in a management meeting. Throw out a gem like, "The rest of this is just window dressing! We have got to get back on the critical path!" Then one should authoritatively whack the PERT chart. The PERT chart already put the fear of god into them. Once you invoke the wrath of the Critical Path, everybody shuts up.

See also:

Frederick W. Taylor

Industrial Engineering

Fuller, R. Buckminster. Critical Path. New York: St. Martin's Press, 1981.

"Conventional critical-path conceptioning is linear and self-underinformative. Only spherically expanding and contracting, spinning, polarly involuting and evoluting orbital-system feedbacks are both comprehensively and incisively informative. Spherical-orbital critical-feedback circuits are pulsative, tidal, importing and exporting. Critical-path elements are not overlapping linear modules in a plane: they are systematically interspiraling complexes of omni-interrelevant regenerative feedback circuits."

- R. Buckminster Fuller

One of the last books written by polymathic genius Buckminster Fuller before his passing in 1983, Critical Path represents the culmination of a life-long mission to convince humanity of its "option for success"--that is, the option to produce a high standard of living for all people on an ecologically sustainable basis. In his book, Fuller traces the origins and evolution of humanity's social, political, and economic systems from prehistory, through the development of the great empires, to the vast international corporate and political systems of today, and makes a strong case for pursuing "omni-integrated, omni-successful humanity".

At first glance, the book may seem a little "out there" and more than a little idealistic, but Fuller was never one to hide his infectious optimism and he does in fact succeed in presenting an interesting alternative interpretation of history, as well as some very original ideas for making sustainable development possible on a global scale. Despite the convoluted Buckyspeak quote above, the book is actually quite readable, which is a bit surprising if you've seen Fuller's Synergetics.

Table of Contents

1. Introduction: Twilight of the World's Power Structures
2. Speculative Prehistory of Humanity
3. Humans in Universe
4. Legally Piggily
5. Self-Disciplines of Buckminster Fuller
6. The Geoscope
7. World Game
8. Critical Path: Part One
9. Critical Path: Part Two
10. Critical Path: Part Three
11. Critical Path: Part Four
12. Chronology of Scientific Discoveries and Artifacts
13. Chronological Inventory of Prominent Scientific, Technological, Economic and Political World Events: 1895 to Date

In digital circuits, the critical path is the slowest path through asynchronous logic between a set of source and load flip flops that share a common clock signal. Since the speed of any circuit is limited by the longest delay along its paths, the critical delay along the critical path of a circuit can be a useful metric of circuit performance as well as a rough optimization guide for locating bottlenecks. It also defines the minimum period of the clock and is therefore used to verify that all timing constraints in a given design are met.

For example, in a very simple combinational circuit, we can assign each logic gate a specific gate delay value based on a rough approximation of its performance (a kind of gate "cost"). Each path in the circuit is then traced and all the corresponding gate delays are added together. The path with the largest cost is the critical path.

Of course, due to its algorithmic complexity, non-trivial critical path analysis for real production circuits requires a serious digital logic CAD package.