What is recorded here?
Graham bounded how much a fixed-list schedule can worsen when task priorities, durations, precedence constraints or the number of identical processors are changed. Adding processors sounds like an automatic way to finish work faster. A greedy scheduler can behave differently: starting a ready task earlier may put later tasks in an unfavorable order. Graham modeled tasks with fixed lengths and dependencies, assigned without interruption to identical processors. He gave a bound on the finishing-time ratio after changing the priority list, shortening tasks, removing dependencies or changing the processor count. For equal processor counts the bound becomes 2 minus the reciprocal of that count. The comparison is about a specified scheduling rule, not the best possible use of extra hardware. This account does not reproduce every original diagram or supply a certified formula transcription. The central ratio was separately reconstructed from total work and an idle-covering dependency chain; this does not certify every original sharpness construction.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
The scheduling results use the paper’s machine, dependency and task-duration model. They bound specified list-scheduling behavior and illustrate anomalies; they do not establish that adding resources always worsens performance or solve every scheduling objective optimally. Changes in precedence, communication cost and processor heterogeneity need separate analysis.
Read the original work
- R. L. Graham, Bounds for Certain Multiprocessing Anomalies, author-hosted original scan
- Publisher Crossref deposit for Graham1966 scheduling-anomaly paper
This English explanation is an editorial reading view. It does not replace the complete original work or certify its science.
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People and systems
R. L. Graham
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English catalogue narrative
Graham: why a greedy schedule can slow down after apparent improvements
Graham bounded how much a fixed-list schedule can worsen when task priorities, durations, precedence constraints or the number of identical processors are changed.
Adding processors sounds like an automatic way to finish work faster. A greedy scheduler can behave differently: starting a ready task earlier may put later tasks in an unfavorable order. Graham modeled tasks with fixed lengths and dependencies, assigned without interruption to identical processors. He gave a bound on the finishing-time ratio after changing the priority list, shortening tasks, removing dependencies or changing the processor count. For equal processor counts the bound becomes 2 minus the reciprocal of that count. The comparison is about a specified scheduling rule, not the best possible use of extra hardware. This account does not reproduce every original diagram or supply a certified formula transcription. The central ratio was separately reconstructed from total work and an idle-covering dependency chain; this does not certify every original sharpness construction.
Scientific scope
The scheduling results use the paper’s machine, dependency and task-duration model. They bound specified list-scheduling behavior and illustrate anomalies; they do not establish that adding resources always worsens performance or solve every scheduling objective optimally. Changes in precedence, communication cost and processor heterogeneity need separate analysis.
People and systems
R. L. Graham