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Linear ordering and application to placement

Learn about Linear Ordering technique for initial module placement in interconnected systems. Algorithm starts from lightly connected modules ensuring efficient net cuts. Discover gain calculation methods and challenges with global nets.

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Linear ordering and application to placement

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  1. Linear ordering and application to placement By S. Kang

  2. Linear Ordering generates a linear sequence of elements of a set of interconnected elements. This sequence is used for constructive initial-placement methods. Important difference from other previous techniques: starts the ordering process from the most lightly connected module. Abstract

  3. Problem • With a set of connected modules, we want to put the components in a linear sequence so that the number of nets cut by a plane separating two adjacent components is minimized.

  4. Solution • Algorithm Linear_Ordering • S = Set of all modules • Order = sequence of ordered modules (now empty) • Begin • Seed = selected seed module; • Order = seed; • S = S – seed; Repeat { Compute gain for each module m; If a tie { Select module that terminates the largest number of nets; } If still a tie { Select the module with the largest number of continuing nets; } If still a tie { Select the module with the least number of connections; } Else break tie however desired Order = Order + new module; S = S – new module; } until S is empty End

  5. Gain Calculation • New net: a net created with the current module • Terminated net: a net that ends with the current module • Continuing net: an already created net that does not terminate with this module • Gain = terminated nets – new nets

  6. Net Example terminating new Module under consideration continuing

  7. Example

  8. Linear ordering does not use look-ahead for tie breaking, so it is not sufficient for real circuits. Problem: Global nets Global vs Local nets Local nets – nets connected to a select few modules Global nets – nets connected to every module in the set Problems

  9. What’s wrong with Global Nets? Picking a seed • No matter what seed is picked, it will contain a net connected to every other module in the set. • In practice, this causes less than ideal choices for future module selection. What to do about them • Ignore them! • Because of folding, treating the special case of global nets is not necessarily ideal in placement

  10. Folding Example A B C D E F A B C F D E F E D E D F A B C A B C

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