1 / 21

Creating and Exploiting Flexibility in Steiner Trees

ER UCLA. Creating and Exploiting Flexibility in Steiner Trees. Elaheh Bozorgzadeh, Ryan Kastner, Majid Sarrafzadeh Embedded and Reconfigurable System Design (ER LAB) Computer Science Department UCLA. Outline. Introduction Definition and Preliminaries

guywilliams
Download Presentation

Creating and Exploiting Flexibility in Steiner Trees

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ER UCLA Creating and Exploiting Flexibility in Steiner Trees Elaheh Bozorgzadeh, Ryan Kastner, Majid Sarrafzadeh Embedded and Reconfigurable System Design (ER LAB) Computer Science Department UCLA 38th Design Automation Conference, Las Vegas, June 19, 2001

  2. Outline • Introduction • Definition and Preliminaries • Flexibility in Rectilinear Steiner Tree • Our Approach to Create and Exploit Flexibility • Experimental Results • Conclusion and Future Work 38th Design Automation Conference, Las Vegas, June 19, 2001

  3. Global Routing • Routability • Important factor in global routing solution • Satisfied if detailed router is able to find feasible solution from global router. • Depends on highly constrained regions in global routing solution like congested regions. • Delay • Wire delay is becoming increasingly important • Only 10 % of the nets are timing critical. Routability can be emphasized more when routing non-critical nets. 38th Design Automation Conference, Las Vegas, June 19, 2001

  4. Flexibility under Routing • Flexibility: • Geometrical property of RST • Related to routability of steiner tree • Flexible Edge • Non-horizontal/vertical edge route • Has more than one shortest path • Exploited as soft edge in the routing algorithm proposed by Hu and Sepatnekar (ICCAD2000) Flexible edges Steiner Node 38th Design Automation Conference, Las Vegas, June 19, 2001

  5. Pattern Routing and Flexibility • Pattern routing the flexible edges • More than one patterns defined • More ability to maneuver the congested region Congested Area 38th Design Automation Conference, Las Vegas, June 19, 2001

  6. Flexibility under Routing • Two given RSTs with same topology • Study impact of flexibility in congestion Flexible RST Non-flexible RST 38th Design Automation Conference, Las Vegas, June 19, 2001

  7. Flexibility under Routing • Two given RSTs with same topology • Study impact of flexibility in congestion Flexible RST Non-flexible RST 38th Design Automation Conference, Las Vegas, June 19, 2001

  8. Flexibility Function • Flexibility of an edge Two possible functions • Flexibility of an edge increases if w or l increases. w l 38th Design Automation Conference, Las Vegas, June 19, 2001

  9. Rectilinear Steiner Tree Constraints • Given RST is stable (introduced by Ho, et.al DAC 89) • Topology of RST remains unchanged stable unstable Two RSTs with same topology 38th Design Automation Conference, Las Vegas, June 19, 2001

  10. Generating Flexibility in RST • Problem Formulation: • Given a stable Rectilinear Steiner Tree, • Maximize the flexibility of the RST • Subject to: •  Topology remains unchanged (and thus if we do min-length edge connection, total length remains unchanged) •  No initial flexible edge is degraded in flexibility. 38th Design Automation Conference, Las Vegas, June 19, 2001

  11. Flexible Edges • Flexible edges can be generated by moving themovable edges in RST. Movable Edge: • Steiner-to-steiner edge. • Edge degree of each steiner point is 3. • parallel edges exists at both ends. • Flexible candidate exists at least at one end. parallel edges flexible candidate movable edge 38th Design Automation Conference, Las Vegas, June 19, 2001

  12. Flexible Edges • Flexible edges can be generated by moving themovable edges in RST. Movable Edge: • Steiner-to-steiner edge. • Edge degree of each steiner point is 3. • parallel edges exists at both ends. • Flexible candidate exists at least at one end. parallel edges flexible candidate movable edge 38th Design Automation Conference, Las Vegas, June 19, 2001

  13. Pseudo code • Input: Edge Set of an RST S • Output: RST R Algorithm:Generate Flexible Tree • Begin • For Each edge e • If e and its adjacent edges are a movable set • Create Movable Set • Check Overlap • For each movable set M • If M has no overlap • Move edge M • Move Overlapped edges • End 38th Design Automation Conference, Las Vegas, June 19, 2001

  14. Example of Flexible RST Construction 38th Design Automation Conference, Las Vegas, June 19, 2001

  15. Example of Flexible RST Construction 38th Design Automation Conference, Las Vegas, June 19, 2001

  16. Example of Flexible RST Construction 38th Design Automation Conference, Las Vegas, June 19, 2001

  17. Complexity of Our Algorithm • Algorithm GenerateFlexibleTreegenerates the most flexible RST from a given stable RST under the constraints of wirelength and topology and stability remaining unchanged. • Our method solves the problem optimally. • If a linear flexibility function is used, the time complexity of the algorithm is O(E). • If quadratic flexibility function is used, the time complexity of the algorithm is O(E+2k)(pseudo-polynomial), where E is the edges in RST and k in the number of overlapping movable set pairs (k is normally small). 38th Design Automation Conference, Las Vegas, June 19, 2001

  18. Preliminary Experiments • Preliminary Experiments to show relationship between routability and flexibility (many other flows are possible) Maze route the nets other than nets in C C = 4 terminal Nets Route nets in C in nonflexible pattern Route nets in C in flexible pattern Compare Congestion! Pattern-route flexible edges (L-shape, Z-shape) 38th Design Automation Conference, Las Vegas, June 19, 2001

  19. Experiments • MCNC standard cell Benchmarks and ISPD98 benchmark • Circuits placed by placer DRAGON 38th Design Automation Conference, Las Vegas, June 19, 2001

  20. Conclusions and Future Work • Introduced flexibility , a geometrical property of Steiner trees related to routability. • Proposed an algorithm to generate optimally a flexible RST from given stable RST, which can be applied in early stages to assign the location of Steiner points in order to deal with congestion better. • Preliminary experimental results show that flexible Steiner tree cause less congestion on routing resources • Developing constructive Steiner tree algorithms which generate and exploit the flexibility in routing is a suggested future work. 38th Design Automation Conference, Las Vegas, June 19, 2001

  21. Introduction • Global Routing • Finding approximate path (route) for each net • Generating steiner tree for each net • Steiner tree construction with minimum cost is NP-hard. • Objectives • Minimizing wirelength Like Maze router and extended versions • Minimizing the required number of vias • Minimizing delay Buffer insertion, wiresizing • Minimizing Congestion • Our cost: Total excess demand of routing edges in grid graph Route edge 38th Design Automation Conference, Las Vegas, June 19, 2001

More Related