Professor T. C. Hu ISPD-2018 Lifetime Achievement Commemoration - PowerPoint Presentation

Slide1

Professor T. C. Hu ISPD-2018 Lifetime Achievement Commemoration

Slide2

Influence of Professor T. C. Hu’s Works on Fundamental Approaches in Layout

Andrew B. KahngCSE and ECE DepartmentsUC San Diegohttp://vlsicad.ucsd.edu

Slide3

Professor T. C. HuIntroduced combinatorial optimization, and mathematical programming formulations and methods, to VLSI LayoutMany works reflect unique ability to combine geometric, graph-theoretic, and combinatorial-algorithmic ideas

1961: Gomory-Hu cut tree1973: Adolphson-Hu cut-based linear placement1985: Hu-Moerder hyperedge net model1985: Hu-Shing - routingApplications of duality: flows and cuts, shadow price  Professor C.-K. Cheng in next talk

Slide4

Professor T. C. Hu

Slide5

A Few ExamplesTentative Assignment / Competitive PricingOptimal Linear Ordering

Hyperedge Net ModelThe Prim-Dijkstra TradeoffThe Discrete Plateau Problem and Finding a Wide Path

Slide6

A Few ExamplesTentative Assignment / Competitive PricingOptimal Linear Ordering

Hyperedge Net ModelThe Prim-Dijkstra TradeoffThe Discrete Plateau Problem and Finding a Wide Path

Slide7

TACP and Shadow Price (1)

TACP: tentative assignment and competitive pricingApplication: Fixed-outline floorplanningFixed die, fixed block aspect ratio  classical “packing” that minimizes whitespace, etc. !!!Seeks “perfect” rectilinear floorplanning: zero whitespaceIrregular block shapeOverlapping blocks

Slide8

TACP and Shadow Price (2)

Shadow price in linear programming dualityPrimal-dual iterations in global routingLocal density in global placementGlobal densityMore recent: constraint-oriented local density

 

 

Better cell spreading, better wirelength!

Slide9

A Few ExamplesTentative Assignment / Competitive PricingOptimal Linear Ordering

Hyperedge Net ModelThe Prim-Dijkstra TradeoffThe Discrete Plateau Problem and Finding a Wide Path

Slide10

Linear Placement

Optimal linear ordering (O.L.O.) problem pins in holes, pin per holeHoles in a line, unit distance apart

Minimize the wirelength

Gomory

and Hu /

Adolphson

and Hu

max flow values between any source / sink nodes can be obtained with

max flow problems, giving

fundamental cuts

fundamental cuts are lower bound for O.L.O.

 

The min-cut defines an ordered partition that is consistent with an optimal vertex order in the linear placement problem.

Slide11

Minimum Cuts in Placement

Recursive min-cut[Cheng87]: universal application to VLSI placementCapo: top-down, min-cut bisectionFeng Shui: general purpose mixed-size placerDuality between max flows and min cuts[Yang96]: flow-based balanced netlist bipartitionMLPart: multilevel KL-FM/ flat KL-FM / flow-based partitioning

Slide12

Linear Placements Today

Single-row placementVariable cell widthFixed row length with free sitesFixed cell orderingMulti-row placementLocal layout effect-awareReorderable cellsSupport of multi-height cells

Slide13

A Few ExamplesTentative Assignment / Competitive PricingOptimal Linear Ordering

Hyperedge Net ModelThe Prim-Dijkstra TradeoffThe Discrete Plateau Problem and Finding a Wide Path

Slide14

Net Modeling

“Multiterminal Flows in a Hypergraph”, Hu and

Moerder

, 1985

Challenging question:

How should a hyperedge of a hypergraph be modeled by graph edges in a graph model of the hypergraph?

Applications for analytic placement, for exploiting sparse-matrix codes for layouts

New hyperedge net model -

p pin nodes and one star node to represent a p-pin hyperedge

Slide15

Transform netlist hypergraphAdd one star node for each signal netConnect star node to each pin node (via a graph edge)

Sparse, symmetric + exactly captures true cut costStar model: [Brenner01], BonnPlace [Brenner08]Example Transformation

Example circuit with 5 modules

and 3 nets

Equivalent hypergraph model

Slide16

A Few ExamplesTentative Assignment / Competitive PricingOptimal Linear Ordering

Hyperedge Net ModelThe Prim-Dijkstra TradeoffThe Discrete Plateau Problem and Finding a Wide Path

Slide17

The Prim-Dijkstra Tradeoff

Prim’s Minimum Spanning Tree (MST)Iteratively add edge eij to T, such that vi ϵ T, v

i

∉ T and

d

ij

is minimum

Minimizes tree wirelength (WL)

Dijkstra’s Shortest Path Tree (SPT)

Iteratively add edge

e

ij

to T, such that v

i

ϵ

T, v

i

∉ T and l

i + dij is minimum (where

is source-to-sink pathlength of

)Minimizes source-to-sink pathlengths (PLs) Prim-Dijkstra Tradeoff (Alpert, Hu, Huang, Kahng, 1993)“PD1” tradeoff: iteratively add eij to T that minimizes c  li + dijc = 0  Prim’s MSTc = 1  Dijkstra’s SPT // c enables balancing of tree WL, source-sink PLs“PD2” tradeoff: iteratively add eij to T that minimizes ( lip + dij )1/p

p = ∞  Prim’s MST;p = 1  Dijkstra’s

SPT

 

Slide18

Prim-Dijkstra Construction

Prim’s Minimum Spanning Tree (MST)

Minimizes wirelength

Dijkstra’s Shortest Path Tree (SPT)

Minimizes source-sink pathlengths

Prim-Dijkstra (PD) tradeoff

Directly trades off the

Prim, Dijkstra constructions

0

But large pathlengths to nodes 3,4,5

2

1

3

4

5

2

1

0

3

4

5

But large tree

wirelength!

0

2

1

3

4

5

Slide19

PD Tradeoff: 25 Years of Impact

Widely used In EDA for timing estimation, buffer tree construction and global routingIn flood control, biomedical, military, wireless sensor networks, etc.Simple and fast – O(n log n)Alpert et al., DAC06: PD is practically ‘free’

Yesterday: “PD Revisited”

Iterative repair of spanning tree

Detour-aware

Steinerization

Better WL, PL tradeoff

Slide20

A Few ExamplesTentative Assignment / Competitive PricingOptimal Linear Ordering

Hyperedge Net ModelThe Prim-Dijkstra TradeoffThe Discrete Plateau Problem and Finding a Wide Path

Slide21

Connection Finding

Basic element of any routing approach- routing (Hu and Shing, 1985)Find connections given edge and vertex costsComprehend existence of “turn” at vertexProvide unified elements for

Dijkstra’s algorithm

Best-first (A*) search

 

Slide22

Proc. Nat. Acad. Sci., October 1992

Discrete version of Plateau’s minimum-surface problem

Solved using duality of cuts and flow

Slide23

Towards Robust (Wide) Path Finding

Robust path finding problemSource-destination routing with prescribed widthSeek minimum-cost path that has robustness (width) = dE.g., a mobile agent with finite width

Slide24

Network Flow Approach

Discretize routing environmentA minimum cut in flow networkContain all vertices and edges on a robust pathCorrespond to a maximum flow by dualityReturn a robust path

Slide25

Applications Today

Relevant to many difficult problemsBus routing, bus feedthrough determination, etc.IC package routingPer-net PI/SI requirementNeed traces of various widthWide path finding (with multiple commodities) can be useful

Slide26

Conclusion

Slide27

T. C. Hu

W. T. Torres

K-C. Tan

Y. S.

Kuo

P. A. Tucker

A. B. Kahng

K. E. Moerder

M.-T.

Shing

F. Ruskey

D. Adolphson

B. N. Tien

D.R. van

Baronaigien

Y.

Koda

P. Evans

A. Smith

K. Wong

J. Sawada

S. Chow

M.R. Kindl

M.M. Cordeiro

J. Chen

G. Robins

C.J. Alpert

K.D. Boese

Y. Chen

K. Masuko

P. Gupta

L. Hagen

D.J. Huang

B. Liu

S. Mantik

I. Markov

S. Muddu

S. Reda

C-W.A. Tsao

Q. Wang

X. Xu

M. Alexander

T. Zhang

A Ramani

S.

Adya

G.

Pruesse

G. Thomas

A. Zaki

S-J. Su

Y-H. Hsu

C-C. Jung

Professor Hu’s 96 Ph.D. Descendants

S. Kang

C. H. Park

W. Chan

S. Muddu

K. Samadi

K. Jeong

R. O. Topaloglu

T. Chan

P. Sharma

S. Nath

J. Li

M. Weston

B.

Bultena

A. Erickson

A.

Mamakani

V. Irvine

A. Williams

L. Bolotnyy

C. Taylor

K. Chawla

R. Layer

N. Brunelle

A. M. Eren

G. Xu

V. Maffei

G. Viamontes

K-H. Chang

S. Krishnaswamy

S. Plaza

J. Roy

D. Papa

D. Lee

M. Kim

J. Hu

H. J. Garcia

R. Cochran

N. Abdullah

K. Nepal

K. Dev

X. Zhan

S. Hashemi

R. Azimi

J. Lee

L. Cheng

R. Ghaida

A. A. Kagalwalla

L. Lai

M. Gottscho

S. Wang

Y. Badr

Slide28

Thank you, Professor Hu.