Professor T C Hu ISPD2018 Lifetime Achievement Commemoration

Professor T. C. Hu ISPD-2018 Lifetime Achievement Commemoration A. B. Kahng, 180327 ISPD--2018

Influence of Professor T. C. Hu’s Works on Fundamental Approaches in Layout Andrew B. Kahng CSE and ECE Departments UC San Diego http: //vlsicad. ucsd. edu A. B. Kahng, 180327 ISPD--2018

Professor T. C. Hu • Introduced combinatorial optimization, and mathematical programming formulations and methods, to VLSI Layout • Many works reflect unique ability to combine geometric, graph-theoretic, and combinatorialalgorithmic ideas • • 1961: Gomory-Hu cut tree 1973: Adolphson-Hu cut-based linear placement 1985: Hu-Moerder hyperedge net model 1985: Hu-Shing - routing • Applications of duality: flows and cuts, shadow price Professor C. -K. Cheng in next talk A. B. Kahng, 180327 ISPD--2018 3

Professor T. C. Hu A. B. Kahng, 180327 ISPD--2018 4

A Few Examples • Tentative Assignment / Competitive Pricing • Optimal Linear Ordering • Hyperedge Net Model • The Prim-Dijkstra Tradeoff • The Discrete Plateau Problem and Finding a Wide Path A. B. Kahng, 180327 ISPD--2018 5

A Few Examples • Tentative Assignment / Competitive Pricing • Optimal Linear Ordering • Hyperedge Net Model • The Prim-Dijkstra Tradeoff • The Discrete Plateau Problem and Finding a Wide Path A. B. Kahng, 180327 ISPD--2018 6

TACP and Shadow Price (1) • TACP: tentative assignment and competitive pricing • Application: Fixed-outline floorplanning • Fixed die, fixed block aspect ratio classical “packing” that minimizes whitespace, etc. !!! • Seeks “perfect” rectilinear floorplanning: zero whitespace • Irregular block shape • Overlapping blocks A. B. Kahng, 180327 ISPD--2018 7

TACP and Shadow Price (2) • Shadow price in linear programming duality • Primal-dual iterations in global routing • Local density in global placement • Global density • More recent: constraint-oriented local density Better cell spreading, better wirelength! A. B. Kahng, 180327 ISPD--2018 8

A Few Examples • Tentative Assignment / Competitive Pricing • Optimal Linear Ordering • Hyperedge Net Model • The Prim-Dijkstra Tradeoff • The Discrete Plateau Problem and Finding a Wide Path A. B. Kahng, 180327 ISPD--2018 9

Linear Placement • The min-cut defines an ordered partition that is consistent with an optimal vertex order in the linear placement problem. A. B. Kahng, 180327 ISPD--2018 10

Minimum Cuts in Placement • Recursive min-cut • [Cheng 87]: universal application to VLSI placement • Capo: top-down, min-cut bisection • Feng Shui: general purpose mixed-size placer • Duality between max flows and min cuts • [Yang 96]: flow-based balanced netlist bipartition • MLPart: multilevel KL-FM/ flat KL-FM / flow-based partitioning A. B. Kahng, 180327 ISPD--2018 11

Linear Placements Today • Single-row placement • Variable cell width • Fixed row length with free sites • Fixed cell ordering • Multi-row placement • Local layout effect-aware • Reorderable cells • Support of multi-height cells A. B. Kahng, 180327 ISPD--2018 12

A Few Examples • Tentative Assignment / Competitive Pricing • Optimal Linear Ordering • Hyperedge Net Model • The Prim-Dijkstra Tradeoff • The Discrete Plateau Problem and Finding a Wide Path A. B. Kahng, 180327 ISPD--2018 13

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 sparsematrix codes for layouts • New hyperedge net model - p pin nodes and one star node to represent a p-pin hyperedge A. B. Kahng, 180327 ISPD--2018 14

Example Transformation • Transform netlist hypergraph • Add one star node for each signal net • Connect star node to each pin node (via a graph edge) • Sparse, symmetric + exactly captures true cut cost • Star model: [Brenner 01], Bonn. Place [Brenner 08] Example circuit with 5 modules and 3 nets Equivalent hypergraph model A. B. Kahng, 180327 ISPD--2018 15

A Few Examples • Tentative Assignment / Competitive Pricing • Optimal Linear Ordering • Hyperedge Net Model • The Prim-Dijkstra Tradeoff • The Discrete Plateau Problem and Finding a Wide Path A. B. Kahng, 180327 ISPD--2018 16

The Prim-Dijkstra Tradeoff • A. B. Kahng, 180327 ISPD--2018 17

Prim-Dijkstra Construction Prim’s Minimum Spanning Tree (MST) Minimizes wirelength 5 But large pathlengths to nodes 3, 4, 5 Prim-Dijkstra (PD) tradeoff 4 5 0 3 1 4 2 Dijkstra’s Shortest Path Tree (SPT) Minimizes source-sink pathlengths 3 1 5 But large tree wirelength! 0 4 2 Directly trades off the Prim, Dijkstra constructions 0 3 1 2 A. B. Kahng, 180327 ISPD--2018 18

PD Tradeoff: 25 Years of Impact • Widely used • In EDA for timing estimation, buffer tree construction and global routing • In flood control, biomedical, military, wireless sensor networks, etc. • Simple and fast – O(n log n) • Alpert et al. , DAC 06: PD is practically ‘free’ • Yesterday: “PD Revisited” • Iterative repair of spanning tree • Detour-aware Steinerization • Better WL, PL tradeoff A. B. Kahng, 180327 ISPD--2018 19

A Few Examples • Tentative Assignment / Competitive Pricing • Optimal Linear Ordering • Hyperedge Net Model • The Prim-Dijkstra Tradeoff • The Discrete Plateau Problem and Finding a Wide Path A. B. Kahng, 180327 ISPD--2018 20

Connection Finding • A. B. Kahng, 180327 ISPD--2018 21

Proc. Nat. Acad. Sci. , October 1992 • Discrete version of Plateau’s minimumsurface problem • Solved using duality of cuts and flow A. B. Kahng, 180327 ISPD--2018 22

Towards Robust (Wide) Path Finding • Robust path finding problem • Source-destination routing with prescribed width • Seek minimum-cost path that has robustness (width) = d • E. g. , a mobile agent with finite width A. B. Kahng, 180327 ISPD--2018 23

Network Flow Approach • Discretize routing environment • A minimum cut in flow network • Contain all vertices and edges on a robust path • Correspond to a maximum flow by duality • Return a robust path A. B. Kahng, 180327 ISPD--2018 24

Applications Today • Relevant to many difficult problems • Bus routing, bus feedthrough determination, etc. • IC package routing • Per-net PI/SI requirement • Need traces of various width • Wide path finding (with multiple commodities) can be useful A. B. Kahng, 180327 ISPD--2018 25

Conclusion A. B. Kahng, 180327 ISPD--2018 26

Professor Hu’s 96 Ph. D. Descendants A. Smith G. Thomas W. T. Torres A. Zaki G. Robins K-C. Tan D. Adolphson B. N. Tien F. Ruskey T. C. Hu M. -T. Shing L. Hagen Y. Koda K. D. Boese G. Pruesse C. J. Alpert P. Evans S. Muddu K. Wong C-W. A. Tsao R. Layer S. Adya J. Sawada D. J. Huang N. Brunelle A Ramani S. Chow K. Masuko G. Viamontes M. Weston I. Markov K-H. Chang A. Williams B. Liu S. Krishnaswamy B. Bultena S. Mantik A. Erickson Y. Chen A. Mamakani S. Reda V. Irvine Q. Wang X. Xu M. R. Kindl M. M. Cordeiro K. E. Moerder S-J. Su Y-H. Hsu C-C. Jung A. B. Kahng P. Gupta P. Sharma S. Muddu C. H. Park R. O. Topaloglu K. Samadi K. Jeong S. Kang T. Chan P. A. Tucker T. Zhang D. R. van Baronaigien J. Chen Y. S. Kuo M. Alexander L. Bolotnyy A. M. Eren C. Taylor G. Xu K. Chawla V. Maffei S. Plaza R. Cochran J. Roy N. Abdullah D. Papa K. Nepal D. Lee K. Dev M. Kim X. Zhan J. Hu S. Hashemi H. J. Garcia R. Azimi J. Lee L. Cheng R. Ghaida A. A. Kagalwalla L. Lai S. Nath M. Gottscho J. Li S. Wang W. Chan Y. Badr A. B. Kahng, 180327 ISPD--2018 27

Thank you, Professor Hu. A. B. Kahng, 180327 ISPD--2018 28