ABSTRACT
Tree structures and algorithms provide a fundamental and powerful data abstraction and methods for computer science and operations research. In particular, they enable significant advancement of IC physical design techniques and design optimization. For the last half century, Prof. T. C. Hu has areas in computer science, including network flows, integer programming, shortest paths, binary trees, global routing, etc. In this article, we select and summarize three important and interesting tree-related topics (ancestor trees, column generation, and alphabetical trees) in the highlights of Prof. T. C. Hu's contributions to physical design.
- C. Albrecht, "Provably Good Global Routing by A New Approximation Algorithm for Multicommodity Flow", Proc. ISPD, 2000, pp. 19--25. Google ScholarDigital Library
- F. Alvelos and J. M. V. de Carvalho, "An Extended Model and a Column Generation Algorithm for the Planar Multicommodity Flow Problem", Networks 50(1) (2007), pp. 3--16. Google ScholarDigital Library
- W. Ben-Ameur and J. Neto, "Acceleration of Cutting-Plane and Column Generation Algorithms: Applications to Network Design", Networks 49(1) (2007), pp. 3--17. Google ScholarDigital Library
- R. C. Carden, J. Li and C. K. Cheng, "A Global Router with a Theoretical Bound on the Optimal Solution", IEEE Trans. on CAD 15(2) (1996), pp. 208--216. Google ScholarDigital Library
- Y. C. Chang, Y.-W. Chang, G. M. Wu and S. W. Wu, "B*-Trees: A New Representation for Non-Slicing Floorplans", Proc. DAC, 2000, pp. 458--463. Google ScholarDigital Library
- S.-J. Chen and C. K. Cheng, "Tutorial on VLSI Partitioning", VLSI Design 11(3) (2000), pp. 175--218.Google ScholarCross Ref
- C. K. Cheng, "The Optimal Partitioning of Networks", Networks 22(3) (1992), pp. 297--315.Google ScholarCross Ref
- C. K. Cheng and T. C. Hu, "Ancestor Tree for Arbitrary Multi-Terminal Cut Functions", Annals of Operations Research 33(3) (1991), pp. 199--213.Google ScholarCross Ref
- C. K. Cheng and T. C. Hu, "Maximum Concurrent Flows and Minimum Ratio Cuts", Algorithmica 8(1) (1992), pp. 233--249. Google ScholarDigital Library
- C. Contardo, J.-F. Cordeau and B. Gendron, "An Exact Algorithm Based on Cut-and-Column Generation for the Capacitated Location-Routing Problem", INFORMS Journal on Computing 26(1) (2014), pp. 88--102. Google ScholarDigital Library
- L. R. Ford and D. R. Fulkerson, "Maximal Flow through a Network", Canadian Journal of Mathematics 8(3) (1956), pp. 399--404.Google ScholarCross Ref
- V. Gabrel, A. Knippel and M. Minoux, "Exact Solution of Multicommodity Network Optimization Problems with General Step Cost Functions", Operations Research Letters 25(1) (1999), pp. 15--23. Google ScholarDigital Library
- E. N. Gilbert and E. F. Moore, "Variable Length Binary Encodings", Bell System Technical Journal 38 (1959), pp. 933--968.Google ScholarCross Ref
- R. E. Gomory and T. C. Hu, "Multi-Terminal Network Flows", Journal of SIAM 9(4) (1961), pp. 551--570.Google Scholar
- J. Gondzio, P. González-Brevis and P. Munari, "New Developments in the Primal-Dual Column Generation Technique", European Journal of Operational Research 224(1) (2013), pp. 41--51.Google ScholarCross Ref
- J. Gondzio, P. González-Brevis and P. Munari, "Large-Scale Optimization with the Primal-Dual Column Generation Method", Mathematical Programming Computation 8(1) (2016), pp. 47--82.Google ScholarCross Ref
- P.-N. Guo, T. Takahashi, C. K. Cheng and T. Yoshimura, "Floorplanning Using a Tree Representation", IEEE Trans. on CAD 20(2) (2001), pp. 281--289. Google ScholarDigital Library
- J. Hu and S. S. Sapatnekar, "A Survey on Multi-Net Global Routing for Integrated Circuits", Integration, the VLSI Journal 31(1) (2001), pp. 1--49.Google ScholarCross Ref
- T. C. Hu, "Multi-Commodity Network Flows", Operations Research 11(3) (1963), pp. 344--360. Google ScholarDigital Library
- T. C. Hu and A. B. Kahng, Linear and Integer Programming Made Easy, Springer, 2016. Google ScholarDigital Library
- T. C. Hu and M. T. Shing, "A Decomposition Algorithm for Circuit Routing", Mathematical Programming Study 24 (1985), pp. 87--103.Google ScholarCross Ref
- T. C. Hu and M. T. Shing, Combinatorial Algorithms, 2nd Ed., Dover Publications, 2002. Google ScholarDigital Library
- T. C. Hu and A. C. Tucker, "Optimal Computer Search Trees and Variable-Length Alphabetical Codes", Journal of SIAM 21(4) 1971, pp.514--532.Google Scholar
- J. Huang, X. L. Hong, C. K. Cheng and E. S. Kuh, "An Efficient Timing-Driven Global Routing Algorithm", Proc. DAC, 1993, pp. 596--600. Google ScholarDigital Library
- J. Janacek, M. Kohani, M. Koniorczyk and P. Marton, "Optimization of Periodic Crew Schedules with Application of Column Generation Method", Transportation Research Part C: Emerging Technologies 83 (2017), pp. 165--178.Google ScholarCross Ref
- G.-W. Jeong, K. Lee, S. Park and K. Park, "A Branch-and-Price Algorithm for the Steiner Tree Packing Problem", Computers & Operations Research 29(3) (2002), pp. 221--241. Google ScholarDigital Library
- D. G. Jørgensen and M. Meyling, "A Branch-and-Price Algorithm for Switch-Box Routing", Networks 40(1) (2002), pp. 13--26.Google ScholarCross Ref
- A. B. Kahng, J. Lienig, I. L. Markov and J. Hu, VLSI Physical Design: From Graph Partitioning to Timing Closure, Springer, 2011. Google ScholarDigital Library
- D. E. Knuth, "Optimum Binary Search Trees", Acta Informatica 1 (1971), pp. 14--25. Google ScholarDigital Library
- M. E. Kuo and C. K. Cheng, "A Network Flow Approach for Hierarchical Tree Partitioning", Proc. DAC, 1997, pp. 512--517. Google ScholarDigital Library
- G. Laporte, "The Vehicle Routing Problem: An Overview of Exact and Approximate Algorithms", European Journal of Operational Research 59(3) (1992), pp. 345--358.Google ScholarCross Ref
- L.-T. Liu, M.-T. Kuo, C. K. Cheng and T. C. Hu, "A Replication Cut for Two-Way Partitioning", IEEE Trans. on CAD 14(5) (1995), pp. 623--630. Google ScholarDigital Library
- J. Liu, S. Zhou, H. Zhu and C. K. Cheng, "An Algorithmic Approach for Generic Parallel Adders", Proc. ICCAD, 2003, pp. 734--740. Google ScholarDigital Library
- M. E. Lubbecke and J. Desrosiers, "Selected Topics in Column Generation", Operations Research 53(6) (2005), pp. 1007--1023. Google ScholarDigital Library
- T. Nishi and T. Izuno, "Column Generation Heuristics for Ship Routing and Scheduling Problems in Crude Oil Transportation with Split Deliveries", Computers & Chemical Engineering 60 (2014), pp. 329--338.Google ScholarCross Ref
- M. Pedram and H. Vaishnav, "Technology Decomposition Using Optimal Alphabetic Trees", Proc. ECDA, 1993, pp. 573--577.Google ScholarCross Ref
- D. Potthoff, D. Huisman and G. Desaulniers, "Column Generation with Dynamic Duty Selection for Railway Crew Rescheduling", Transportation Science 44 (2010), pp. 493--505. Google ScholarDigital Library
- H. Vaishnav and M. Pedram, "Alphabetic Trees - Theory and Applications in Layout-Driven Logic Synthesis", IEEE Trans. on CAD 42(2) (2002), pp. 219--223. Google ScholarDigital Library
- A. Vittal and M. Marek-Sadowska, "Minimal Delay Interconnect Design Using Alphabetic Trees", Proc. DAC, 1994, pp. 392--396. Google ScholarDigital Library
- T. H. Wu, A. Davoodi and J. T. Linderoth, "GRIP: Global Routing via Integer Programming", IEEE Trans. on CAD 30(1) (2011), pp. 72--84. Google ScholarDigital Library
- B. Yao, H. Chen, C. K. Cheng and R. Graham, "Floorplan Representations: Complexity and Connections", ACM Trans. on DAES 8(1) (2003), pp. 55--80. Google ScholarDigital Library
- E. F. Y. Young, C. C. N. Chu and Z. C. Shen, "Twin Binary Sequences: A Nonredundant Representation for General Nonslicing Floorplan", IEEE Trans. on CAD 22(4) (2003), pp. 457--469. Google ScholarDigital Library
- Y. Zhu, J. Liu, H. Zhu and C. K. Cheng, "Timing-Power Optimization for Mixed-Radix Ling Adders by Integer Linear Programming", Proc. ASP-DAC, 2008, pp. 131--137. Google ScholarDigital Library
- Brief Biography of Dr. Te Chiang Hu, The Institute for Operations Research and the Management Sciences, http://www.informs.org/Explore/History-of-O.R.-Excellence/Biographical-Profiles/Hu-Te-Chiang/.Google Scholar
- Column Generation and Dantzig-Wolfe Decomposition, Group for Research in Decision Analysis (GERAD), http://www.science4all.org/article/column-generation/.Google Scholar
- Duality Theory in LP, http://www.slideshare.net/jyothimonc/duality-in-linear-programming/.Google Scholar
Index Terms
- Tree Structures and Algorithms for Physical Design
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