Tree Structures and Algorithms for Physical Design

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.

[1]  Gilbert Laporte,et al.  The vehicle routing problem: An overview of exact and approximate algorithms , 1992 .

[2]  Malgorzata Marek-Sadowska,et al.  Minimal Delay Interconnect Design Using Alphabetic Trees , 1994, 31st Design Automation Conference.

[3]  Ronald L. Graham,et al.  Floorplan representations: Complexity and connections , 2003, TODE.

[4]  Nadine Gottschalk,et al.  Vlsi Physical Design From Graph Partitioning To Timing Closure , 2016 .

[5]  W. Ben‐Ameur,et al.  Acceleration of cutting-plane and column generation algorithms: Applications to network design , 2007 .

[6]  Josef Kittler,et al.  Combinatorial Algorithms , 2016, Lecture Notes in Computer Science.

[7]  D. R. Fulkerson,et al.  Maximal Flow Through a Network , 1956 .

[8]  José M. Valério de Carvalho,et al.  An extended model and a column generation algorithm for the planar multicommodity flow problem , 2007, Networks.

[9]  Michel Minoux,et al.  Exact solution of multicommodity network optimization problems with general step cost functions , 1999, Oper. Res. Lett..

[10]  Jacek Gondzio,et al.  Large-scale optimization with the primal-dual column generation method , 2013, Math. Program. Comput..

[11]  T. C. Hu,et al.  Optimal Computer Search Trees and Variable-Length Alphabetical Codes , 1971 .

[12]  David Grove Jørgensen,et al.  A branch-and-price algorithm for switch-box routing , 2002, Networks.

[13]  Jean-François Cordeau,et al.  An Exact Algorithm Based on Cut-and-Column Generation for the Capacitated Location-Routing Problem , 2014, INFORMS J. Comput..

[14]  Chung-Kuan Cheng,et al.  Ancestor tree for arbitrary multi-terminal cut functions , 1990, IPCO.

[15]  Chung-Kuan Cheng,et al.  A network flow approach for hierarchical tree partitioning , 1997, DAC.

[16]  Yi Zhu,et al.  Timing-power optimization for mixed-radix Ling adders by integer linear programming , 2008, 2008 Asia and South Pacific Design Automation Conference.

[17]  Kyungsik Lee,et al.  A branch-and-price algorithm for the Steiner tree packing problem , 2002, Comput. Oper. Res..

[18]  Yao-Wen Chang,et al.  B*-trees: a new representation for non-slicing floorplans , 2000, Proceedings 37th Design Automation Conference.

[19]  Xianlong Hong,et al.  An Efficient Timing-Driven Global Routing Algorithm , 1993, 30th ACM/IEEE Design Automation Conference.

[20]  Jacek Gondzio,et al.  New developments in the primal-dual column generation technique , 2013, Eur. J. Oper. Res..

[21]  Jacques Desrosiers,et al.  Selected Topics in Column Generation , 2002, Oper. Res..

[22]  E. F. Moore,et al.  Variable-length binary encodings , 1959 .

[23]  Chung-Kuan Cheng,et al.  A replication cut for two-way partitioning , 1995, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[24]  H. G. Daellenbach,et al.  Technical Note - Forest Outturn Optimization by Dantzig-Wolfe Decomposition and Dynamic Programming Column Generation , 1985, Oper. Res..

[25]  T. C. Hu.  Multi-Commodity Network Flows , 1963 .

[26]  Jianhua Liu,et al.  An Algorithmic Approach for Generic Parallel Adders , 2003, ICCAD 2003.

[27]  Tatsushi Nishi,et al.  Column generation heuristics for ship routing and scheduling problems in crude oil transportation with split deliveries , 2014, Comput. Chem. Eng..

[28]  Azadeh Davoodi,et al.  GRIP: Global Routing via Integer Programming , 2011, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[29]  Donald E. Knuth,et al.  Optimum binary search trees , 1971, Acta Informatica.

[30]  M. Pedram,et al.  Technology decomposition using optimal alphabetic trees , 1993, 1993 European Conference on Design Automation with the European Event in ASIC Design.

[31]  Andrew B. Kahng,et al.  Linear and Integer Programming Made Easy , 2016 .

[32]  J. V. D. Carvalho,et al.  An extended model and a column generation algorithm for the planar multicommodity flow problem , 2007 .

[33]  Man-Tak Shing,et al.  A decomposition algorithm for circuit routing , 1985 .

[34]  Chung-Kuan Cheng,et al.  Tutorial on VLSI Partitioning , 2000, VLSI Design.

[35]  T. C. Hu,et al.  Multi-Terminal Network Flows , 1961 .

[36]  Chung-Kuan Cheng,et al.  Maximum concurrent flows and minimum cuts , 1992, Algorithmica.

[37]  Takeshi Yoshimura,et al.  Floorplanning using a tree representation , 2001, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[38]  Sachin S. Sapatnekar,et al.  A survey on multi-net global routing for integrated circuits , 2001, Integr..

[39]  Massoud Pedram,et al.  Alphabetic trees-theory and applications in layout-driven logicsynthesis , 2001, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[40]  Chung-Kuan Cheng,et al.  The optimal partitioning of networks , 1992, Networks.

[41]  Peter Marton,et al.  Optimization of periodic crew schedules with application of column generation method , 2017 .

[42]  Daniel Potthoff,et al.  Column Generation with Dynamic Duty Selection for Railway Crew Rescheduling , 2008, Transp. Sci..

[43]  Chung-Kuan Cheng,et al.  A global router with a theoretical bound on the optimal solution , 1996, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[44]  Evangeline F. Y. Young,et al.  Twin binary sequences: a non-redundant representation for general non-slicing floorplan , 2002, ISPD '02.

[45]  Christoph Albrecht,et al.  Provably good global routing by a new approximation algorithm for multicommodity flow , 2000, ISPD '00.