Heuristics, Experimental Subjects, and Treatment Evaluation in Bigraph Crossing Minimization

The bigraph crossing problem, embedding the two node sets of a bipartite graph along two parallel lines so that edge crossings are minimized, has applications to circuit layout and graph drawing. Experimental results for several previously known and two new heuristics suggest continued exploration of the problem, particularly sparse instances. We emphasize careful design of experimental subject classes and present novel views of the results. All source code, data, and scripts are available on-line

[1]  Vaughn Betz,et al.  VPR: A new packing, placement and routing tool for FPGA research , 1997, FPL.

[2]  Bernd Becker,et al.  k-Layer Straightline Crossing Minimization by Speeding Up Sifting , 2000, Graph Drawing.

[3]  Franc Brglez,et al.  A universal client for distributed networked design and computing , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[4]  Akihiro Sugimoto,et al.  An Approximation Algorithm for the Two-Layered Graph Drawing Problem , 1999, COCOON.

[5]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[6]  Brendan D. McKay,et al.  On an edge crossing problem , 1986 .

[7]  Malgorzata Marek-Sadowska,et al.  The crossing distribution problem [IC layout] , 1995, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[8]  Nevin Kapur,et al.  Synthesis of wiring signature-invariant equivalence class circuit mutants and applications to benchmarking , 1998, Proceedings Design, Automation and Test in Europe.

[9]  Emden R. Gansner,et al.  A Technique for Drawing Directed Graphs , 1993, IEEE Trans. Software Eng..

[10]  Xuemin Lin,et al.  How to draw a directed graph , 1989, [Proceedings] 1989 IEEE Workshop on Visual Languages.

[11]  Jeremy P. Spinrad,et al.  Bipartite permutation graphs , 1987, Discret. Appl. Math..

[12]  P. Franzon,et al.  Generation of tightly controlled equivalence classes for experimental design of heuristics for graph-based np-hard problems , 2000 .

[13]  Matthias F. Stallmann,et al.  Heuristics and Experimental Design for Bigraph Crossing Number Minimization , 1999, ALENEX.

[14]  E. Palmer Graphical evolution: an introduction to the theory of random graphs , 1985 .

[15]  Malgorzata Marek-Sadowska,et al.  The crossing distribution problem , 1991, 1991 IEEE International Conference on Computer-Aided Design Digest of Technical Papers.

[16]  Peter Eades,et al.  Drawing Graphs in Two Layers , 1994, Theor. Comput. Sci..

[17]  Petra Mutzel,et al.  AGD - A Library of Algorithms for Graph Drawing , 1998, Graph Drawing Software.

[18]  Michael Jünger,et al.  Journal of Graph Algorithms and Applications 2-layer Straightline Crossing Minimization: Performance of Exact and Heuristic Algorithms , 2022 .

[19]  Kathryn Fraughnaugh,et al.  Introduction to graph theory , 1973, Mathematical Gazette.

[20]  Matthias F. Stallmann,et al.  Hypercrossing Number: A New and Effective Cost Function for Cell Placement Optimization , 1998 .

[21]  Kurt Mehlhorn,et al.  LEDA: a platform for combinatorial and geometric computing , 1997, CACM.

[22]  Yossi Shiloach,et al.  A Minimum Linear Arrangement Algorithm for Undirected Trees , 1979, SIAM J. Comput..

[23]  Erkki Mäkinen,et al.  Experiments on drawing 2-level hierarchical graphs , 1990, Int. J. Comput. Math..

[24]  W. T. Tutte Convex Representations of Graphs , 1960 .

[25]  Frank Harary,et al.  Trees with Hamiltonian square , 1971 .

[26]  David S. Johnson,et al.  Crossing Number is NP-Complete , 1983 .

[27]  Franc Brglez,et al.  Equivalence classes of circuit mutants for experimental design , 1999, ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349).

[28]  Paul Molitor,et al.  Using Sifting for k -Layer Straightline Crossing Minimization , 1999, GD.

[29]  Patrick Healy,et al.  Characterization of Level Non-planar Graphs by Minimal Patterns , 2000, COCOON.

[30]  Matthias F. Stallmann,et al.  Evaluating iterative improvement heuristics for bigraph crossing minimization , 1999, ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349).

[31]  D. Ghosh First Steps Towards Experimental Design in Evaluating Layout Layout Algorithms : Wire Length versus Wire Crossing in Linear Placement Optimization , 1998 .

[32]  Farhad Shahrokhi,et al.  A new lower bound for the bipartite crossing number with applications , 2000, Theor. Comput. Sci..

[33]  Farhad Shahrokhi,et al.  On Bipartite Drawings and the Linear Arrangement Problem , 2001, SIAM J. Comput..

[34]  Brian W. Kernighan,et al.  An efficient heuristic procedure for partitioning graphs , 1970, Bell Syst. Tech. J..

[35]  John N. Warfield,et al.  Crossing Theory and Hierarchy Mapping , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[36]  F. Thomson Leighton,et al.  ARRAYS AND TREES , 1992 .

[37]  Nevin Kapur,et al.  Towards a new benchmarking paradigm in EDA: analysis of equivalence class mutant circuit distributions , 1997, ISPD '97.