Addenda to the Survey of Layout Problems

In 2002, J. Diaz, M. Serna and the author published “A Survey of Graph Layout Problems”, which then was a complete view of the current state of the art of layout problems from an algorithmic point of view. The current review expands the contents of the original survey with updated results from these latest ten years and contributes an extensive bibliography.

[1]  D. Adolphson.  Optimal linear-ordering. , 1973 .

[2]  Juan José Salazar González,et al.  Decorous Lower Bounds for Minimum Linear Arrangement , 2011, INFORMS J. Comput..

[3]  Carl H. FitzGerald.  Optimal indexing of the vertices of graphs , 1974 .

[4]  Rolf H. Möhring,et al.  The Pathwidth and Treewidth of Cographs , 1993, SIAM J. Discret. Math..

[5]  David S. Johnson,et al.  Some Simplified NP-Complete Graph Problems , 1976, Theor. Comput. Sci..

[6]  Thomas Lengauer.  Upper and Lower Bounds on the Complexity of the Min-Cut Linear Arrangement Problem on Trees , 1982 .

[7]  Mohammad Taghi Hajiaghayi,et al.  L22 Spreading Metrics for Vertex Ordering Problems , 2006, SODA.

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

[9]  Jordi Petit Silvestre.  Experiments on the minimum linear arrangement problem , 2001 .

[10]  R. Ravi,et al.  Ordering Problems Approximated: Single-Processor Scheduling and Interval Graph Completion , 1991, ICALP.

[11]  Christos H. Papadimitriou,et al.  The NP-Completeness of the bandwidth minimization problem , 1976, Computing.

[12]  Nisheeth K. Vishnoi,et al.  Integrality gaps for sparsest cut and minimum linear arrangement problems , 2006, STOC '06.

[13]  Johanne Cohen,et al.  Optimal Linear Arrangement of Interval Graphs , 2006, MFCS.

[14]  Jacobo Torán,et al.  The MINSUMCUT Problem , 1991, WADS.

[15]  Koji Nakano.  Linear Layouts of Generalized Hypercubes , 1993, WG.

[16]  Petr A. Golovach,et al.  Graph Searching and Interval Completion , 2000, SIAM J. Discret. Math..

[17]  Jens Gustedt,et al.  On the Pathwidth of Chordal Graphs , 1993, Discret. Appl. Math..

[18]  Alan M. Frieze,et al.  The regularity lemma and approximation schemes for dense problems , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[19]  Fanica Gavril,et al.  Some NP-complete problems on graphs , 2011, CISS 2011.

[20]  Dimitrios M. Thilikos,et al.  A 3-approximation for the pathwidth of Halin graphs , 2006, J. Discrete Algorithms.

[21]  L. H. Harper.  Optimal numberings and isoperimetric problems on graphs , 1966 .

[22]  Uriel Feige,et al.  Approximating the Bandwidth via Volume Respecting Embeddings , 2000, J. Comput. Syst. Sci..

[23]  Maria J. Serna,et al.  Approximating Layout Problems on Random Geometric Graphs , 2001, J. Algorithms.

[24]  Robert Krauthgamer,et al.  A Polylogarithmic Approximation of the Minimum Bisection , 2006, SIAM Rev..

[25]  Dieter Kratsch,et al.  Treewidth and Pathwidth of Permutation Graphs , 1995, SIAM J. Discret. Math..

[26]  Fillia Makedon,et al.  On minimizing width in linear layouts , 1989, Discret. Appl. Math..

[27]  Ivan Hal Sudborough,et al.  Min Cut is NP-Complete for Edge Weigthed Trees , 1986, ICALP.

[28]  Walter Unger,et al.  The complexity of the approximation of the bandwidth problem , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[29]  Fillia Makedon,et al.  Polynomial time algorithms for the MIN CUT problem on degree restricted trees , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[30]  James R. Lee,et al.  An improved approximation ratio for the minimum linear arrangement problem , 2007, Inf. Process. Lett..

[31]  David S. Johnson,et al.  COMPLEXITY RESULTS FOR BANDWIDTH MINIMIZATION , 1978 .

[32]  Yota Otachi,et al.  Bandwidth and pathwidth of three-dimensional grids , 2011, Discret. Math..

[33]  JOSEP DÍAZ,et al.  A survey of graph layout problems , 2002, CSUR.

[34]  Yuan Jinjiang,et al.  Optimal labelling of unit interval graphs , 1995 .

[35]  P. A. GOLOVACH.  The total vertex separation number of a graph , 1997 .

[36]  Sheng-Lung Peng,et al.  On the Treewidth and Pathwidth of Biconvex Bipartite Graphs , 2007, TAMC.

[37]  Frank Thomson Leighton,et al.  Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms , 1999, JACM.

[38]  L. H. Harper.  Optimal Assignments of Numbers to Vertices , 1964 .

[39]  Sheng-Lung Peng,et al.  On the interval completion of chordal graphs , 2006, Discret. Appl. Math..

[40]  Kenichi Hagihara,et al.  The minimum bisection widths of the cube-connected cycles graph and cube graph , 1984 .

[41]  Renate Garbe.  Tree-width and Path-width of Comparability Graphs of interval Orders , 1994, WG.

[42]  Jafar Habibi,et al.  Minimum linear arrangement of Chord graphs , 2008, Appl. Math. Comput..

[43]  林詒勋,et al.  PROFILE MINIMIZATION PROBLEM FOR MATRICES AND GRAPHS , 1994 .

[44]  Santosh S. Vempala,et al.  On Euclidean Embeddings and Bandwidth Minimization , 2001, RANDOM-APPROX.

[45]  Ralf Klasing,et al.  Optimal Embedding of Complete Binary Trees into Lines and Grids , 1991, WG.

[46]  José Torres-Jiménez,et al.  Memetic Algorithms for the MinLA Problem , 2005, Artificial Evolution.

[47]  Anupam Gupta.  Improved Bandwidth Approximation for Trees and Chordal Graphs , 2001, J. Algorithms.

[48]  Jin-Kao Hao,et al.  An effective two-stage simulated annealing algorithm for the minimum linear arrangement problem , 2008, Comput. Oper. Res..

[49]  Konstantin Skodinis.  Computing Optimal Linear Layouts of Trees in Linear Time , 2000, ESA.

[50]  Michael R. Fellows,et al.  On Well-Partial-Order Theory and its Application to Combinatorial Problems of VLSI Design , 1989, SIAM J. Discret. Math..

[51]  Marek Karpinski,et al.  On Approximation Intractability of the Bandwidth Problem , 1997, Electron. Colloquium Comput. Complex..

[52]  José D. P. Rolim,et al.  Optimal Cutwidths and Bisection Widths of 2- and 3-Dimensional Meshes , 1995, WG.

[53]  Norman E. Gibbs,et al.  The bandwidth problem for graphs and matrices - a survey , 1982, J. Graph Theory.

[54]  Alan P. Sprague.  An 0(n log n) Algorithm for Bandwidth of Interval Graphs , 1994, SIAM J. Discret. Math..

[55]  Jinjiang Yuan,et al.  Profile minimization problem for matrices and graphs , 1994 .

[56]  Sorina Dumitrescu,et al.  On explicit formulas for bandwidth and antibandwidth of hypercubes , 2009, Discret. Appl. Math..

[57]  Maria J. Serna,et al.  A Polynomial Time Algorithm for the Cutwidth of Bounded Degree Graphs with Small Treewidth , 2001, ESA.

[58]  Fillia Makedon,et al.  Approximation algorithms for the bandwidth minimization problem for a large class of trees , 2007, Theory of Computing Systems.

[59]  R. Durbin,et al.  Optimal numberings of an N N array , 1986 .

[60]  John R. Gilbert,et al.  Approximating Treewidth, Pathwidth, and Minimum Elimination Tree Height , 1991, WG.

[61]  Michael A. Langston,et al.  Approximation the Pathwidth of Outerplanar Graphs , 1998, Inf. Process. Lett..

[62]  Gerard J. Chang,et al.  The Profile Minimization Problem in Trees , 1994, SIAM J. Comput..

[63]  Stefan Szeider,et al.  The Linear Arrangement Problem Parameterized Above Guaranteed Value , 2007, Theory of Computing Systems.

[64]  Maria J. Serna,et al.  Cutwidth I: A linear time fixed parameter algorithm , 2005, J. Algorithms.

[65]  Ioan Todinca,et al.  Pathwidth of Circular-Arc Graphs , 2007, WG.

[66]  Maria J. Serna,et al.  Cutwidth II: Algorithms for partial w-trees of bounded degree , 2005, J. Algorithms.

[67]  Michael R. Fellows,et al.  Layout permutation problems and well-partially-ordered sets , 1988 .

[68]  Robert Warren,et al.  Lower bounds on the pathwidth of some grid-like graphs , 2008, Discret. Appl. Math..

[69]  Jordi Petit Silvestre,et al.  Approximation heuristics and benchmarkings for the MinLA problem , 1997 .

[70]  Daniel Berend,et al.  Minimal cutwidth linear arrangements of abelian Cayley graphs , 2008, Discret. Math..

[71]  B. Monien.  The bandwidth minimization problem for caterpillars with hair length 3 is NP-complete , 1986 .

[72]  Ivan Hal Sudborough,et al.  The Vertex Separation and Search Number of a Graph , 1994, Inf. Comput..

[73]  Robert Malcolm Macgregor,et al.  On partitioning a graph: a theoretical and empirical study. , 1978 .

[74]  Haim Kaplan,et al.  Four Strikes Against Physical Mapping of DNA , 1995, J. Comput. Biol..

[75]  Eitan M. Gurari,et al.  Improved Dynamic Programming Algorithms for Bandwidth Minimization and the MinCut Linear Arrangement Problem , 1984, J. Algorithms.

[76]  Mike Paterson,et al.  A Short Proof of the Dilation of a Toroidal Mesh in a Path , 1993, Inf. Process. Lett..

[77]  Bojan Mohar,et al.  Optimal linear labelings and eigenvalues of graphs , 1992, Discret. Appl. Math..

[78]  Fillia Makedon,et al.  Approximation Algorithms for the Bandwidth Minimization Problem for a Large Class of Trees , 1991, ICCI.

[79]  Pim van 't Hof,et al.  Computing the Cutwidth of Bipartite Permutation Graphs in Linear Time , 2012, SIAM J. Discret. Math..

[80]  Ilya Safro,et al.  Graph minimum linear arrangement by multilevel weighted edge contractions , 2006, J. Algorithms.

[81]  Uriel Feige,et al.  Hardness results for approximating the bandwidth , 2011, J. Comput. Syst. Sci..

[82]  Thomas Lengauer.  Black-white pebbles and graph separation , 2004, Acta Informatica.

[83]  C. Pandu Rangan,et al.  On Finding the Minimum Bandwidth of Interval Graphs , 1991, Inf. Comput..

[84]  Fillia Makedon,et al.  Polynomial Time Algorithms for the Min Cut Problem on Degree Restricted Trees , 1982, FOCS.

[85]  O. Svensson,et al.  Inapproximability Results for Sparsest Cut, Optimal Linear Arrangement, and Precedence Constrained Scheduling , 2007, FOCS 2007.

[86]  Dieter Kratsch,et al.  Approximating the Bandwidth for Asteroidal Triple-Free Graphs , 1999, J. Algorithms.

[87]  James B. Saxe,et al.  Dynamic-Programming Algorithms for Recognizing Small-Bandwidth Graphs in Polynomial Time , 1980, SIAM J. Algebraic Discret. Methods.

[88]  Stefan Szeider,et al.  Fixed-Parameter Complexity of Minimum Profile Problems , 2007, Algorithmica.

[89]  Susanne E. Hambrusch,et al.  Planar linear arrangements of outerplanar graphs , 1988 .

[90]  André Raspaud,et al.  Cutwidth of the Bruijn Graph , 1995, RAIRO Theor. Informatics Appl..

[91]  Joseph Naor,et al.  Divide-and-conquer approximation algorithms via spreading metrics , 2000, JACM.

[92]  David Muradian.  The bandwidth minimization problem for cyclic caterpillars with hair length 1 is NP-complete , 2003, Theor. Comput. Sci..

[93]  Mark D. Hansen.  Approximation algorithms for geometric embeddings in the plane with applications to parallel processing problems , 1989, 30th Annual Symposium on Foundations of Computer Science.

[94]  Dieter Kratsch,et al.  Bandwidth of Chain Graphs , 1998, Inf. Process. Lett..

[95]  Béla Bollobás,et al.  Edge-isoperimetric inequalities in the grid , 1991, Comb..

[96]  Marek Karpinski,et al.  An Approximation Algorithm for the Bandwidth Problem on Dense Graphs , 1997, Electron. Colloquium Comput. Complex..

[97]  Maria J. Serna,et al.  Convergence Theorems for Some Layout Measures on Random Lattice and Random Geometric Graphs , 2000, Combinatorics, Probability and Computing.

[98]  Timo Poranen,et al.  A Genetic Hillclimbing Algorithm for the Optimal Linear Arrangement Problem , 2005, Fundam. Informaticae.

[99]  David Harel,et al.  A Multi-scale Algorithm for the Linear Arrangement Problem , 2002, WG.

[100]  Pinar Heggernes,et al.  Cutwidth of Split Graphs, Threshold Graphs, and Proper Interval Graphs , 2008, WG.

[101]  Mihalis Yannakakis,et al.  A polynomial algorithm for the MIN CUT linear arrangement of trees , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[102]  Chuan Yi Tang,et al.  Graph Searching on Some Subclasses of Chordal Graphs , 2000, Algorithmica.

[103]  Christos H. Papadimitriou,et al.  The bisection width of grid graphs , 1990, SODA '90.

[104]  James R. Lee,et al.  Improved approximation algorithms for minimum-weight vertex separators , 2005, STOC '05.

[105]  Santosh S. Vempala,et al.  Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems , 1998, STOC '98.

[106]  Jordi Petit,et al.  Combining Spectral Sequencing and Parallel Simulated Annealing for the MINLA Problem , 2003, Parallel Process. Lett..

[107]  M. Fellows,et al.  Beyond NP-completeness for problems of bounded width: hardness for the W hierarchy , 1994, Symposium on the Theory of Computing.

[108]  Fillia Makedon,et al.  Bandwidth Minimization: An approximation algorithm for caterpillars , 2005, Mathematical systems theory.

[109]  Frank Thomson Leighton,et al.  Graph bisection algorithms with good average case behavior , 1984, Comb..

[110]  Dieter Kratsch,et al.  Treewidth and Minimum Fill-in on d-Trapezoid Graphs , 1998, J. Graph Algorithms Appl..

[111]  Satish Rao,et al.  New approximation techniques for some ordering problems , 1998, SODA '98.