The Open Problems Project

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[1]  Timothy M. Chan,et al.  Space-efficient algorithms for computing the convex hull of a simple polygonal line in linear time , 2004, Comput. Geom..

[2]  David P. Dobkin,et al.  Delaunay graphs are almost as good as complete graphs , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[3]  Subhash Suri,et al.  Surface approximation and geometric partitions , 1994, SODA '94.

[4]  John Iacono,et al.  Packing 2×2 unit squares into grid polygons is NP-complete , 2009, CCCG.

[5]  Arnold L. Rosenberg,et al.  Comparing Queues and Stacks as Mechanisms for Laying out Graphs , 1992, SIAM J. Discret. Math..

[6]  Martin Dietzfelbinger,et al.  Lower Bounds for Sorting of Sums , 1987, Theor. Comput. Sci..

[7]  Joseph O'Rourke,et al.  Computational geometry column 46 , 2004, SIGA.

[8]  David R. Wood,et al.  Optimal three-dimensional orthogonal graph drawing in the general position model , 2003, Theor. Comput. Sci..

[9]  Esther M. Arkin,et al.  On the maximum scatter TSP , 1997, SODA '97.

[10]  J. Nelissen.  New approaches to the pallet loading problem , 1993 .

[11]  Joseph S. B. Mitchell,et al.  Generating Random Polygons with Given Vertices , 1996, Comput. Geom..

[12]  Johannes Blömer,et al.  Computing Sums of Radicals in Polynomial Time , 1991, FOCS.

[13]  Martin Held,et al.  Heuristics for the Generation of Random Polygons , 1996, CCCG.

[14]  Ileana Streinu,et al.  A Pseudo-Algorithmic Separation of Lines from Pseudo-Lines , 1995, Inf. Process. Lett..

[15]  Csaba D. Tóth,et al.  Distinct Distances in the Plane , 2001, Discret. Comput. Geom..

[16]  Iwan Jensen,et al.  Counting Polyominoes: A Parallel Implementation for Cluster Computing , 2003, International Conference on Computational Science.

[17]  Masud Hasan,et al.  Equiprojective Polyhedra , 2003, CCCG.

[18]  Ileana Streinu,et al.  A combinatorial approach to planar non-colliding robot arm motion planning , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[19]  Marc Noy,et al.  On the chromatic number of some geometric type Kneser graphs , 2005, Comput. Geom..

[20]  Sándor P. Fekete,et al.  Approximation of Geometric Dispersion Problems , 1998, Algorithmica.

[21]  Joseph O'Rourke,et al.  Vertex-edge pseudo-visibility graphs: characterization and recognition , 1997, SCG '97.

[22]  Jorge Urrutia,et al.  Perfect divisions of a cake , 1998, CCCG.

[23]  Andrew Chi-Chih Yao,et al.  On Constructing Minimum Spanning Trees in k-Dimensional Spaces and Related Problems , 1977, SIAM J. Comput..

[24]  Antonio Hernández-Barrera,et al.  Finding an o(n2 log n) Algorithm Is Sometimes Hard , 1996, Canadian Conference on Computational Geometry.

[25]  Erik D. Demaine,et al.  Hinged Dissections Exist , 2007, SCG '08.

[26]  Sándor P. Fekete,et al.  Simplicity and hardness of the maximum traveling salesman problem under geometric distances , 1999, SODA '99.

[27]  Alok Aggarwal,et al.  The angular-metric traveling salesman problem , 1997, SODA '97.

[28]  Boris Aronov,et al.  Star Unfolding of a Polytope with Applications , 1997, SIAM J. Comput..

[29]  Csaba D. Tóth.  A Note on Binary Plane Partitions , 2001, SCG '01.

[30]  Micha Sharir,et al.  On levels in arrangements of lines, segments, planes, and triangles , 1997, SCG '97.

[31]  Gerhard J. Woeginger,et al.  The Maximum Traveling Salesman Problem Under Polyhedral Norms , 1998, IPCO.

[32]  J. Csima,et al.  There exist 6n/13 ordinary points , 1993, Discret. Comput. Geom..

[33]  U. S. R. Murty.  How Many Magic Configurations are There , 1971 .

[34]  Prosenjit Bose,et al.  Partitions of Complete Geometric Graphs into Plane Trees , 2004, GD.

[35]  Gert Vegter,et al.  In handbook of discrete and computational geometry , 1997 .

[36]  Michael S. Payne,et al.  Unit Distance Graphs with Ambiguous Chromatic Number , 2007, Electron. J. Comb..

[37]  David R. Wood,et al.  Three-Dimensional Grid Drawings with Sub-quadratic Volume , 2003, GD.

[38]  Bojan Mohar.  Bar-Magnet Polyhedra and NS-Orientations of Maps , 2006, Discret. Comput. Geom..

[39]  Boris Aronov,et al.  Nonoverlap of the star unfolding , 1991, SCG '91.

[40]  Michael T. Goodrich,et al.  Almost optimal set covers in finite VC-dimension , 1995, Discret. Comput. Geom..

[41]  László Lovász,et al.  On Conway's Thrackle Conjecture , 1995, SCG '95.

[42]  Jayme Luiz Szwarcfiter,et al.  Hamilton Paths in Grid Graphs , 1982, SIAM J. Comput..

[43]  Michael Hoffmann,et al.  The Euclidean degree-4 minimum spanning tree problem is NP-hard , 2009, SCG '09.

[44]  Joseph O'Rourke.  Computational geometry column 18 , 1993, SIGA.

[45]  Ioannis G. Tollis,et al.  Algorithms for Incremental Orthogonal Graph Drawing in Three Dimensions , 1999, J. Graph Algorithms Appl..

[46]  Steven Skiena,et al.  Hamiltonian triangulations for fast rendering , 1996, The Visual Computer.

[47]  David Eppstein,et al.  Flipping Cubical Meshes , 2001, Engineering with Computers.

[48]  On levels in arrangements of curves , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[49]  Balázs Keszegh,et al.  Improved Upper Bounds on the Reflexivity of Point Sets , 2007, CCCG.

[50]  János Pach,et al.  How to draw a planar graph on a grid , 1990, Comb..

[51]  Esther M. Arkin,et al.  On the Reflexivity of Point Sets , 2001, WADS.

[52]  Jeff Erickson,et al.  Lower bounds for linear satisfiability problems , 1995, SODA '95.

[53]  Joseph S. B. Mitchell,et al.  Separation and approximation of polyhedral objects , 1992, SODA '92.

[54]  Michael L. Fredman,et al.  How Good is the Information Theory Bound in Sorting? , 1976, Theor. Comput. Sci..

[55]  Wolfgang Maass,et al.  Approximation schemes for covering and packing problems in image processing and VLSI , 1985, JACM.

[56]  Goos Kant,et al.  A Better Heuristic for Orthogonal Graph Drawings , 1994, ESA.

[57]  Grant Cairns,et al.  Bounds for Generalized Thrackles , 2000, Discret. Comput. Geom..

[58]  F. Frances Yao,et al.  Efficient binary space partitions for hidden-surface removal and solid modeling , 1990, Discret. Comput. Geom..

[59]  I. Ventura,et al.  On polygons enclosing point sets , 1992 .

[60]  David Eppstein,et al.  Ununfoldable polyhedra with convex faces , 1999, Comput. Geom..

[61]  Joseph O'Rourke,et al.  Narrowing light rays with mirrors , 2001, CCCG.

[62]  Jirí Matousek,et al.  Dynamic half-space range reporting and its applications , 2005, Algorithmica.

[63]  Prosenjit Bose,et al.  Online Routing in Triangulations , 1999, SIAM J. Comput..

[64]  Günter Rote,et al.  There are not too many magic configurations , 2007, SCG '07.

[65]  Christos H. Papadimitriou,et al.  On Two Geometric Problems Related to the Traveling Salesman Problem , 1984, J. Algorithms.

[66]  Kenneth Falconer,et al.  Unsolved Problems In Geometry , 1991 .

[67]  Xiang-Yang Li,et al.  Distributed spanner with bounded degree for wireless ad hoc networks , 2002, Proceedings 16th International Parallel and Distributed Processing Symposium.

[68]  Michael T. Goodrich,et al.  On the Complexity of Optimization Problems for 3-dimensional Convex Polyhedra and Decision Trees , 1997, Comput. Geom..

[69]  Erik D. Demaine,et al.  Geometric folding algorithms - linkages, origami, polyhedra , 2007 .

[70]  Joseph O'Rourke,et al.  Computational geometry column 32 , 1997, Int. J. Comput. Geom. Appl..

[71]  Esther M. Arkin,et al.  The Freeze-Tag Problem: How to Wake Up a Swarm of Robots , 2002, SODA '02.

[72]  David R. Wood,et al.  Stacks, Queues and Tracks: Layouts of Graph Subdivisions , 2005, Discret. Math. Theor. Comput. Sci..

[73]  Stefan Felsner,et al.  Hamiltonicity and colorings of arrangement graphs , 2000, SODA '00.

[74]  Lenwood S. Heath,et al.  Laying out Graphs Using Queues , 1992, SIAM J. Comput..

[75]  Timothy M. Chan.  A dynamic data structure for 3-d convex hulls and 2-d nearest neighbor queries , 2006, SODA '06.

[76]  Ronald L. Graham,et al.  Euclidean Ramsey Theory , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[77]  Giri Narasimhan,et al.  Geometric spanner networks , 2007 .

[78]  Joseph S. B. Mitchell,et al.  Minimum-link paths among obstacles in the plane , 1990, SCG '90.

[79]  Erik D. Demaine,et al.  Open problems from cccg 2001 , 2001, CCCG.

[80]  Jon Louis Bentley,et al.  Decomposable Searching Problems I: Static-to-Dynamic Transformation , 1980, J. Algorithms.

[81]  Gerhard J. Woeginger,et al.  The geometric maximum traveling salesman problem , 2002, JACM.

[82]  Christopher Umans,et al.  Hamiltonian cycles in solid grid graphs , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[83]  Sariel Har-Peled,et al.  Polygon-containment and translational min-Hausdorff-distance between segment sets are 3SUM-hard , 2001, SODA '99.

[84]  Paul Erdös,et al.  A colour problem for infinite graphs and a problem in the theory of relations , 1951 .

[85]  David R. Wood,et al.  Minimising the Number of Bends and Volume in 3-Dimensional Orthogonal Graph Drawings with a Diagonal Vertex Layout , 2004, Algorithmica.

[86]  J. O'Rourke.  Computational geometry column 43 , 2002, SIGA.

[87]  Leonidas J. Guibas,et al.  Combinatorial complexity bounds for arrangements of curves and spheres , 1990, Discret. Comput. Geom..

[88]  D. Eppstein.  Hinged Kite Mirror Dissection , 2001, ArXiv.

[89]  Joseph O'Rourke,et al.  Computational geometry column 44 , 2003, SIGA.

[90]  Carl Gutwin,et al.  Classes of graphs which approximate the complete euclidean graph , 1992, Discret. Comput. Geom..

[91]  P. Erdös.  On Sets of Distances of n Points , 1946 .

[92]  Paul Chew,et al.  There are Planar Graphs Almost as Good as the Complete Graph , 1989, J. Comput. Syst. Sci..

[93]  Jianbo Qian,et al.  How much precision is needed to compare two sums of square roots of integers? , 2006, Inf. Process. Lett..

[94]  Marek Chrobak,et al.  A lower bound on the size of universal sets for planar graphs , 1989, SIGA.

[95]  Esther M. Arkin,et al.  Optimal covering tours with turn costs , 2001, SODA '01.

[96]  Walter Schnyder,et al.  Embedding planar graphs on the grid , 1990, SODA '90.

[97]  Bettina Speckmann,et al.  Tight degree bounds for pseudo-triangulations of points , 2001, CCCG.

[98]  Barry Joe,et al.  Construction of three-dimensional Delaunay triangulations using local transformations , 1991, Comput. Aided Geom. Des..

[99]  Samir Khuller,et al.  Low degree spanning trees of small weight , 1994, STOC '94.

[100]  Erik D. Demaine,et al.  On Rolling Cube Puzzles , 2007, CCCG.

[101]  Markus W. Schäffter,et al.  Drawing Graphs on Rectangular Grids , 1995, Discret. Appl. Math..

[102]  Scott A. Mitchell,et al.  A Characterization of the Quadrilateral Meshes of a Surface Which Admit a Compatible Hexahedral Mesh of the Enclosed Volume , 1996, STACS.

[103]  P Erd,et al.  On Sets of Distances of N Points in Euclidean Space , 2022 .

[104]  Francis Chin,et al.  On Hamiltonian Tetrahedralizations Of Convex Polyhedra , 2005 .

[105]  Antonios Symvonis,et al.  Three-dimensional orthogonal graph drawing algorithms , 2000, Discret. Appl. Math..

[106]  Erik D. Demaine,et al.  Unfolding some classes of orthogonal polyhedra , 1998, CCCG.

[107]  Trapping Light With Mirrors , 2004 .

[108]  L. A S Z L,et al.  Crossing Numbers and Hard Erdős Problems in Discrete Geometry , 1997 .

[109]  Jack Snoeyink,et al.  Counting and enumerating pseudo-triangulations with the greedy flip algorithm ∗ , 2005 .

[110]  Alan Saalfeld.  Joint triangulations and triangulation maps , 1987, SCG '87.

[111]  Robert J. Fowler,et al.  Optimal Packing and Covering in the Plane are NP-Complete , 1981, Inf. Process. Lett..

[112]  G. Koester.  4-critical 4-valent planar graphs constructed with crowns. , 1990 .

[113]  Franz Aurenhammer,et al.  Towards compatible triangulations , 2001, Theor. Comput. Sci..

[114]  Stan Wagon.  A machine resolution of a four-color hoax , 2002, CCCG.

[115]  Tomás Kaiser.  Transversals of d-Intervals , 1997, Discret. Comput. Geom..

[116]  L. A. Oa,et al.  Crossing Numbers and Hard Erd} os Problems in Discrete Geometry , 1997 .

[117]  Yanpei Liu,et al.  A Linear Algorithm for 2-bend Embeddings of Planar Graphs in the Two-dimensional Grid , 1998, Discret. Appl. Math..

[118]  Günter Rote,et al.  Partitioning a Polygon into Two Mirror Congruent Pieces , 2008, CCCG.

[119]  Joseph O'Rourke,et al.  Partitioning Regular Polygons into Circular Pieces I: Convex Partitions , 2003, CCCG.

[120]  Samir Khuller,et al.  Low-Degree Spanning Trees of Small Weight , 1996, SIAM J. Comput..

[121]  David R. Wood,et al.  Queue Layouts, Tree-Width, and Three-Dimensional Graph Drawing , 2002, FSTTCS.

[122]  Pat Morin,et al.  In-Place Planar Convex Hull Algorithms , 2002, LATIN.

[123]  David Eppstein,et al.  Hinged dissections of polyominoes and polyforms , 1999, CCCG.

[124]  Jeff Kahn,et al.  Entropy and sorting , 1992, STOC '92.

[125]  Kurt Mehlhorn,et al.  A Strong and Easily Computable Separation Bound for Arithmetic Expressions Involving Radicals , 2000, Algorithmica.

[126]  Kurt Mehlhorn,et al.  A Generalized and improved constructive separation bound for real algebraic expressions , 2000 .

[127]  Micha Sharir,et al.  Lines Avoiding Unit Balls in Three Dimensions , 2005, Discret. Comput. Geom..

[128]  Thomas M. Liebling,et al.  Constrained paths in the flip-graph of regular triangulations , 2007, Computational geometry.

[129]  Oswin Aichholzer,et al.  Triangulations without pointed spanning trees , 2008, Comput. Geom..

[130]  Jason F. Shepherd,et al.  A constructive approach to constrained hexahedral mesh generation , 2009, Engineering with Computers.

[131]  Ge Xia,et al.  On the Dilation of Delaunay Triangulations of Points in Convex Position , 2009, CCCG.

[132]  David R. Wood.  Three-Dimensional Orthogonal Graph Drawing , 2000 .

[133]  T. A. Brown.  Simple paths on convex polyhedra , 1961 .

[134]  David Eppstein,et al.  Linear complexity hexahedral mesh generation , 1996, SCG '96.

[135]  Joseph O'Rourke.  Vertex pi-lights for monotone mountains , 1997, CCCG.

[136]  Jorge Urrutia,et al.  On Polygons Enclosing Point Sets II , 2009, Graphs Comb..

[137]  Randall Dougherty,et al.  Unflippable Tetrahedral Complexes , 2004, Discret. Comput. Geom..

[138]  I. Jensen.  Enumerations of Lattice Animals and Trees , 2000, cond-mat/0007239.

[139]  H. Edelsbrunner,et al.  Tetrahedrizing Point Sets in Three Dimensions , 1988, ISSAC.

[140]  Stan Wagon,et al.  Rhombic Penrose Tilings Can Be 3-Colored , 2000, Am. Math. Mon..

[141]  Timothy M. Chan.  Euclidean Bounded-Degree Spanning Tree Ratios , 2003, SCG '03.

[142]  Günter Rote,et al.  Counting triangulations and pseudo-triangulations of wheels , 2001, CCCG.

[143]  Timothy M. Chan.  Output-sensitive results on convex hulls, extreme points, and related problems , 1995, SCG '95.

[144]  K. Dowsland.  An exact algorithm for the pallet loading problem , 1987 .

[145]  Joseph O'Rourke,et al.  Unfolding Convex Polyhedra via Quasigeodesics , 2007, ArXiv.

[146]  Jorge Urrutia,et al.  Radial Perfect Partitions of Convex Sets in the Plane , 1998, JCDCG.

[147]  David R. Wood,et al.  Tree-Partitions of k-Trees with Applications in Graph Layout , 2003, WG.

[148]  Franz Aurenhammer,et al.  Convexity minimizes pseudo-triangulations , 2002, CCCG.

[149]  Joseph S. B. Mitchell,et al.  The Discrete Geodesic Problem , 1987, SIAM J. Comput..

[150]  E. Szemerédi,et al.  Unit distances in the Euclidean plane , 1984 .

[151]  Greg N. Frederickson,et al.  Hinged dissections : swinging & twisting , 2002 .