_id,doi,title
6608,10.1016/j.cagd.2019.06.003,"Holes and dependences in an ordered complex"
530,10.1016/j.comgeo.2017.06.014,"Multiple covers with balls I: Inclusion–exclusion"
187,10.4230/LIPIcs.SoCG.2018.34,"The multi-cover persistence of Euclidean balls"
188,10.4230/LIPIcs.SoCG.2018.35,"Smallest enclosing spheres and Chernoff points in Bregman geometry"
87,10.1214/18-AAP1389,"Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics"
312,10.1137/16M1097201,"On the optimality of the FCC lattice for soft sphere packing"
5678,10.1007/s00454-018-0049-2,"Poisson–Delaunay Mosaics of Order k"
1072,,"The Morse theory of Čech and delaunay complexes"
1173,10.1007/s00493-016-3308-y,"The Voronoi functional is maximized by the Delaunay triangulation in the plane"
718,10.1017/apr.2017.20,"Expected sizes of poisson Delaunay mosaics and their discrete Morse functions"
1022,10.1093/mnras/stw2862,"The topology of the cosmic web in terms of persistent Betti numbers"
688,10.4230/LIPIcs.SoCG.2017.39,"Topological data analysis with Bregman divergences"
6288,,"Poisson-Delaunay mosaics of order k"
84,10.1201/9781315119601,"Computational topology for structural molecular biology"
1662,10.1016/j.aim.2015.10.004,"Approximation and convergence of the intrinsic volume"
1295,10.1016/j.endm.2016.09.030,"Multiple covers with balls II: Weighted averages"
1289,10.1016/j.patrec.2015.12.012,"The classification of endoscopy images with persistent homology"
1495,,"Relaxed disk packing"
1793,10.1371/journal.pone.0127657,"DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots"
3585,10.1016/j.comgeo.2015.04.001,"Proof of correctness of the digital Delaunay triangulation algorithm"
1578,10.1016/j.comgeo.2015.04.001,"Triangulations from topologically correct digital Voronoi diagrams"
1567,,"Shape, homology, persistence, and stability"
2035,10.1007/s10208-014-9223-y,"The persistent homology of a self-map"
1568,10.1109/SYNASC.2014.81,"The classification of endoscopy images with persistent homology"
2905,10.4171/120-1/3,"Persistent homology: Theory and practice"
1876,,"Functionals on triangulations of delaunay sets"
2177,10.1137/1.9781611973402.11,"On the computational complexity of betti numbers reductions from matrix rank"
2255,10.1007/s10851-013-0468-x,"Stable length estimates of tube-like shapes"
1929,10.1007/s10958-014-2165-8,"An algorithm for cartographic generalization that preserves global topology"
2155,10.1145/2582112.2582167,"The morse theory of Čech and Delaunay filtrations"
2859,10.4310/HHA.2013.v15.n1.a3,"Homology and robustness of level and interlevel sets"
2906,10.1137/1.9781611972931.6,"3D kinetic alpha complexes and their implementation"
2843,10.1007/978-3-642-37067-0,"Stable length estimates of tube-like shapes"
2887,10.1073/pnas.1222821110,"Genotypic recognition and spatial responses by rice roots"
2822,10.1073/pnas.1304354110,"3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture"
2815,10.1007/s00454-013-9517-x,"Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions"
2912,10.4213/rm9503,"Configuration space for shortest networks "
3256,10.1007/s00454-011-9382-4,"Dual complexes of cubical subdivisions of ℝn"
3310,10.1016/j.patrec.2011.10.007,"A point calculus for interlevel set homology"
2902,,"Fractal and computational geometry for generalizing cartographic objects"
2849,10.1070/RM2012v067n06ABEH004820,"On the configuration space of Steiner minimal trees"
3133,10.1145/2261250.2261287,"Alexander duality for functions: The persistent behavior of land and water and shore"
2903,10.1109/ISVD.2012.11,"The adaptive topology of a digital image"
2941,10.1070/RM2012v067n04ABEH004807,"On the optimality of functionals over triangulations of Delaunay sets"
3134,10.1145/2261250.2261265,"Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions"
3159,10.1371/journal.pone.0036715,"Hierarchical ordering of reticular networks"
2911,,"Open problems in discrete and computational geometry"
3333,,"Homology and robustness of level and interlevel sets"
3965,10.1145/1963190.1970375,"Computing elevation maxima by searching the Gauss sphere"
3377,10.1007/s10208-011-9090-8,"Quantifying transversality by measuring the robustness of intersections"
3334,10.1007/s00454-010-9313-9,"Letter from the new editors-in-chief"
3311,,"Alpha shapes - a survey"
3335,10.1007/978-3-642-25249-5_3,"Alpha, Betti and the Megaparsec Universe: On the topology of the Cosmic Web"
3796,10.1007/978-3-642-19391-0_2,"Covering and packing with spheres by diagonal distortion in R^n"
3312,10.1109/ICCV.2011.6126475," Detailed reconstruction of 3D plant root shape"
3313,10.1109/ICCV.2011.6126271,"Diffusion runs low on persistence fast"
3853,10.1007/978-3-642-15375-4_19,"Mean-payoff automaton expressions"
3795,10.1007/978-3-642-15014-2_3,"The stability of the apparent contour of an orientable 2-manifold"
3901,10.1109/TVCG.2010.139,"Computing robustness and persistence for images"
3848,10.1007/978-3-642-15775-2_1,"The robustness of level sets"
3849,10.1007/978-3-642-15155-2_2,"Persistent homology under non-uniform error"
3899,,"Computational Topology: An Introduction"
3964,10.1007/s10208-010-9060-6,"Lipschitz functions have L_p-stable persistence"
3578,10.1007/b106657_6,"Stability and computation of medial axes: a state-of-the-art report"
3966,10.1007/s10208-008-9027-z,"Extending persistence using Poincare and Lefschetz duality"
3967,,"Persistent homology for kernels, images, and cokernels"
3968,10.1007/978-3-642-10470-1_4,"The persistent Morse complex segmentation of a 3-manifold"
3974,10.1145/1377676.1377720,"Reeb spaces of piecewise linear mappings"
3970,10.1371/journal.pone.0002856,"Comparison of pattern detection methods in microarray time series of the segmentation clock"
3969,,"Persistent homology - a survey"
3971,10.1016/j.comgeo.2007.11.001,"Time-varying Reeb graphs for continuous space-time data"
3577,10.1007/978-3-540-33265-7_5,"Skeletal structures"
3972,10.1007/s00454-006-1276-5,"Stability of persistence diagrams"
3977,10.1007/s00454-006-1274-7,"Inclusion-exclusion formulas from independent complexes"
3561,10.1145/1236246.1236267,"Weak witnesses for Delaunay triangulations of submanifolds"
3973,10.1007/s10208-005-0200-3,"Inequalities for the curvature of curves and surfaces"
3981,10.1007/978-3-540-73951-7_34,"Alpha-beta witness complexes"
3975,10.1109/FOCS.2007.33,"Inferring local homology from sampled stratified spaces"
3976,10.1021/pr070018+,"Protein-protein interfaces: Properties, preferences, and projections"
3511,"US 7,050,876 B1","Manufacturing methods and systems for rapid production of hearing-aid shells"
3559,10.1145/1137856.1137877,"Vines and vineyards by updating persistence in linear time"
3978,10.1002/prot.20811,"Evaluating the quality of NMR structures by local density of protons"
3980,10.1007/s00454-006-1265-8,"Extreme elevation on a 2-manifold"
3512,"US 7,023,432 B2","Method, apparatus and computer products that reconstruct surfaces from data points"
3979,10.1145/1147954.1147957,"Interface surfaces for protein-protein complexes"
3510,"US 6,996,505 B1","Method, apparatus and computer program products for automatically generating NURBS models of triangulated surfaces using homeomorphism"
3560,10.1145/1137856.1137878,"Persistence-sensitive simplification of functions on 2-manifolds"
3509,"US 6,853,373 B2","Methods, apparatus and computer program products for modeling three-dimensional colored objects"
3982,10.1142/9789812702456_0007,"Coarse and reliable geometric alignment for protein docking"
3576,,"The geometry of biomolecular solvation"
3557,http://dx.doi.org/10.2312/SGP/SGP05/009-011,"Surface tiling with differential topology"
3983,10.1021/bi0516879,"Experimental validation of the docking orientation of Cdc25 with its Cdk2-CycA protein substrate"
3558,,"Extraction and simplification of iso-surfaces in tandem"
3984,10.1109/TVCG.2004.3,"A topological hierarchy for functions on triangulated surfaces"
3989,10.1109/VISUAL.2004.68,"Local and global comparison of continuous functions"
3985,10.1007/s00454-004-1122-6,"Loops in Reeb graphs of 2-manifolds"
3574,,"Biological applications of computational topology"
3986,10.1007/s00454-004-1099-1,"The area derivative of a space-filling diagram"
3575,10.1017/CBO9781139106962.003,"Jacobi sets of multiple Morse functions"
3987,10.1109/TVCG.2004.32,"Simplification of three-dimensional density maps"
3988,10.1007/978-3-540-30219-3_19,"Local search heuristic for rigid protein docking"
3990,10.1007/s00454-004-2864-x,"Computing the writhing number of a polygonal knot"
3991,10.1007/3-540-36477-3_7,"Area and perimeter derivatives of a union of disks"
3573,10.1007/978-3-642-55566-4_17,"Surface reconstruction by wrapping finite sets in space"
3992,10.1073/pnas.0537830100,"The weighted-volume derivative of a space-filling diagram"
3997,10.1109/VISUAL.2003.1250365,"A multi-resolution data structure for two-dimensional Morse-Smale functions"
3993,10.1007/s00454-003-2926-5,"Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds"
3556,10.1145/777792.777846,"Morse-Smale complexes for piecewise linear 3-manifolds"
3999,10.1007/978-3-540-44400-8_14,"Relaxed scheduling in dynamic skin triangulation"
3994,10.1016/S0925-7721(02)00124-4,"Area, perimeter and derivatives of a skin curve"
3584,,"Computing linking numbers of a filtration"
3996,10.1007/s00454-002-2885-2,"Topological persistence and simplification"
4003,,"Computing the writhing number of a polygonal knot"
3998,10.1007/s003660200020,"An experimental study of sliver exudation"
4000,10.1142/S0218195902000785,"Fast software for box intersections"
3508,"US 6,377,865 B1","Methods of generating three-dimensional digital models of objects by wrapping point cloud data points"
3995,10.1145/592642.592647,"Algorithmic issues in modeling motion"
4002,10.1016/S0925-7721(01)00020-7,"Design and analysis of planar shape deformation"
4007,10.1007/s00454-001-0007-1,"Dynamic skin triangulation"
3586,,"Geometry and Topology for Mesh Generation"
3507,"US 6,182,016 B1","Molecular classification for property prediction"
4005,,"Dynamic skin triangulation"
4001,10.1016/S0925-7721(01)00021-9,"Shape space from deformation"
4006,10.3217/jucs-007-05-0379,"180 wrapped tubes"
3555,10.1145/335305.335338,"Smoothing and cleaning up slivers"
4008,10.1109/SFCS.2000.892133,"Topological persistance and simplification"
4010,10.1145/355483.355487,"Sliver exudation"
4004,10.1007/s004540010063,"Edgewise subdivision of a simplex"
4009,10.1142/S0218195900000164,"Adaptive simplicial grids from cross-sections of monotone complexes"
3583,,"Triangulations and meshes in computational geometry"
3572,,"Spielereien mit Kreisen und Kugeln. Zum Thema Form und Verformung"
4014,10.1007/PL00009412,"Deformable smooth surface design"
3554,,"Mesh association: formulation and algorithms"
3582,,"Topology preserving edge contraction"
3571,,"Computational topology"
4019,10.1109/PCCGA.1998.732056,"Shape space from deformation"
4015,10.1007/BFb0054315,"Shape reconstruction with Delaunay complex"
3506,"US 5,850,229","Apparatus and method for geometric morphing"
4011,10.1002/(SICI)1097-0134(19981001)33:1<1::AID-PROT1>3.0.CO;2-O,"Analytical shape computation of macromolecules: I. molecular area and volume through alpha shape"
4016,10.1117/12.302448,"Wrapping 3D scanning data"
3570,10.1007/978-3-662-03567-2_17,"Auditory Morse analysis of triangulated manifolds"
4012,10.1002/(SICI)1097-0134(19981001)33:1<18::AID-PROT2>3.0.CO;2-H,"Analytical shape computation of macromolecules: II. Inaccessible cavities in proteins"
4017,10.1002/pro.5560070905,"Anatomy of protein pockets and cavities: Measurement of binding site geometry and implications for ligand design"
4013,10.1016/S0166-218X(98)00067-5,"On the definition and the construction of pockets in macromolecules"
4020,,"Geometry for modeling biomolecules"
4021,387910.1016/S0925-7721(96)00006-5,"A combinatorial approach to cartograms"
4022,10.1007/PL00009291,"Cutting dense point sets in half"
4023,10.1007/PL00009295,"Inclusion-exclusion complexes for pseudodisk collections"
4018,10.1142/S0218195997000223,"Triangulating topological spaces"
4026,10.1007/BF01975867,"Incremental topological flipping works for regular triangulations"
4027,10.1007/BF01955043,"Lines in space: Combinatorics and algorithms"
4030,10.1016/S0006-3495(96)79664-9,"Effects of molecular shape representations on boundary element method for protein electrostatics computations"
4024,10.1109/38.511855,"Viewing geometric protein structures from inside a CAVE"
4031,10.1016/S0006-3495(96)79670-4,"Analytical method for molecular shapes: Area, volume, cavities, interface and pockets"
3553,,"Geometric modeling in CAVE"
4025,10.1016/S0166-218X(96)00054-6,"Triangulating the surface of a molecule"
4034,,"Algebraic decomposition of non-convex polyhedra"
4028,10.1007/BF02574053,"The union of balls and its dual shape"
4035,10.1007/BF02574025,"Improved bounds on weak ε-nets for convex sets"
3551,10.1109/HICSS.1995.375331,"Measuring proteins and voids in proteins"
4029,10.1016/0167-8396(95)00016-Y,"An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere"
3552,,"Alpha shapes: definition and software"
4033,"10.1137/S0097539790179919 ","Selecting heavily covered points"
4038,10.1007/BF01182771,"Algorithms for bichromatic line-segment problems and polyhedral terrains"
3550,,"Modeling with simplicial complexes (topology, geometry and algorithms)"
4039,10.1007/BF01377183,"Ray shooting in polygons using geodesic triangulations"
4032,10.1007/BF02574381,"Counting triangle crossings and halving planes"
4037,10.1145/174462.156635,"Three-dimensional alpha shapes"
4040,10.1007/BF02573974,"An upper bound for conforming Delaunay triangulations"
4045,10.1007/BF02573973,"Diameter, width, closest line pair, and parametric searching"
4041,10.1137/0222031,"On the zone theorem for hyperplane arrangements"
4042,"10.1137/0222036 ","A quadratic time algorithm for the minmax length triangulation"
3568,,"Geometric algorithms"
4036,"10.1137/0222077 ","Computing a face in an arrangement of line segments and related problems"
3569,10.1007/978-3-662-04245-8_1,"Computational geometry"
4044,10.1007/BF02573962,"Edge insertion for optimal triangulations"
3581,10.1016/0925-7721(92)90009-H,"Counting and cutting cycles of lines and rods in space"
4046,10.1145/147508.147511,"An optimal algorithm for intersecting line segments in the plane"
4053,10.1007/BF01285815,"The number of edges of many faces in a line segment arrangement"
4047,10.1016/0304-3975(92)90319-B,"Arrangements of curves in the plane - topology, combinatorics, and algorithms"
4043,10.1137/0913058,"An O(n^2 log n) time algorithm for the MinMax angle triangulation"
4048,10.1016/0020-0190(92)90133-G,"Optimal time bounds for some proximity problems in the plane"
4050,10.1007/BF02293046,"Guest editor's foreword"
4049,10.1007/BFb0023816,"Edge insertion for optimal triangulations"
4052,10.1016/0304-3975(91)90261-Y,"A singly exponential stratification scheme for real semi-algebraic varieties and its applications"
4057,10.1016/0022-0000(91)90013-U,Corrigendum
3566,,"A hyperplane incidence problem with applications to counting distances"
3567,,"Lines in space – A collection of results"
4058,,"Computing a face in an arrangement of line segments"
4054,10.1007/BFb0038185,"On the zone theorem for hyperplane arrangements"
4059,10.1007/3-540-54233-7_172,"Ray shooting in polygons using geodesic triangulations"
4061,10.1007/BF02574698,"Euclidean minimum spanning trees and bichromatic closest pairs"
4055,10.1109/SFCS.1991.185400,"A quadratic time algorithm for the minmax length triangulation"
4062,10.1007/BF02574700,"Points and triangles in the plane and halving planes in space"
4051,"10.1137/0220016 ","An O(n log^2 h) time algorithm for the three-dimensional convex hull problem"
4056,10.1016/0097-3165(91)90042-F,"A lower bound on the number of unit distances between the vertices of a convex polygon"
4064,10.1080/01621459.1990.10475313,"Computing least median of squares regression lines and guided topological sweep"
4069,10.1007/BF02122779,"An acyclicity theorem for cell complexes in d dimension"
4071,10.1145/98524.98535,"An O(n^2log n) time algorithm for the MinMax angle triangulation"
4076,10.1145/98524.98567," Euclidean minimum spanning trees and bichromatic closest pairs"
4060,10.1016/S0747-7171(08)80068-5,"Tetrahedrizing point sets in three dimensions"
4065,10.1016/0012-365X(90)90147-A,"Covering convex sets with non-overlapping polygons"
4072," 10.1007/BF02187784","The complexity and construction of many faces in arrangements of lines and of segments"
4077,10.1145/98524.98548,"Points and triangles in the plane and halving planes in space"
4066,10.1007/BF02187785,"The complexity of many cells in arrangements of planes and related problems"
4073,10.1109/FSCS.1990.89543,"Counting and cutting cycles of lines and rods in space"
4078,10.1145/98524.98551,"Slimming down by adding; selecting heavily covered points"
4067,10.1007/3-540-52921-7_91,"A hyperplane Incidence problem with applications to counting distances"
4074,10.1007/BF02187783,"Combinatorial complexity bounds for arrangements of curves and spheres"
3565,10.1007/978-1-4613-8997-2_25,"Probing convex polytopes"
4063,10.1145/77635.77639,"Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms"
4068," 10.1007/BF02187778","The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2"
4070,10.1080/00207169008803871,"Ranking intervals under visibility constraints"
4075,10.1007/BF01840404,"Searching for empty convex polygons"
4088,10.1007/BF02187742,"Implicitly representing arrangements of lines or segments"
4083,10.1137/0218025,"Partitioning space for range queries"
4084,10.1016/0304-3975(89)90133-3,"Testing the necklace condition for shortest tours and optimal factors in the plane"
4089,10.1007/BF02187745,"On arrangements of Jordan arcs with three intersections per pair"
4080,10.1007/BF00181432,"Circles through two points that always enclose many points"
4085,10.1145/73833.73850,"An acyclicity theorem for cell complexes in d dimension"
3549,,"Spatial triangulations with dihedral angle conditions"
4092,10.1007/BFb0035760,"A singly exponential stratification scheme for real semi-algebraic varieties and its applications"
4093,10.1007/BF02187720,"The complexity of cutting complexes"
4079,,"On the number of furthest neighbor pairs in a point set"
4081,10.1007/BF02187733,"The upper envelope of piecewise linear functions: Algorithms and applications"
4086,10.1007/BF02187734,"The upper envelope of piecewise linear functions: Tight bounds on the number of faces "
4087,10.1007/3-540-51084-2_31,"Tetrahedrizing point sets in three dimensions"
4082,10.1016/0022-0000(89)90038-X,"Topologically sweeping an arrangement"
4090,10.1016/0890-5401(88)90049-1,"Minimum polygonal separation"
4096,10.1007/3-540-19488-6_117,"Geometric structures in computational geometry"
4091,"10.1137/0217054 ","Probing convex polygons with X-Rays"
4097,10.1007/3-540-19488-6_118,"Arrangements of curves in the plane - topology, combinatorics, and algorithms"
4095,10.1109/TC.1987.5009474,"An improved algorithm for constructing kth-order Voronoi diagrams"
3900,,"Algorithms in Combinatorial Geometry"
4100,10.1007/BF02187875,"Linear space data structures for two types of range search"
3514,10.1109/SFCS.1987.44,"On the lower envelope of bivariate functions and its applications"
4101,10.1016/0020-0190(87)90120-7,"Zooming by repeated range detection"
4102,10.1016/0196-6774(87)90015-0,"Space searching for intersecting objects"
4094,10.1016/0020-0190(87)90038-X,"A tight lower bound on the size of visibility graphs"
4103,10.1016/0097-3165(86)90078-6,"On the maximal number of edges of many faces in an arrangement"
4108,10.1007/BF02187681,"Voronoi diagrams and arrangements"
3580,10.1007/BF01840438,"Edge-skeletons in arrangements with applications"
4110,10.1137/0215019,"Constructing belts in two-dimensional arrangements with applications"
3579,,"How often can you see yourself in a convex configuration of mirrors?"
4104,10.1137/0215023,"Optimal point location in a monotone subdivision"
4109,10.1093/comjnl/29.1.76,"Rectangular point location in d-dimensions with applications"
4105,10.1137/0215024,"Constructing arrangements of lines and hyperplanes with applications"
4098,10.1016/0097-3165(86)90075-0,"The number of extreme pairs of finite point-sets in Euclidean spaces"
4106,10.1016/S0747-7171(86)80020-7,"Computing a ham-sandwich cut in two dimensions"
4099,10.1016/0020-0190(86)90088-8,"Halfplanar range search in linear space and O(n0.695) query time"
4107,10.1016/0012-365X(86)90008-7,"The complexity of cells in 3-dimensional arrangements"
4115,10.1016/0196-6774(85)90039-2,"Computing the extreme distances between two convex polygons"
4111,10.1016/0020-0190(85)90107-3,"Finding extreme-points in 3-dimensions and solving the post-office problem in the plane"
4116,10.1016/0304-3975(85)90005-2,"Finding Transversals for Sets of Simple Geometric-Figures"
4112,10.1016/0196-6774(85)90030-6,"Batched dynamic solutions to decomposable searching problems"
4113,10.1016/0097-3165(85)90017-2,"On the number of line separations of a finite set in the plane"
4120,10.1016/S0747-7171(85)80028-6,"Optimal solutions for a class of point retrieval problems"
4114,10.1007/BF01908077,"Investigation of Proportional Link Linkage Clustering Methods"
4122,10.1007/3-540-12920-0_1,"Key-problems and key-methods in computational geometry"
4123,10.1016/0734-189X(84)90142-7,"Some methods of computational geometry applied to computer graphics"
3513,,"Ham-sandwich theorems applied to intersection problems"
4117,,"Computing the connected components of simple rectilinear geometrical objects in D-Space"
4118,10.1016/S0734-189X(84)80041-9,"Stationing guards in rectilinear art galleries"
4125,10.1016/0031-3203(84)90064-5,"An optimal algorithm for constructing the weighted Voronoi diagram in the plane"
4119,10.1007/BFb0030307,"Monotone edge sequences in line arrangements and applications"
4121,10.1007/BF01890115,"Efficient algorithms for agglomerative hierarchical clustering methods"
4127,10.1080/00207168308803365,"A new approach to rectangle intersections part 2"
3562,,"On expected- and worst-case segment trees"
4128,"10.1109/TIT.1983.1056714 ","On the shape of a set of points in the plane"
3563,,"Graphics in Flatland: a case study"
4124,10.1007/BFb0036908,"On the number of equal-sized semispaces of a set of points in the plane"
3564,,"Neue Entwicklungen im Bereich Datenstrukturen"
4126,10.1080/00207168308803364,"A new approach to rectangle intersections part 1"
4130,10.1016/0020-0190(82)90090-4,"Polygonal intersection searching"
4129,10.1007/BF01934440,"Stabbing line segments"
4131,10.1016/0020-0190(82)90068-0,"On the equivalence of some rectangle problems"
4132,10.1016/0020-0190(81)90053-3,"On the intersection of Orthogonal objects"
4133,10.1016/0304-3975(81)90103-1,"A space-optimal solution of general region location"