Selected Open Problems in Discrete Geometry and Optimization
DOI10.1007/978-3-319-00200-2_18zbMath1273.90114OpenAlexW172577939MaRDI QIDQ2849006
Antoine Deza, Károly Bezdek, Yinyu Ye
Publication date: 13 September 2013
Published in: Discrete Geometry and Optimization (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-3-319-00200-2_18
Semidefinite programming (90C22) Convex programming (90C25) (n)-dimensional polytopes (52B11) Linear programming (90C05) Combinatorial optimization (90C27) Semi-infinite programming (90C34) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Packing and covering in (2) dimensions (aspects of discrete geometry) (52C15) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Convex sets in (2) dimensions (including convex curves) (52A10) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21) Helly-type theorems and geometric transversal theory (52A35) Tilings in (2) dimensions (aspects of discrete geometry) (52C20) Combinatorial complexity of geometric structures (52C45)
Related Items
Uses Software
Cites Work
- Localization from incomplete noisy distance measurements
- Sensor network localization, Euclidean distance matrix completions, and graph realization
- A counterexample to the Hirsch conjecture
- Contact numbers for congruent sphere packings in Euclidean 3-space
- A note on the complexity of \(L _{p }\) minimization
- (Robust) edge-based semidefinite programming relaxation of sensor network localization
- Comparing SOS and SDP relaxations of sensor network localization
- Two tree-width-like graph invariants
- On bar frameworks, stress matrices and semidefinite programming
- Covering large balls with convex sets in spherical space
- Theory of semidefinite programming for sensor network localization
- Realizability of graphs
- Realizability of graphs in three dimensions
- Orthocentric simplices and biregularity
- Classical topics in discrete geometry
- The volume of relaxed Boolean-quadric and cut polytopes
- On the maximum number of touching pairs in a finite packing of translates of a convex body
- Sur un nouvel invariant des graphes et un critère de planarité. (On a new graph invariant and a planarity criterion)
- A new graph parameter related to bounded rank positive semidefinite matrix completions
- A proof of the Kepler conjecture
- Über zwei Probleme bezüglich konvexer Körper von P. Erdős und von V.L. Klee
- Das Problem der dreizehn Kugeln
- Universal Rigidity and Edge Sparsification for Sensor Network Localization
- The Gram Dimension of a Graph
- Deriving Finite Sphere Packings
- A semidefinite programming approach to tensegrity theory and realizability of graphs
- Hyperplane Arrangements with Large Average Diameter
- A Distributed SDP Approach for Large-Scale Noisy Anchor-Free Graph Realization with Applications to Molecular Conformation
- Simplices of Maximal Volume or Minimal Total Edge Length in Hyperbolic Space
- Coverings by convex bodies and inscribed balls
- Exploiting Sparsity in SDP Relaxation for Sensor Network Localization
- Algorithmic Aspects of Wireless Sensor Networks
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item