Distinct Distances: Open Problems and Current Bounds

• DOI: 10.48550/arxiv.1406.1949
• Publication Date: 2014-01-01
• Authors: Sheffer, Adam
• Keywords: Computational Geometry (cs.CG); FOS: Computer and information sciences; FOS: Mathematics; Mathematics - Combinatorics; Computer Science - Computational Geometry; 0102 computer and information sciences; Combinatorics (math.CO); 01 natural sciences

We survey the variants of Erd��s' distinct distances problem and the current best bounds for each of those.<br/>Many recent results were added, a few fixes, and two new sections (bipartite problems and connections to Additive Combinatorics)<br/>