Name
Abstract | ||
|---|---|---|
Heilbronn's triangle problem asks for the least \mathsuch that n points lying in the unit disc necessarily contain a triangle of area at most \math. Heilbronn initially conjectured \math. As a result of concerted mathematical effort it is currently known that there are positive constants c and C such that \mathfor every constant \math.We resolve Heilbronn's problem in the expected case: If we uniformly at random put n points in the unit disc then (i) the area of the smallest triangle has expectation \math(1=n3 ); and (ii) the smallest triangle has area \math(1=n3 ) with probability almost one. Our proof uses the incompressibility method based on Kolmogorov complexity. |
Year | DOI | Venue |
|---|---|---|
1999 | 10.1109/CCC.1999.766269 | IEEE Conference on Computational Complexity |
Keywords | Field | DocType |
positive constants c,incompressibility method,expected case,n point,unit disc,expected size,smallest triangle,concerted mathematical effort,kolmogorov complexity,triangle problem,multidimensional systems,computer science,computational complexity,history,computational geometry,upper bound | Discrete mathematics,Binary logarithm,Combinatorics,Kolmogorov complexity,Computational geometry,Mathematics,Computational complexity theory | Conference |
ISSN | ISBN | Citations |
1093-0159 | 0-7695-0075-7 | 4 |
PageRank | References | Authors |
0.60 | 4 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tao Jiang | 1 | 366 | 33.90 |
| Ming Li | 2 | 5595 | 829.00 |
| Paul Vitányi | 3 | 2130 | 287.76 |