Name
Abstract | ||
|---|---|---|
Lovász proved (see [7]) that given real numbers p1,..., pn, one can round them up or down to integers ϵ1,..., ϵn, in such a way that the total rounding error over every interval (i.e., sum of consecutive pi’s) is at most \(1-\frac{1}{n+1}\). Here we show that the rounding can be done so that for all \(d = 1,...,\left\lfloor {\frac{{n + 1}}{2}} \right\rfloor \), the total rounding error over every union of d intervals is at most \(\left(1-\frac{d}{n+1}\right)d\). This answers a question of Bohman and Holzman [1], who showed that such rounding is possible for each value of d separately. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1007/s00493-017-3769-7 | Combinatorica |
Keywords | Field | DocType |
05C65, 11K38 | Integer,Discrete mathematics,Combinatorics,Round-off error,Rounding,Real number,Mathematics | Journal |
Volume | Issue | ISSN |
39.0 | 1.0 | 1439-6912 |
Citations | PageRank | References |
0 | 0.34 | 5 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ron Holzman | 1 | 287 | 43.78 |
| Nitzan Tur | 2 | 0 | 0.34 |