#### Filter Results:

- Full text PDF available (1)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

- Amitabha Bagchi, Sohit Bansal
- ArXiv
- 2008

We study the graph constructed on a Poisson point process in d dimensions by connecting each point to the k points nearest to it. This graph a.s. has an infinite cluster if k > kc(d) where kc(d), known as the critical value, depends only on the dimension d. This paper presents an improved upper bound of 188 on the value of kc(2). We also show that if k ≥… (More)

- Amitabha Bagchi, Sohit Bansal
- PODC
- 2008

We study the graph <i>NN(d,k)</i> constructed on a Poisson point process in <i>d</i> dimensions by connecting each point to the <i>k</i> points nearest to it. We show that if <i>k</i> geq 188, <i>NN(2,k)</i> has an infinite connected component and this infinite component has an infinite subset of points with the property that the distance along the edges of… (More)

- ‹
- 1
- ›