In geometric graph theory, a unit disk graph is the intersection graph of a family of unit disks in the Euclidean plane. That is, it is a graph withâ€¦Â (More)

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2016

2016

- Haim Kaplan, Wolfgang Mulzer, Liam Roditty, Paul Seiferth
- Algorithmica
- 2016

Let $$S \subset \mathbb {R}^2$$ SâŠ‚R2 be a set of n sites. The unit disk graph $${{\mathrm{UD}}}(S)$$ UD(S) on S has vertex set Sâ€¦Â (More)

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2009

2009

- Emmanuelle Lebhar, Zvi Lotker
- 2009 IEEE International Symposium on Parallelâ€¦
- 2009

Modeling communications in wireless networks is a challenging task, since it requires a simple mathematical object on whichâ€¦Â (More)

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2008

2008

Motivated by a satellite communications problem, we consider a generalised colouring<lb>problem on unit disk graphs. A colouringâ€¦Â (More)

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2007

2007

- Mathieu Couture, Michel Barbeau, Prosenjit Bose, Paz Carmi, Evangelos Kranakis
- Algorithmica
- 2007

We present the first location-oblivious distributed unit disk graph coloring algorithm having a provable performance ratio ofâ€¦Â (More)

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Highly Cited

2005

Highly Cited

2005

- Stefan Funke, Alexander Kesselman, Ulrich Meyer, Michael Segal
- WiMob'2005), IEEE International Conference onâ€¦
- 2005

Several routing schemes in ad hoc networks first establish a virtual backbone and then route messages via backbone nodes. Oneâ€¦Â (More)

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2004

Highly Cited

2004

- Fabian Kuhn, Thomas Moscibroda, Roger Wattenhofer
- DIALM-POMC
- 2004

Finding a good embedding of a unit disk graph given by its connectivity information is a problem of practical importance in aâ€¦Â (More)

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Highly Cited

2003

Highly Cited

2003

- Fabian Kuhn, Aaron Zollinger
- DIALM-POMC
- 2003

In this paper we study a model for ad-hoc networks close enough to reality as to represent existing networks, being at the sameâ€¦Â (More)

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Highly Cited

1998

Highly Cited

1998

- Heinz Breu, David G. Kirkpatrick
- Comput. Geom.
- 1998

Unit disk graphs are the intersection graphs of unit diameter closed disks in the plane. This paper reduces SATISFIABILITY to theâ€¦Â (More)

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1997

1997

- Madhav V. Marathe, Venkatesh Radhakrishnan, Harry B. Hunt, S. S. Ravi
- Theor. Comput. Sci.
- 1997

We characterize the complexity of a number of basic optimization problems for unit disk graphs speciied hierarchically as inâ€¦Â (More)

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Highly Cited

1995

Highly Cited

1995

- Madhav V. Marathe, H. Breu, Harry B. Hunt, S. S. Ravi, Daniel J. Rosenkrantz
- Networks
- 1995

Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristicsâ€¦Â (More)

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