1. A problem arising in frequency assignment to cellular antennas
Shakhar Smorodinsky
Mathematics department
Ben-Gurion university of the NEGEV

2. cellular networks – a base-station
every client within range can
communicate with base station
r=range

3. cellular networks – multiple base-stations
more antennas 
increase covered region
backbone network:
between base-stations
radio link:
client  base-station

4. interfering base-stations
base-stations using same frequency 
interference in intersection of regions

5. base-stations use different frequencies
non-interfering base-stations
base-stations use different frequencies 
no interference!

6. base-station frequency assignment
Common approach:
Coloring: intersecting base-stations must use different frequencies
too restrictive and costly :
New approach

7. How about antennas as points?

8. Problem
For many antennas,
Can we reduce # of frequencies ?