Improved Approximation Algorithms for Geometric Set Cover

Ken Clarkson

Kasturi Varadarajan

Bell Labs

Univ. Iowa

The set cover problem

For example: siting of basestations

Simplified cases of basestation siting

(A few) old set cover results

If `c := |bb(C)^{:**:} |`, `n := |bb(S)|`, can get within factor:

New results: hypothesis

New results: conclusion

*(a little bit of actual new combinatorial geometry)



`epsilon`-nets: equivalent points

`epsilon`-nets: a different approach

`epsilon`-nets using `F_0(R)`

Small `epsilon`-nets `=>` small covers

Small `epsilon`-nets `=>` small covers: LP

Small `epsilon`-nets `=>` small covers: doubling

Small `F_0(R)` `=>` small `epsilon`-nets: alteration

Small `F_0(R)` `=>` small `epsilon`-nets: analysis

Small `F_0(R)` `=>` small `epsilon`-nets:

final analysis

Terrain guarding: visibility

More visibility

If also:

Why ownership?

Order claim


Concluding remarks