# Combinatorial Optimization with Explicit Delineation of the Ground Set by a Collection of Subsets

@article{Dror2008CombinatorialOW, title={Combinatorial Optimization with Explicit Delineation of the Ground Set by a Collection of Subsets}, author={Moshe Dror and James B. Orlin}, journal={SIAM J. Discrete Math.}, year={2008}, volume={21}, pages={1019-1034} }

- Published in SIAM J. Discrete Math. 2008
DOI:10.1137/050636589

We examine a selective list of combinatorial optimization problems in NP with respect to inapproximability (Arora and Lund (1997)) given that the ground set of elements $N$ has additional characteristics. For each problem in this paper, the set $N$ is expressed explicitly by subsets of $N$ either as a partition or in the form of a cover. The problems examined are generalizations of well-known classical graph problems and include the minimal spanning tree problem, a number of elementary machine… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 37 REFERENCES

## Arc routing : theory, solutions and applications

VIEW 11 EXCERPTS

## Generalized Steiner Problems and Other Variants

VIEW 25 EXCERPTS

## Polynomial time approximation schemes for Euclidean TSP and other geometric problems

VIEW 9 EXCERPTS

HIGHLY INFLUENTIAL

## Production planning problems in printed circuit board assembly

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Generalized spanning trees

VIEW 4 EXCERPTS

## Hardness of approximations

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Computers and Intractability: A Guide to the Theory of NP-Completeness

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Combinatorial Optimization: Networks and Matroids

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Some NP-Complete Geometric Problems

VIEW 19 EXCERPTS

HIGHLY INFLUENTIAL