Maximum bounded 3-dimensional matching is MAX SNP-complete
Information Processing Letters
The minimum labeling spanning trees
Information Processing Letters
On the minimum label spanning tree problem
Information Processing Letters
A note on the minimum label spanning tree
Information Processing Letters
Wavelength rerouting in optical networks, or the Venetian Routing problem
Journal of Algorithms
Approximation and hardness results for label cut and related problems
Journal of Combinatorial Optimization
Labeled Traveling Salesman Problems: Complexity and approximation
Discrete Optimization
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Consider a matroid M=(E,B), where B denotes the family of bases of M, and assign a color c(e) to every element e@?E (the same color can go to more than one element). The palette of a subset F of E, denoted by c(F), is the image of F under c. Assume also that colors have prices (in the form of a function @p(@?), where @? is the label of a color), and define the chromatic price as: @p(F)=@?"@?"@?"c"("F")@p(@?). We consider the following problem: find a base B@?B such that @p(B) is minimum. We show that the greedy algorithm delivers a lnr(M)-approximation of the unknown optimal value, where r(M) is the rank of matroid M. By means of a reduction from SETCOVER, we prove that the lnr(M) ratio cannot be further improved, even in the special case of partition matroids, unless NP@?DTIME(n^l^o^g^l^o^g^n). The results apply to the special case where M is a graphic matroid and where the prices @p(@?) are restricted to be all equal. This special case was previously known as the minimum label spanning tree (MLST) problem. For the MLST, our results improve over the ln(n-1)+1 ratio achieved by Wan, Chen and Xu in 2002. Inspired by the generality of our results, we study the approximability of coloring problems with different objective function @p(F), where F is a common independent set on matroids M"1,...,M"k and, more generally, to independent systems characterized by the k-for-1 property.