The Complexity of Tree Multicolorings
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
A 27/26-Approximation Algorithm for the Chromatic Sum Coloring of Bipartite Graphs
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Information and Computation
Buffer minimization using max-coloring
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The complexity of chromatic strength and chromatic edge strength
Computational Complexity
Complexity results for minimum sum edge coloring
Discrete Applied Mathematics
Minimum sum edge colorings of multicycles
Discrete Applied Mathematics
Minimum sum set coloring of trees and line graphs of trees
Discrete Applied Mathematics
A short proof of the NP-completeness of minimum sum interval coloring
Operations Research Letters
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The present article concentrates on the dogleg-free Manhattan model where horizontal and vertical wire segments are positioned on different sides of the board and each net (wire) has at most one horizontal segment. While the minimum width can be found in linear time in the single row routing, apparently there was no efficient algorithm to find the minimum wire length. We show that there is no hope to find such an algorithm because this problem is ${\cal NP}$-complete even if each net has only two terminals. The results on dogleg-free Manhattan routing can be connected with other application areas related to interval graphs. In this paper we define the minimum value interval placement problem. There is given a set of weighted intervals and $w$ rows and the intervals have to be placed without overlapping into rows so that the sum of the interval values, which is the value of a function of the weight and the row number assigned to the interval, is minimum. We show that this problem is ${\cal NP}$-complete. This implies the ${\cal NP}$-completeness of other problems including the minimum wire length routing and the sum coloring on interval graphs.