An introduction to chromatic sums
CSC '89 Proceedings of the 17th conference on ACM Annual Computer Science Conference
On chromatic sums and distributed resource allocation
Information and Computation
Minimum color sum of bipartite graphs
Journal of Algorithms
Routing with Minimum Wire Length in the Dogleg-Free Manhattan Model is $\cal NP$-Complete
SIAM Journal on Computing
Edge-chromatic sum of trees and bounded cyclicity graphs
Information Processing Letters
Journal of Algorithms
The Complexity of Tree Multicolorings
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Approximation Results for the Optimum Cost Partition Problem
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
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
Discrete Applied Mathematics
Minimum sum multicoloring on the edges of trees
Theoretical Computer Science - Approximation and online algorithms
Complexity results for minimum sum edge coloring
Discrete Applied Mathematics
Min sum edge coloring in multigraphs via configuration LP
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Minimum sum edge colorings of multicycles
Discrete Applied Mathematics
An effective heuristic algorithm for sum coloring of graphs
Computers and Operations Research
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In this paper, we study the minimum sum set coloring (MSSC) problem which consists in assigning a set of x(v) positive integers to each vertex v of a graph so that the intersection of sets assigned to adjacent vertices is empty and the sum of the assigned set of numbers to each vertex of the graph is minimum. The MSSC problem occurs in two versions: non-preemptive and preemptive. We show that the MSSC problem is strongly NP-hard both in the preemptive case on trees and in the non-preemptive case in line graphs of trees. Finally, we give exact parameterized algorithms for these two versions on trees and line graphs of trees.