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
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
A short proof that “proper = unit”
Discrete Mathematics - Special issue on partial ordered sets
Journal of Algorithms
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
Improved bounds for scheduling conflicting jobs with minsum criteria
ACM Transactions on Algorithms (TALG)
Models of Greedy Algorithms for Graph Problems
Algorithmica
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Priority algorithms for graph optimization problems
Theoretical Computer Science
Universality considerations in VLSI circuits
IEEE Transactions on Computers
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We consider the sum coloring (chromatic sum) problem and the sum multi-coloring problem for restricted families of graphs. In particular, we consider the graph classes of proper intersection graphs of axis-parallel rectangles, proper interval graphs, and unit disk graphs. All the above-mentioned graph classes belong to a more general graph class of (k+1)-clawfree graphs (respectively, for k=4,2,5). We prove that sum coloring is NP-hard for penny graphs and unit square graphs which implies NP-hardness for unit disk graphs and proper intersection graphs of axis-parallel rectangles. We show a 2-approximation algorithm for unit square graphs, with the assumption that the geometric representation of the graph is given. For sum multi-coloring, we confirm that the greedy first-fit coloring, after ordering vertices by their demands, achieves a k-approximation for the preemptive version of sum multi-coloring on (k+1)-clawfree graphs. Finally, we study priority algorithms as a model for greedy algorithms for the sum coloring problem and the sum multi-coloring problem. We show various inapproximation results under several natural input representations.