A coloring problem for weighted graphs
Information Processing Letters
Buffer Allocation in Regular Dataflow Networks: An Approach Based on Coloring Circular-Arc Graphs
HIPC '96 Proceedings of the Third International Conference on High-Performance Computing (HiPC '96)
Buffer minimization using max-coloring
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Weighted coloring: further complexity and approximability results
Information Processing Letters
Approximating interval coloring and max-coloring in chordal graphs
Journal of Experimental Algorithmics (JEA)
Batch processing with interval graph compatibilities between tasks
Discrete Applied Mathematics
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Batch Coloring Flat Graphs and Thin
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
On the Maximum Edge Coloring Problem
Approximation and Online Algorithms
Weighted coloring on planar, bipartite and split graphs: Complexity and approximation
Discrete Applied Mathematics
Max-Coloring Paths: Tight Bounds and Extensions
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Weighted Coloring: further complexity and approximability results
Information Processing Letters
"Rent-or-buy" scheduling and cost coloring problems
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Approximating the max-edge-coloring problem
Theoretical Computer Science
On the max-weight edge coloring problem
Journal of Combinatorial Optimization
Improved approximation algorithms for the max-edge coloring problem
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
Improved approximation algorithms for the Max Edge-Coloring problem
Information Processing Letters
Clique clustering yields a PTAS for max-coloring interval graphs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Weighted coloring: further complexity and approximability results
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
Capacitated max -batching with interval graph compatibilities
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Max-coloring paths: tight bounds and extensions
Journal of Combinatorial Optimization
Theoretical Computer Science
On the complexity of the max-edge-coloring problem with its variants
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
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Given a graph G = (V, E) and positive integral vertex weights w : V → N, the max-coloring problem seeks to find a proper vertex coloring of G whose color classes C1, C2, ..., Ck, minimize ${\sum_{i=1}^{k}}{\it max}_{v\epsilon C{_{i}} {\it w}(v)}$. The problem arises in scheduling conflicting jobs in batches and in minimizing buffer size in dedicated memory managers. In this paper we present three approximation algorithms and one inapproximability result for the max-coloring problem. We show that if for a class of graphs ${\mathcal G}$, the classical problem of finding a proper vertex coloring with fewest colors has a c-approximation, then for that class ${\mathcal G}$ of graphs, max-coloring has a 4c-approximation algorithm. As a consequence, we obtain a 4-approximation algorithm to solve max-coloring on perfect graphs, and well-known subclasses such as chordal graphs, and permutation graphs. We also obtain constant-factor algorithms for max-coloring on classes of graphs such as circle graphs, circular arc graphs, and unit disk graphs, which are not perfect, but do have a constant-factor approximation for the usual coloring problem. As far as we know, these are the first constant-factor algorithms for all of these classes of graphs. For bipartite graphs we present an approximation algorithm and a matching inapproximability result. Our approximation algorithm returns a coloring whose weight is within $\frac{8}{7}$ times the optimal. We then show that for any ε 0, it is impossible to approximate max-coloring on bipartite graphs to within a factor of $(\frac{8}{7} - \epsilon)$ unless P = NP. Thus our approximation algorithm yields an optimum approximation factor. Finally, we also present an exact sub-exponential algorithm and a PTAS for max-coloring on trees.