Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
A coloring problem for weighted graphs
Information Processing Letters
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Buffer minimization using max-coloring
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Latency constrained aggregation in sensor networks
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Batch processing with interval graph compatibilities between tasks
Discrete Applied Mathematics
Batch Coloring Flat Graphs and Thin
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
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
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Max-coloring and online coloring with bandwidths on interval graphs
ACM Transactions on Algorithms (TALG)
Approximation algorithms for the max-coloring problem
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Capacitated max -batching with interval graph compatibilities
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Theoretical Computer Science
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We are given an interval graph G = (V,E) where each interval I ∈ V has a weight wI ∈ R+. The goal is to color the intervals V with an arbitrary number of color classes C1,C2,..., Ck such that Σi=1k maxI∈Ci wI is minimized. This problem, called max-coloring interval graphs, contains the classical problem of coloring interval graphs as a special case for uniform weights, and it arises in many practical scenarios such as memory management. Pemmaraju, Raman, and Varadarajan showed that max-coloring interval graphs is NP-hard (SODA'04) and presented a 2-approximation algorithm. Closing a gap which has been open for years, we settle the approximation complexity of this problem by giving a polynomial-time approximation scheme (PTAS), that is, we show that there is an (1+ε)-approximation algorithm for any ε 0. Besides using standard preprocessing techniques such as geometric rounding and shifting, our main building block is a general technique for trading the overlap structure of an interval graph for accuracy, which we call clique clustering.