On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Dotted interval graphs and high throughput genotyping
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating minimum coloring and maximum independent set in dotted interval graphs
Information Processing Letters
Optimization problems in multiple-interval graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Journal of Computer and System Sciences
ACM Transactions on Algorithms (TALG)
Optimization problems in dotted interval graphs
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
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Dotted interval graphs were introduced by Aumann et al. [Y. Aumann, M. Lewenstein, O. Melamud, R. Pinter, Z. Yakhini, Dotted interval graphs and high throughput genotyping, in: ACM-SIAM Symposium on Discrete Algorithms, SODA 2005, pp. 339-348] as a generalization of interval graphs. The problem of coloring these graphs found application in high-throughput genotyping. Jiang [M. Jiang, Approximating minimum coloring and maximum independent set in dotted interval graphs, Information Processing Letters 98 (2006) 29-33] improves the approximation ratio of Aumann et al. [Y. Aumann, M. Lewenstein, O. Melamud, R. Pinter, Z. Yakhini, Dotted interval graphs and high throughput genotyping, in: ACM-SIAM Symposium on Discrete Algorithms, SODA 2005, pp. 339-348]. In this work we improve the approximation ratio of Jiang [M. Jiang, Approximating minimum coloring and maximum independent set in dotted interval graphs, Information Processing Letters 98 (2006) 29-33] and Aumann et al. [Y. Aumann, M. Lewenstein, O. Melamud, R. Pinter, Z. Yakhini, Dotted interval graphs and high throughput genotyping, in: ACM-SIAM Symposium on Discrete Algorithms, SODA 2005, pp. 339-348]. In the exposition we develop a generalization of the problem of finding the maximum number of non-attacking queens on a triangle.