B. Doerr and A. Srivastav. Recursive randomized coloring beats fair dice random colorings. In A. Ferreira and H. Reichel, editors, Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science (STACS) 2001, volume 2010 of Lecture Notes in Computer Science, pages 183-194, Berlin{Heidelberg, 2001. Springer Verlag. Home/Search Document Details and Download
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Balanced k-Colorings - Biedl, Cenek, Chan, Demaine.. (2001) (Correct)
....to give the Akiyama and Urrutia result [2] i.e. we can prove there is always an almostbalanced 2 coloring. In Section 4 we show that a simpler divide and conquer algorithm (which has apparently been known in the field of discrepancy theory [18] but has never been published until recently [13]) computes k colorings which are slightly less balanced than the colorings computed by the algorithm in Section 2. Both algorithms can be implemented efficiently in polynomial time. Recently, Doerr and Srivastav [13] used a randomized recursive approach to obtain colorings with low discrepancies. ....
....the field of discrepancy theory [18] but has never been published until recently [13] computes k colorings which are slightly less balanced than the colorings computed by the algorithm in Section 2. Both algorithms can be implemented efficiently in polynomial time. Recently, Doerr and Srivastav [13] used a randomized recursive approach to obtain colorings with low discrepancies. Finally, in Section 5 we show that for k 2 finding almost balanced k colorings is NP complete for line families of dimension at least maxf3; k Gamma 1g. For k = 2; 3, this result even holds for the special case ....
Benjamin Doerr and Anand Srivastav. Recursive randomized coloring beats fair dice random colorings. In A. Ferreira and H. Reichel, editors, Proceedings of the 18th Annual symposium on Theoretical Aspects of Computer Science (STACS
Typical Rounding Problems - Doerr Self-citation (Doerr) (Correct)
....is justi ed by the fact that most results are of this type. We showed that the classical results of Beck and Spencer and Lov asz, Spencer and Vesztergombi on the relation of both rounding problems can be strengthened in this situation. We analyzed both the worst and average case. Like in [7], our results indicate that the assumption of decreasing discrepancies is both natural and powerful. We have to leave it as an open problem how tight our bounds are. Another open problem is for which vectors x the rounding problem is hardest. Small vectors cause lower errors, and as w(a) 3 ....
B. Doerr and A. Srivastav. Recursive randomized coloring beats fair dice random colorings. In A. Ferreira and H. Reichel, editors, Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science (STACS) 2001, volume 2010 of Lecture Notes in Computer Science, pages 183-194, Berlin{Heidelberg, 2001. Springer Verlag.
Structured Randomized Rounding and Coloring - Doerr (2001) Self-citation (Doerr) (Correct)
....is that we also obtain some more information about the random coloring. For example, we may prescribe that our colorings should be 4 fair, that is, have equal sized color classes. This can be useful in some applications, e.g. the recursive method to construct balanced multi colorings of [DS01] uses fair colorings. A nice thing from the technical point of view is that we get these fair colorings without extra technical diculties. Usually, working with fair colorings is more dicult, since the hypergeometric distribution is harder to analyze than the binomial one (cf. Chv atal [Chv79] and ....
....principle connecting geometric and combinatorial discrepancies) rely on the concept of fair colorings. We refer to the rst chapter of Matou sek [Mat99] for the details. Another example is the recursive method to construct balanced multi colorings from 2 color discrepancy information (cf. [DS01]) If X 2 E , then fairness can be obtained by recoloring some vertices in the larger color class. This increases the discrepancy by a factor of at most 2. With our structured random colorings, we can get fairness for free . To show how such structural knowledge about the random coloring can be ....
B. Doerr and A. Srivastav. Recursive randomized coloring beats fair dice random colorings. In A. Ferreira and H. Reichel, editors, Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science (STACS) 2001, volume 2010 of Lecture Notes in Computer Science, pages 183-194, Berlin{Heidelberg, 2001. Springer Verlag.
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