Geodesic
Arranging numbers on circles to reach maximum total variations
The electronic journal of combinatorics, Tome 14 (2007)
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The dartboard problem is to arrange $n$ numbers on a circle to obtain maximum risk, which is the sum of the $q$-th power of the absolute differences of adjacent numbers, for $q\ge 1$. Curtis showed that the dartboard problem admits a greedy algorithm. We generalize the dartboard problem by considering more circles and the goal is to arrange $kn$ number on $k$ circles to obtain the maximum risk. In this paper, we characterize an optimal arrangement for $k=2$ and show that the generalized dartboard problem also admits a greedy algorithm.
DOI : 10.37236/965
Classification : 05A05, 05B30 
@article{10_37236_965,
     author = {Ying-Jie Liao and Min-Zheng Shieh and Shi-Chun Tsai},
     title = {Arranging numbers on circles to reach maximum total variations},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/965},
     zbl = {1122.05002},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/965/}
}
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Ying-Jie Liao; Min-Zheng Shieh; Shi-Chun Tsai. Arranging numbers on circles to reach maximum total variations. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/965

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