The Experts below are selected from a list of 1833 Experts worldwide ranked by ideXlab platform
Levcopoulos Christos - One of the best experts on this subject based on the ideXlab platform.
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Shortcuts for the circle
'Elsevier BV', 2019Co-Authors: Bae, Sang Won, De Berg Mark, Cheong Otfried, Gudmundsson Joachim, Levcopoulos ChristosAbstract:Let C be the unit circle in R2. We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k⩾1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1⩽k⩽7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2+Θ(1/k[Formula presented]) for any k
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Shortcuts for the circle
'Elsevier BV', 2019Co-Authors: Bae, Sang Won, Cheong Otfried, Gudmundsson Joachim, Mt Mark De ,berg, Levcopoulos ChristosAbstract:\u3cp\u3e Let C be the unit circle in R \u3csup\u3e2\u3c/sup\u3e . We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k⩾1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1⩽k⩽7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2+Θ([formula presented]) for any k. \u3c/p\u3
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Shortcuts for the circle
Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017Co-Authors: Bae, Sang Won, Cheong Otfried, Gudmundsson Joachim, Mt Mark De ,berg, Levcopoulos ChristosAbstract:Let C be the unit circle in R^2. We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k >= 1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1 <= k <= 7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2 + Theta(1/k^(2/3)) for any k
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Shortcuts for the Circle
2017Co-Authors: Bae, Sang Won, De Berg Mark, Cheong Otfried, Gudmundsson Joachim, Levcopoulos ChristosAbstract:Let $C$ be the unit circle in $\mathbb{R}^2$. We can view $C$ as a plane graph whose vertices are all the points on $C$, and the distance between any two points on $C$ is the length of the smaller arc between them. We consider a graph augmentation problem on $C$, where we want to place $k\geq 1$ \emph{shortcuts} on $C$ such that the diameter of the resulting graph is minimized. We analyze for each $k$ with $1\leq k\leq 7$ what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of~$k$. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is $2 + \Theta(1/k^{\frac{2}{3}})$ for any~$k$.Comment: An extended abstract appeared in ISAAC 201
Bae, Sang Won - One of the best experts on this subject based on the ideXlab platform.
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Shortcuts for the circle
'Elsevier BV', 2019Co-Authors: Bae, Sang Won, De Berg Mark, Cheong Otfried, Gudmundsson Joachim, Levcopoulos ChristosAbstract:Let C be the unit circle in R2. We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k⩾1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1⩽k⩽7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2+Θ(1/k[Formula presented]) for any k
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Shortcuts for the circle
'Elsevier BV', 2019Co-Authors: Bae, Sang Won, Cheong Otfried, Gudmundsson Joachim, Mt Mark De ,berg, Levcopoulos ChristosAbstract:\u3cp\u3e Let C be the unit circle in R \u3csup\u3e2\u3c/sup\u3e . We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k⩾1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1⩽k⩽7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2+Θ([formula presented]) for any k. \u3c/p\u3
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Shortcuts for the circle
Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017Co-Authors: Bae, Sang Won, Cheong Otfried, Gudmundsson Joachim, Mt Mark De ,berg, Levcopoulos ChristosAbstract:Let C be the unit circle in R^2. We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k >= 1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1 <= k <= 7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2 + Theta(1/k^(2/3)) for any k
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Shortcuts for the Circle
2017Co-Authors: Bae, Sang Won, De Berg Mark, Cheong Otfried, Gudmundsson Joachim, Levcopoulos ChristosAbstract:Let $C$ be the unit circle in $\mathbb{R}^2$. We can view $C$ as a plane graph whose vertices are all the points on $C$, and the distance between any two points on $C$ is the length of the smaller arc between them. We consider a graph augmentation problem on $C$, where we want to place $k\geq 1$ \emph{shortcuts} on $C$ such that the diameter of the resulting graph is minimized. We analyze for each $k$ with $1\leq k\leq 7$ what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of~$k$. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is $2 + \Theta(1/k^{\frac{2}{3}})$ for any~$k$.Comment: An extended abstract appeared in ISAAC 201
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Shortcuts for the circle
'Cornell University Library', 2016Co-Authors: Bae, Sang Won, Cheong Otfried, Mt Mark De ,berg, Gudmundsson JoachimAbstract:Let C be the unit circle in R2. We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k > 1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1 6 k 6 7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2 + (1=k 23 ) for any k
Gudmundsson Joachim - One of the best experts on this subject based on the ideXlab platform.
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Shortcuts for the circle
'Elsevier BV', 2019Co-Authors: Bae, Sang Won, De Berg Mark, Cheong Otfried, Gudmundsson Joachim, Levcopoulos ChristosAbstract:Let C be the unit circle in R2. We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k⩾1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1⩽k⩽7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2+Θ(1/k[Formula presented]) for any k
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Shortcuts for the circle
'Elsevier BV', 2019Co-Authors: Bae, Sang Won, Cheong Otfried, Gudmundsson Joachim, Mt Mark De ,berg, Levcopoulos ChristosAbstract:\u3cp\u3e Let C be the unit circle in R \u3csup\u3e2\u3c/sup\u3e . We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k⩾1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1⩽k⩽7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2+Θ([formula presented]) for any k. \u3c/p\u3
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Shortcuts for the circle
Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017Co-Authors: Bae, Sang Won, Cheong Otfried, Gudmundsson Joachim, Mt Mark De ,berg, Levcopoulos ChristosAbstract:Let C be the unit circle in R^2. We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k >= 1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1 <= k <= 7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2 + Theta(1/k^(2/3)) for any k
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Shortcuts for the Circle
2017Co-Authors: Bae, Sang Won, De Berg Mark, Cheong Otfried, Gudmundsson Joachim, Levcopoulos ChristosAbstract:Let $C$ be the unit circle in $\mathbb{R}^2$. We can view $C$ as a plane graph whose vertices are all the points on $C$, and the distance between any two points on $C$ is the length of the smaller arc between them. We consider a graph augmentation problem on $C$, where we want to place $k\geq 1$ \emph{shortcuts} on $C$ such that the diameter of the resulting graph is minimized. We analyze for each $k$ with $1\leq k\leq 7$ what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of~$k$. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is $2 + \Theta(1/k^{\frac{2}{3}})$ for any~$k$.Comment: An extended abstract appeared in ISAAC 201
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Shortcuts for the circle
'Cornell University Library', 2016Co-Authors: Bae, Sang Won, Cheong Otfried, Mt Mark De ,berg, Gudmundsson JoachimAbstract:Let C be the unit circle in R2. We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k > 1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1 6 k 6 7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2 + (1=k 23 ) for any k
Cheong Otfried - One of the best experts on this subject based on the ideXlab platform.
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Shortcuts for the circle
'Elsevier BV', 2019Co-Authors: Bae, Sang Won, De Berg Mark, Cheong Otfried, Gudmundsson Joachim, Levcopoulos ChristosAbstract:Let C be the unit circle in R2. We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k⩾1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1⩽k⩽7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2+Θ(1/k[Formula presented]) for any k
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Shortcuts for the circle
'Elsevier BV', 2019Co-Authors: Bae, Sang Won, Cheong Otfried, Gudmundsson Joachim, Mt Mark De ,berg, Levcopoulos ChristosAbstract:\u3cp\u3e Let C be the unit circle in R \u3csup\u3e2\u3c/sup\u3e . We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k⩾1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1⩽k⩽7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2+Θ([formula presented]) for any k. \u3c/p\u3
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Shortcuts for the circle
Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017Co-Authors: Bae, Sang Won, Cheong Otfried, Gudmundsson Joachim, Mt Mark De ,berg, Levcopoulos ChristosAbstract:Let C be the unit circle in R^2. We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k >= 1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1 <= k <= 7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2 + Theta(1/k^(2/3)) for any k
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Shortcuts for the Circle
2017Co-Authors: Bae, Sang Won, De Berg Mark, Cheong Otfried, Gudmundsson Joachim, Levcopoulos ChristosAbstract:Let $C$ be the unit circle in $\mathbb{R}^2$. We can view $C$ as a plane graph whose vertices are all the points on $C$, and the distance between any two points on $C$ is the length of the smaller arc between them. We consider a graph augmentation problem on $C$, where we want to place $k\geq 1$ \emph{shortcuts} on $C$ such that the diameter of the resulting graph is minimized. We analyze for each $k$ with $1\leq k\leq 7$ what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of~$k$. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is $2 + \Theta(1/k^{\frac{2}{3}})$ for any~$k$.Comment: An extended abstract appeared in ISAAC 201
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Shortcuts for the circle
'Cornell University Library', 2016Co-Authors: Bae, Sang Won, Cheong Otfried, Mt Mark De ,berg, Gudmundsson JoachimAbstract:Let C be the unit circle in R2. We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k > 1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1 6 k 6 7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2 + (1=k 23 ) for any k
Mt Mark De ,berg - One of the best experts on this subject based on the ideXlab platform.
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Shortcuts for the circle
'Elsevier BV', 2019Co-Authors: Bae, Sang Won, Cheong Otfried, Gudmundsson Joachim, Mt Mark De ,berg, Levcopoulos ChristosAbstract:\u3cp\u3e Let C be the unit circle in R \u3csup\u3e2\u3c/sup\u3e . We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k⩾1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1⩽k⩽7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2+Θ([formula presented]) for any k. \u3c/p\u3
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Shortcuts for the circle
Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017Co-Authors: Bae, Sang Won, Cheong Otfried, Gudmundsson Joachim, Mt Mark De ,berg, Levcopoulos ChristosAbstract:Let C be the unit circle in R^2. We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k >= 1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1 <= k <= 7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2 + Theta(1/k^(2/3)) for any k
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Shortcuts for the circle
'Cornell University Library', 2016Co-Authors: Bae, Sang Won, Cheong Otfried, Mt Mark De ,berg, Gudmundsson JoachimAbstract:Let C be the unit circle in R2. We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k > 1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1 6 k 6 7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a Strictly Decreasing Function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2 + (1=k 23 ) for any k