S. Arora. Approximation schemes for NP-hard geometric optimization problems: A survey. Mathematical Programming, Series B, 97:43--69, 2003. Home/Search Document Details and Download
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Euclidean Bounded-Degree Spanning Tree Ratios - Timothy Chan School (2003) (3 citations) (Correct)
....The K = 3 case is especially appealing, since once rooted, a degree 3 tree becomes a binary tree. For this bounded degree spanning tree problem, Christofides algorithm no longer gives a 3 2 approximation factor; the celebrated techniques of Arora and Mitchell do not seem to work either [2]. We thus return to the idea of constructing a solution by traversing the MST and analyzing the weight of the solution as a factor of the MST weight. The doubling strategy still applies; in fact, it is possible, using the triangle inequality alone, to get an approximation factor of 2 (K ....
....factors for bounded degree spanning trees. Khuller, Raghavachari, and Young [10] took an in depth look into this question and managed to achieve factors 3 2 and 5 4 for K = 3 and K = 4 respectively in the plane. Since then, no improvements have been made, despite frequent references to their work [2, 3, 7, 8, 11, 16, 17]. We report the first progress in 8 years: in the Euclidean plane, there always exists degree 3 and degree 4 spanning trees with weights within factors 1.402 and 1.143 respectively of the MST weight. Such trees can be constructed in polynomial time. Immediately, we obtain a factor 1.402 and ....
S. Arora. Approximation schemes for NP-hard geometric optimization problems: a survey. Manuscript, 2002. http://www.cs.princeton.edu/ ~arora/pubs/arorageo.ps.
Approximation Schemes for Degree-restricted MST and Red-Blue.. - Arora, Chang (2003) (7 citations) Self-citation (Arora) (Correct)
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S. Arora. Approximation schemes for NP-hard geometric optimization problems: A survey. Math Programming, 2003 Available from www.cs.princeton.edu/arora.
A Quasi-Polynomial Time Approximation Scheme for Minimum.. - Remy, Steger (2006) (Correct)
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S. Arora. Approximation schemes for NP-hard geometric optimization problems: A survey. Mathematical Programming, Series B, 97:43--69, 2003.
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S. Arora. Approximation schemes for NP-hard geometric optimization problems: A survey. Mathematical Programming, Series B, 97:43--69, 2003.
Approximation Schemes for Node-Weighted - Geometric Steiner Tree (2005) (Correct)
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S. Arora. Approximation schemes for NP-hard geometric optimization problems: A survey. Mathematical Programming, Series B, 97:43--69, 2003.
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S. Arora. Approximation schemes for NP-hard geometric optimization problems: A survey. Math. Programming, 97:43--69, 2003.
Euclidean Bounded-Degree Spanning Tree Ratios - Timothy Chan School (2003) (3 citations) (Correct)
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S. Arora. Approximation schemes for NP-hard geometric optimization problems: a survey. Math. Programming, 97:27-42, 2003.
Degree-Bounded Minimum Spanning Trees - Jothi, Raghavachari (2004) (Correct)
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S. Arora, Approximation schemes for NP-hard geometric optimization problems: A survey, Math. Programming 97, pp. 43-69, 2003.
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