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An Approximation Algorithm for Minimum Convex Cover with Logarithmic Performance Guarantee
[chapter]
2001
Lecture Notes in Computer Science
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The problem Minimum Convex Cover of covering a given polygon with a minimum number of (possibly overlapping) convex polygons is known to be NP -hard, even for polygons without holes [3] . ...
We propose a polynomial-time approximation algorithm for this problem for polygons with or without holes that achieves an approximation ratio of O(log n), where n is the number of vertices in the input ...
We want to thank anonymous referees for pointing us to [9, 13] and for additional suggestions. ...
doi:10.1007/3-540-44676-1_28
fatcat:4ilrtahjfzck3cj4ax4irniuui
An Approximation Algorithm for Minimum Convex Cover with Logarithmic Performance Guarantee
2003
SIAM journal on computing (Print)
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The problem Minimum Convex Cover of covering a given polygon with a minimum number of (possibly overlapping) convex polygons is known to be NP -hard, even for polygons without holes [3] . ...
We propose a polynomial-time approximation algorithm for this problem for polygons with or without holes that achieves an approximation ratio of O(log n), where n is the number of vertices in the input ...
We want to thank anonymous referees for pointing us to [9, 13] and for additional suggestions. ...
doi:10.1137/s0097539702405139
fatcat:uucqvhlbpzc3fl7u7hqcts4qsu
Page 6462 of Mathematical Reviews Vol. , Issue 2004h
[page]
2004
Mathematical Reviews
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approximation algorithm for minimum convex cover with logarithmic performance guarantee. ...
Furthermore, we show that MINIMUM CONVEX COVER is APX-hard; i.e., there ex- ists a constant 06 >0 such that no polynomial-time algorithm can achieve an approximation ratio of 1 +06. ...
On the Reflexivity of Point Sets
[chapter]
2001
Lecture Notes in Computer Science
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We prove that it is NPcomplete to determine the convex cover or the convex partition number, and we give logarithmic-approximation algorithms for determining each. ...
We prove various combinatorial bounds and provide efficient algorithms to compute reflexivity, both exactly (in special cases) and approximately (in general). ...
Algorithmic results that give logarithmic approximations for convex cover number, convex partitioning number, and (Steiner) reflex-ivity. ...
doi:10.1007/3-540-44634-6_18
fatcat:jwrkuhg6a5e5rlvd6fkq42s4ci
Optimal simplification of polygonal chain for rendering
2007
Proceedings of the twenty-third annual symposium on Computational geometry - SCG '07
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For a given polygonal chain, we study the min-# problem, which consists in finding an approximate and ordered subchain with a minimum number of vertices. ...
Previous approaches simplify the input chain relative to an approximation criterion which minimizes the gap between the original chain and the simplified subchain. ...
CONCLUSION Our algorithm computes an approximation with a minimum number of vertices and our hybrid criterion guarantees that the approximation retains the shape of the original chain. ...
doi:10.1145/1247069.1247102
dblp:conf/compgeom/Buzer07
fatcat:pru5tlwj3vhlnnfnkl6bfcltk4
Maximum Clique and Minimum Clique Partition in Visibility Graphs
[chapter]
2000
Lecture Notes in Computer Science
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We present an approximation algorithm for the problem that achieves a logarithmic approximation ratio by iteratively applying the algorithm for nding maximum weighted cliques. ...
This problem is APX-hard for polygons without holes (i.e., there exists a constant > 0 such that no polynomial time algorithm can achieve an approximation ratio of 1 + ). ...
As for computational complexity results, Minimum Convex Cover with(out) Holes can be approximated with a logarithmic approximation ratio 8]. ...
doi:10.1007/3-540-44929-9_16
fatcat:cguatpq4ibddhpzxsotrve4764
Algorithms for connected set cover problem and fault-tolerant connected set cover problem
2009
Theoretical Computer Science
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These are the first approximation algorithms for CSC problems in general graphs with guaranteed performance ratios. ...
In this paper, we present two approximation algorithms for the minimum CSC problem, and one approximation algorithm for the minimum (2, m)-CSC problem. Performance ratios are analyzed. ...
For the general case, there is no known approximation algorithm with guaranteed performance ratio. ...
doi:10.1016/j.tcs.2008.11.005
fatcat:tojffnyxhrhr7efcmt5y4lqoce
Optimal simplification of polygonal chains for subpixel-accurate rendering
2009
Computational geometry
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For a given polygonal chain, we study the min-# problem, which consists of finding an approximate and ordered subchain with a minimum number of vertices under a given approximation criterion. ...
Previous algorithms with near-linear time performance produced geometrical inconsistencies and former methods used to preserve the features of the original chain required a quadratic time complexity. ...
Acknowledgements The author would like to thank the reviewers for their helpful suggestions. ...
doi:10.1016/j.comgeo.2008.03.002
fatcat:mvst6jywwng2ldn4fzt46wcx5i
An optimal resource allocation with joint carrier aggregation in 4G-LTE
2015
2015 International Conference on Computing, Networking and Communications (ICNC)
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2014 pre-print arXiv:1405.6448v1 fatcat:2akxb3qfjnf5rhgtrtejfpc2cyOther Versions
In addition, every user subscribing for the mobile service is guaranteed to have a minimum quality-of-service (QoS) with a priority criterion. ...
Finally, we present simulation results for the performance of our rate allocation algorithm. ...
Therefore, the algorithm gives priority to the users with adaptive real-time applications with guaranteed minimum QoS for all service subscribers. ...
doi:10.1109/iccnc.2015.7069330
dblp:conf/iccnc/AbdelhadiC15
fatcat:laylgil7gjdg3bkz6szgwblhlu
Approximation of Multiobjective Optimization Problems
[chapter]
2001
Lecture Notes in Computer Science
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We provide approximation algorithms with tight performance guarantees for bi-objective problems and make progress for the more challenging case of three and more objectives. ...
We characterize when such an approximation can be efficiently constructed and investigate the problem of computing minimum size approximate convex Pareto sets, both for discrete and convex problems. ...
Is there a generalization of the Chord algorithm with a poly-logarithmic performance guarantee? And what is the optimal ratio attainable by any algorithm with access to a Comb routine? ...
doi:10.1007/3-540-44634-6_1
fatcat:zlo3jhdomvdkdp5ysrcd6cihfy
A logarithmic approximation for polymatroid congestion games
2016
Operations Research Letters
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For general non-decreasing cost functions we devise an H rk -approximation algorithm, where rk is the sum of the ranks of the player-specific polymatroids and H rk denotes the rk-th harmonic number. ...
The approximation guarantee is best possible up to a constant factor. As a special case, our result (partially) settles an open problem of Ackermann et al. (H. Ackermann, H. Röglin, and B. Vöcking. ...
We thank Rico Zenklusen for his contribution to Lemma 2, Rudi Pendavingh and Jorn van der Pol for their contribution to the matroid version of this lemma, and an anonymous reviewer for his helpful comments ...
doi:10.1016/j.orl.2016.09.001
fatcat:shtoyn54lveazgsnfe6ix54v4a
Page 635 of Mathematical Reviews Vol. , Issue 98A
[page]
1998
Mathematical Reviews
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Summary: “Polynomial-time approximation algorithms with non- trivial performance guarantees are presented for the problems of (a) partitioning the vertices of a weighted graph into k blocks so as to maximize ...
It is shown that Nesterov and Nemirovskii’s universal barrier function of a convex cone is the logarithm of the convex cone’s characteris- tic function. ...
Logarithmic regret algorithms for online convex optimization
2007
Machine Learning
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In this paper, we give algorithms that achieve regret O(log(T )) for an arbitrary sequence of strictly convex functions (with bounded first and second derivatives). ...
Zinkevich showed that a simple online gradient descent algorithm achieves additive regret O( √ T ), for an arbitrary sequence of T convex cost functions (of bounded gradients), with respect to the best ...
Acknowledgements Many thanks to Adam Kalai for many critical contributions to this research. We would also like to thank Sanjeev Arora, Rob Schapire and an anonymous referee for helpful comments. ...
doi:10.1007/s10994-007-5016-8
fatcat:gpjreytldbax7ny2ouj2scbbii
Rank minimization via online learning
2008
Proceedings of the 25th international conference on Machine learning - ICML '08
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A salient feature of our online learning approach is that it allows us to give provable approximation guarantees for the rank minimization problem over polyhedral sets. ...
Minimum rank problems arise frequently in machine learning applications and are notoriously difficult to solve due to the non-convex nature of the rank objective. ...
(Barvinok, 2002 ) (Chapter V) describes an approximation algorithm for RMP based on random projections and a generalization of the Johnson-Lindenstrauss Lemma, with an approximation guarantee similar to ...
doi:10.1145/1390156.1390239
dblp:conf/icml/MekaJCD08
fatcat:milb7nakhjeunnc7autxx7b33u
Stackelberg Network Pricing Games
[article]
2008
arXiv
pre-print
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If followers have demands, the single-price algorithm provides a (1+ϵ)m^2-approximation, and the problem is hard to approximate within O(m^ϵ) for some ϵ >0. ...
Our first main result is a tight analysis of a single-price algorithm for the single follower game, which provides a (1+ϵ) m-approximation for any ϵ >0. ...
[19] present a first polynomial time approximation algorithm with a provable performance guarantee, which yields logarithmic approximation ratios. Bouhtou et al. ...
arXiv:0802.2841v1
fatcat:wmo5umfwyvfshpwemvsseiwktm
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