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An Approximation Algorithm for Minimum Convex Cover with Logarithmic Performance Guarantee
[chapter]

2001
*
Lecture Notes in Computer Science
*

The problem

doi:10.1007/3-540-44676-1_28
fatcat:4ilrtahjfzck3cj4ax4irniuui
*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. ...##
###
An Approximation Algorithm for Minimum Convex Cover with Logarithmic Performance Guarantee

2003
*
SIAM journal on computing (Print)
*

The problem

doi:10.1137/s0097539702405139
fatcat:uucqvhlbpzc3fl7u7hqcts4qsu
*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. ...##
###
Page 6462 of Mathematical Reviews Vol. , Issue 2004h
[page]

2004
*
Mathematical Reviews
*

*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
*

We prove that it is NPcomplete to determine the

doi:10.1007/3-540-44634-6_18
fatcat:jwrkuhg6a5e5rlvd6fkq42s4ci
*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. ...##
###
Optimal simplification of polygonal chain for rendering

2007
*
Proceedings of the twenty-third annual symposium on Computational geometry - SCG '07
*

*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. ...

##
###
Maximum Clique and Minimum Clique Partition in Visibility Graphs
[chapter]

2000
*
Lecture Notes in Computer Science
*

We present

doi:10.1007/3-540-44929-9_16
fatcat:cguatpq4ibddhpzxsotrve4764
*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]. ...##
###
Algorithms for connected set cover problem and fault-tolerant connected set cover problem

2009
*
Theoretical Computer Science
*

These are the first

doi:10.1016/j.tcs.2008.11.005
fatcat:tojffnyxhrhr7efcmt5y4lqoce
*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. ...##
###
Optimal simplification of polygonal chains for subpixel-accurate rendering

2009
*
Computational geometry
*

*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. ...

##
###
An optimal resource allocation with joint carrier aggregation in 4G-LTE

2015
*
2015 International Conference on Computing, Networking and Communications (ICNC)
*

In addition, every user subscribing

doi:10.1109/iccnc.2015.7069330
dblp:conf/iccnc/AbdelhadiC15
fatcat:laylgil7gjdg3bkz6szgwblhlu
*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. ...##
###
Approximation of Multiobjective Optimization Problems
[chapter]

2001
*
Lecture Notes in Computer Science
*

We provide

doi:10.1007/3-540-44634-6_1
fatcat:zlo3jhdomvdkdp5ysrcd6cihfy
*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? ...##
###
A logarithmic approximation for polymatroid congestion games

2016
*
Operations Research Letters
*

*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 ...

##
###
Page 635 of Mathematical Reviews Vol. , Issue 98A
[page]

1998
*
Mathematical Reviews
*

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
*

In this paper, we give

doi:10.1007/s10994-007-5016-8
fatcat:gpjreytldbax7ny2ouj2scbbii
*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. ...##
###
Rank minimization via online learning

2008
*
Proceedings of the 25th international conference on Machine learning - ICML '08
*

A salient feature of our online learning approach is that it allows us to give provable

doi:10.1145/1390156.1390239
dblp:conf/icml/MekaJCD08
fatcat:milb7nakhjeunnc7autxx7b33u
*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 ...##
###
Stackelberg Network Pricing Games
[article]

2008
*
arXiv
*
pre-print

If followers have demands, the single-price

arXiv:0802.2841v1
fatcat:wmo5umfwyvfshpwemvsseiwktm
*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. ...
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