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Self-improving algorithms for coordinate-wise maxima

Kenneth L. Clarkson, Wolfgang Mulzer, C. Seshadhri
2012 Proceedings of the 2012 symposuim on Computational Geometry - SoCG '12  
Let OPTD denote the expected depth of an optimal linear comparison tree computing the maxima for distribution D.  ...  Our result requires new tools to understand linear comparison trees for computing maxima.  ...  There is a self-improving algorithm to compute the coordinate-wise maxima whose expected time in the limiting phase is O(ε −1 (n+OPTD)).  ... 
doi:10.1145/2261250.2261291 dblp:conf/compgeom/ClarksonMS12 fatcat:pmudo3hkvfavhaaj7qnb6vj7lu

Self-Improving Algorithms for Coordinatewise Maxima and Convex Hulls

Kenneth L. Clarkson, Wolfgang Mulzer, C. Seshadhri
2014 SIAM journal on computing (Print)  
OPTCH_D) be the expected depth of an optimal linear comparison tree computing the maxima (resp. convex hull) for D. Our maxima algorithm eventually achieves expected running time O(OPTMAX_D + n).  ...  Furthermore, we give a self-improving algorithm for convex hulls with expected running time O(OPTCH_D + n n). Our results require new tools for understanding linear comparison trees.  ...  We would like to thank Eden Chlamtáč for suggesting a simple proof for Claim 3.3.  ... 
doi:10.1137/12089702x fatcat:bjnk5bwwgvdebkre2ddxrojecy

Fast Computation of Output-Sensitive Maxima in a Word RAM [chapter]

Peyman Afshani
2013 Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms  
can be computed in linear expected time without knowing the distribution.  ...  This improves the previous O(n log log h) time algorithm and can be considered surprising since it gives a linear time algorithm when α > 0 is a constant, which is faster than the current best deterministic  ...  In many cases in fact it is possible to compute the maxima in linear time [14, 12, 4, 7] .  ... 
doi:10.1137/1.9781611973402.104 dblp:conf/soda/Afshani14 fatcat:hmob5kjcmjggpp7lzvd6kfvrvu

On Constant Factors in Comparison-Based Geometric Algorithms and Data Structures

Timothy M. Chan, Patrick Lee
2015 Discrete & Computational Geometry  
We can compute the maxima among a set of n points in 3D by a randomized algorithm that uses n lg n + O(n √ lg n) expected number of comparisons (see Section 2.3).  ...  We can compute the h maxima among a set of n points in 3D by a randomized output-sensitive algorithm that uses n lg h + O(n lg 2/3 h) expected number of comparisons (see Section 2.4). 4.  ...  As before, we also obtain the same expected lower bound for randomized algorithms. Lemma 2 . 1 . 21 Given an r-grouping, we can compute the h maxima of S in O(h(n/r) lg r) time.  ... 
doi:10.1007/s00454-015-9677-y fatcat:kfgu6lq3y5citgx7d5xgj6mbze

On Constant Factors in Comparison-Based Geometric Algorithms and Data Structures

Timothy M. Chan, Patrick Lee
2014 Annual Symposium on Computational Geometry - SOCG'14  
We can compute the maxima among a set of n points in 3D by a randomized algorithm that uses n lg n + O(n √ lg n) expected number of comparisons (see Section 2.3).  ...  We can compute the h maxima among a set of n points in 3D by a randomized output-sensitive algorithm that uses n lg h + O(n lg 2/3 h) expected number of comparisons (see Section 2.4). 4.  ...  As before, we also obtain the same expected lower bound for randomized algorithms. Lemma 2 . 1 . 21 Given an r-grouping, we can compute the h maxima of S in O(h(n/r) lg r) time.  ... 
doi:10.1145/2582112.2582166 dblp:conf/compgeom/ChanL14 fatcat:53usx2uf6jfoliwpuh6nyxkxd4

Page 1643 of Mathematical Reviews Vol. , Issue 94c [page]

1994 Mathematical Reviews  
This bound is an improvement over the previously known best upper bound for the expected running time of a random heuristic for the graph coloring problem.” 94c:68083 68Q22 05C30 05C70 65F10 65Y05 68Q25  ...  For bounded degree graphs, it is shown that the expected running time of the heuristic under the P-RAM computation model is bounded by EO(log(n)/loglog(n)).  ... 

Mining Statistically Significant Substrings Based on the Chi-Square Measure [article]

Sourav Dutta, Arnab Bhattacharya
2010 arXiv   pre-print
We show that the algorithms outperform other competing algorithms in the runtime, while maintaining a high approximation ratio of more than 0.96.  ...  Searching for an unusual pattern within such long strings of data has emerged as a requirement for diverse applications.  ...  Approximate Greedy Maximum Maxima Search Algorithm (AGMM) In this section, we propose a linear time greedy algorithm for finding the maximum substring, which is linear in the size of the input string str  ... 
arXiv:1002.4315v2 fatcat:xrnxe27rrnbajadak6vsqtm64y

Page 10286 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews  
Summary: “We present an O(n logn)-time algorithm to solve the three-dimensional layers-of-maxima problem. This is an improve- ment over the prior O(n logn log logn)-time solution.  ...  For simple paths, our algorithm runs in O(nlogn) time, which we show is tight. For self-intersecting paths the problem is related to Hopcroft’s problem; our algorithm runs in O(n?/?  ... 

Synergistic Computation of Planar Maxima and Convex Hull [article]

Jérémy Barbay, Carlos Ochoa
2017 arXiv   pre-print
As intermediate results, we describe and analyze the first adaptive algorithms for Merging Maxima and Merging Convex Hulls.  ...  We consider the extension of their results to the computation of the Maxima Set and the Convex Hull of a set of planar points.  ...  Acknowledgments: The authors would like to thank Javiel Rojas for helping with the bibliography on the computation of the Maxima Set of a set of points.  ... 
arXiv:1702.08545v1 fatcat:svkp7y3vhjedlijwoatrxqfmjq

Page 4943 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
z/2-maxima can be computed in O(n) expected time.  ...  For © > z/2 the authors describe an opti- mal O(nlogn) running time algorithm for identifying the set So, which, under some restrictions, changes to O((n/@) logn) running time for O < 7/2.  ... 

Page 8070 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
Given a plausible assumption, this expectation is less than 4.96 for all but a finite number of 68 COMPUTER SCIENCE values of n.”  ...  Changsha); Wang, Lin (PRC-CSCM; Changsha) The average running time of the recursive ergodic traversal algorithm for binary trees.  ... 

Randomized minimum spanning tree algorithms using exponentially fewer random bits

Seth Pettie, Vijaya Ramachandran
2008 ACM Transactions on Algorithms  
In some cases we are able to reduce the number of random bits from linear to nearly constant without affecting the expected running time.  ...  (For the first two problems there are provably optimal deterministic algorithms with unknown, and possibly superlinear running times.)  ...  Randomized Minimum Spanning Tree Algorithms · 27 ACKNOWLEDGMENTS We would like to thank David Zuckerman for his helpful suggestions.  ... 
doi:10.1145/1328911.1328916 fatcat:mytnhdzm7fc75huzde36ger27y

Computing elevation maxima by searching the gauss sphere

Bei Wang, Herbert Edelsbrunner, Dmitriy Morozov
2011 ACM Journal of Experimental Algorithmics  
Transporting the concept from the smooth to the piecewise linear category, this paper describes an algorithm for finding all local maxima.  ...  We cast light on this improvement by relating the running time to the total absolute Gaussian curvature of the 2-manifold.  ...  The main result of this paper is a new algorithm for computing all elevation maxima of a triangulated surface in R 3 .  ... 
doi:10.1145/1963190.1970375 fatcat:mcwekdg2mbftvcu66cg6eox2f4

Computing Elevation Maxima by Searching the Gauss Sphere [chapter]

Bei Wang, Herbert Edelsbrunner, Dmitriy Morozov
2009 Lecture Notes in Computer Science  
Transporting the concept from the smooth to the piecewise linear category, this paper describes an algorithm for finding all local maxima.  ...  We cast light on this improvement by relating the running time to the total absolute Gaussian curvature of the 2-manifold.  ...  The main result of this paper is a new algorithm for computing all elevation maxima of a triangulated surface in R 3 .  ... 
doi:10.1007/978-3-642-02011-7_26 fatcat:gmqhubjb7rb5npcc4o44jeefom

A comparison of bidding strategies for simultaneous auctions

Teddy Candale, Sandip Sen
2006 ACM SIGecom Exchanges  
We provide a comparison of this algorithm with existing ones, both in terms of utilities generated and computation time, along with a discussion of the strengths and weaknesses of these strategies.  ...  Bidding for multiple items or bundles on online auctions raise challenging problems. We assume that an agent has a valuation function that returns its valuation for an arbitrary bundle.  ...  The MDBI algorithm, on the other hand has only linear complexity, a great advantage for its use in larger problems. Table I. Cumulative profits of different algorithms.  ... 
doi:10.1145/1124566.1124572 fatcat:qbn6ilnrvnacrnxjezudnwbsfi
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