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Self-improving algorithms for coordinate-wise maxima

2012
*
Proceedings of the 2012 symposuim on Computational Geometry - SoCG '12
*

Let OPTD denote the

doi:10.1145/2261250.2261291
dblp:conf/compgeom/ClarksonMS12
fatcat:pmudo3hkvfavhaaj7qnb6vj7lu
*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)). ...##
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Self-Improving Algorithms for Coordinatewise Maxima and Convex Hulls

2014
*
SIAM journal on computing (Print)
*

OPTCH_D) be the

doi:10.1137/12089702x
fatcat:bjnk5bwwgvdebkre2ddxrojecy
*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. ...##
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Fast Computation of Output-Sensitive Maxima in a Word RAM
[chapter]

2013
*
Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms
*

can be

doi:10.1137/1.9781611973402.104
dblp:conf/soda/Afshani14
fatcat:hmob5kjcmjggpp7lzvd6kfvrvu
*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] . ...##
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On Constant Factors in Comparison-Based Geometric Algorithms and Data Structures

2015
*
Discrete & Computational Geometry
*

We can

doi:10.1007/s00454-015-9677-y
fatcat:kfgu6lq3y5citgx7d5xgj6mbze
*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*. ...##
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On Constant Factors in Comparison-Based Geometric Algorithms and Data Structures

2014
*
Annual Symposium on Computational Geometry - SOCG'14
*

We can

doi:10.1145/2582112.2582166
dblp:conf/compgeom/ChanL14
fatcat:53usx2uf6jfoliwpuh6nyxkxd4
*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*. ...##
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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)). ...##
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Mining Statistically Significant Substrings Based on the Chi-Square Measure
[article]

2010
*
arXiv
*
pre-print

We show that the

arXiv:1002.4315v2
fatcat:xrnxe27rrnbajadak6vsqtm64y
*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 ...##
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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?/? ...##
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Synergistic Computation of Planar Maxima and Convex Hull
[article]

2017
*
arXiv
*
pre-print

As intermediate results, we describe and analyze the first adaptive

arXiv:1702.08545v1
fatcat:svkp7y3vhjedlijwoatrxqfmjq
*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. ...##
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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. ...##
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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. ...##
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Randomized minimum spanning tree algorithms using exponentially fewer random bits

2008
*
ACM Transactions on Algorithms
*

In some cases we are able to reduce the number of random bits from

doi:10.1145/1328911.1328916
fatcat:mytnhdzm7fc75huzde36ger27y
*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. ...##
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Computing elevation maxima by searching the gauss sphere

2011
*
ACM Journal of Experimental Algorithmics
*

Transporting the concept from the smooth to the piecewise

doi:10.1145/1963190.1970375
fatcat:mcwekdg2mbftvcu66cg6eox2f4
*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 . ...##
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Computing Elevation Maxima by Searching the Gauss Sphere
[chapter]

2009
*
Lecture Notes in Computer Science
*

Transporting the concept from the smooth to the piecewise

doi:10.1007/978-3-642-02011-7_26
fatcat:gmqhubjb7rb5npcc4o44jeefom
*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 . ...##
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A comparison of bidding strategies for simultaneous auctions

2006
*
ACM SIGecom Exchanges
*

We provide a comparison of this

doi:10.1145/1124566.1124572
fatcat:qbn6ilnrvnacrnxjezudnwbsfi
*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*. ...
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