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A Near-Linear Pseudopolynomial Time Algorithm for Subset Sum
[article]

2017
*
arXiv
*
pre-print

*A*textbook

*pseudopolynomial*

*time*

*algorithm*by Bellman from 1957 solves

*Subset*

*Sum*in

*time*O(nt). This has been improved to O(n Z) by Pisinger [J. ... Given

*a*set Z of n positive integers and

*a*target value t, the

*Subset*

*Sum*problem asks whether any

*subset*of Z

*sums*to t. ... Acknowledgements The author wants to thank Marvin Künnemann and Jesper Nederlof

*for*providing useful comments on

*a*draft of this paper. ...

##
###
A Simple Near-Linear Pseudopolynomial Time Randomized Algorithm for Subset Sum
[article]

2018
*
arXiv
*
pre-print

In this paper, we present

arXiv:1807.11597v3
fatcat:3ugw5nuu7jgxlbewjdjcf5uqmm
*a*simple and elegant randomized*algorithm**for**Subset**Sum*in Õ(n + t)*time*. ... Given*a*multiset S of n positive integers and*a*target integer t, the*Subset**Sum*problem asks to determine whether there exists*a**subset*of S that*sums*up to t. ... Our*algorithm*can solve the modulo p version # p Knapsack in*near*-*linear**pseudopolynomial**time**for*prime p > t. ...##
###
A Simple Near-Linear Pseudopolynomial Time Randomized Algorithm for Subset Sum

2018
*
ACM-SIAM Symposium on Discrete Algorithms
*

In this paper, we present

doi:10.4230/oasics.sosa.2019.17
dblp:conf/soda/JinW19
fatcat:iw4wzk7tjjht5ezek75lkzpa2e
*a*simple and elegant randomized*algorithm**for**Subset**Sum*in Õ(n + t)*time*. ... Bringmann [SODA'17] later gave*a*randomized Õ(n + t)*time**algorithm*using two-stage color-coding. The Õ(n + t) running*time*is believed to be*near*-optimal. ... [1] recently showed that*Subset**Sum*has no O(t 1− n O (1) )*algorithm**for*any > 0, unless the Strong Exponential*Time*Hypothesis (SETH) is false, so the Õ(n + t)*time*bound is likely to be*near*-optimal ...##
###
A Faster Pseudopolynomial Time Algorithm for Subset Sum
[article]

2016
*
arXiv
*
pre-print

We also present

arXiv:1507.02318v3
fatcat:ohujdjf4mncsfe77mycnyylmee
*a*modified*algorithm**for*cyclic groups, which computes all the realizable*subset**sums*within the group in O({√(n)m,m^5/4})*time*, where m is the order of the group. ... Given*a*multiset S of n positive integers and*a*target integer t, the*subset**sum*problem is to decide if there is*a**subset*of S that*sums*up to t. ... We would like to thank Igor Shparlinski and Arne Winterhof*for*pointing out*a*problem in*a*proof. ...##
###
A Faster Pseudopolynomial Time Algorithm for Subset Sum

2017
*
Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms
*

We also present

doi:10.1137/1.9781611974782.68
dblp:conf/soda/KoiliarisX17
fatcat:in5izuljezbvbegr44dbjl5p64
*a*modified*algorithm**for*finite cyclic groups, which computes all the realizable*subset**sums*within the group in O(min{ √ nm, m 5/4 })*time*, where m is the order of the group. ... Given*a*multiset S of n positive integers and*a*target integer t, the*subset**sum*problem is to decide if there is*a**subset*of S that*sums*up to t. ... We would like to thank Igor Shparlinski and Arne Winterhof*for*pointing out*a*problem in*a*proof. ...##
###
The Subset Sum Problem: Reducing Time Complexity of NP-Completeness with Quantum Search

2013
*
Undergraduate Journal of Mathematical Modeling: One + Two
*

The

doi:10.5038/2326-3652.4.2.2
fatcat:xgpwnxum5jajrmi32fbkylnhay
*Subset**Sum*Problem is*a*member of the NP-complete class, so no known polynomial*time**algorithm*exists*for*it. ... Quantum computation offers new insights*for*not only the*Subset**Sum*Problem but also the entire NP-complete class; most notably, Grover's quantum*algorithm**for*an unstructured database search can be tailored ...*For*example, the dynamic programming*algorithm**for*the*Subset**Sum*Problem presented earlier runs in*pseudopolynomial**time*by utilizing optimal substructure and overlapping subproblems. ...##
###
Near-optimal Approximate Discrete and Continuous Submodular Function Minimization
[article]

2019
*
arXiv
*
pre-print

In this paper we provide improved running

arXiv:1909.00171v1
fatcat:npzhhspxsvg6jkye67zt5yiytm
*times*and oracle complexities*for*approximately minimizing*a*submodular function. ... Further, we leverage*a*generalization of this result to obtain efficient*algorithms**for*minimizing*a*broad class of nonconvex functions. ... Acknowledgements We thank Deeparnab Chakrabarty, Yin Tat Lee, Sahil Singla, Kevin Tian, and Sam Chiu-wai Wong*for*helpful conversations. ...##
###
Fast and Simple Modular Subset Sum
[article]

2020
*
arXiv
*
pre-print

In this work, we present two simple

arXiv:2008.10577v3
fatcat:wwaq742yunhtjf6wgkux5tmvda
*algorithms**for*the Modular*Subset**Sum*problem running in*near*-*linear**time*in m, both efficiently implementing Bellman's iteration over ℤ_m. ...*A*series of recent works has provided*near*-optimal*algorithms**for*this problem under the Strong Exponential*Time*Hypothesis. ...*A*simple*near*-*linear**pseudopolynomial**time*randomized*algorithm**for**subset**sum*. In SOSA@SODA, volume 69 of OASICS, pages 17:1-17:6, 2019. 24 Konstantinos Koiliaris and Chao Xu. ...##
###
On Near-Linear-Time Algorithms for Dense Subset Sum
[article]

2020
*
arXiv
*
pre-print

Σ_X/n^2. - We prove

arXiv:2010.09096v1
fatcat:5wll5zp5gfe25blyikammcnvw4
*a*matching conditional lower bound: If*Subset**Sum*is in*near*-*linear**time**for*any setting with t ≪mx_X Σ_X/n^2, then the Strong Exponential*Time*Hypothesis and the Strong k-*Sum*Hypothesis ... Our main question is: When can dense*Subset**Sum*be solved in*near*-*linear**time*Õ(n)? ... However, Galil and Margalit's data structure can even reconstruct solutions, namely after preprocessing X and given t they can compute*a**subset*Y ⊆ X*summing*to t, if it exists, in*time*O(|Y |). ...##
###
Subquadratic Submodular Function Minimization
[article]

2016
*
arXiv
*
pre-print

*For*integer-valued submodular functions, we give an SFM

*algorithm*which runs in O(nM^3 n·EO)

*time*giving the first nearly

*linear*

*time*

*algorithm*in any known regime. ...

*For*real-valued submodular functions with range in [-1,1], we give an

*algorithm*which in Õ(n^5/3·EO/ε^2)

*time*returns an ε-additive approximate solution. ...

*A*special thanks to Bobby Kleinberg

*for*asking the question about approximate SFM. ...

##
###
An improved projection operation for cylindrical algebraic decomposition of three-dimensional space

1988
*
Journal of symbolic computation
*

Observations suggest that the reduction in the projection set size leads to

doi:10.1016/s0747-7171(88)80010-5
fatcat:zr6egjq4dzf6fksnbyqwyjce5q
*a*substantial decrease in the computing*time*of the cad*algorithm*. ...*A*key component of the cylindrical algebraic decomposition (cad)*algorithm*of Collins (1975) is the projection operation: the projecthm of*a*set*A*of r-variate polynomials is defined to be*a*certain set ... Thanks also to Pierre Milman*for*helping me to better understand Zariski's theorem. I am grateful to the referees*for*their helpful comments. ...##
###
A Pseudopolynomial Algorithm for Alexandrov's Theorem
[chapter]

2009
*
Lecture Notes in Computer Science
*

We describe an

doi:10.1007/978-3-642-03367-4_38
fatcat:ov6supumo5edhhkvoqmwjrgzta
*algorithm*based on this differential equation to compute the polyhedron to arbitrary precision given the metric, and prove*a**pseudopolynomial*bound on its running*time*. ... Recent work by Bobenko and Izmestiev describes*a*differential equation whose solution is the polyhedron corresponding to*a*given metric. ... We thank Jeff Erickson and Joseph Mitchell*for*helpful discussions about shortest paths on non-shortest-path triangulations. ...##
###
Bicriteria Network Design Problems
[article]

1998
*
arXiv
*
pre-print

Finally,

arXiv:cs/9809103v1
fatcat:kgal233ohncypjtkchs3asiabu
*for*the class of treewidth-bounded graphs, we provide*pseudopolynomial*-*time**algorithms**for**a*number of bicriteria problems using dynamic programming. ... We show how these*pseudopolynomial*-*time**algorithms*can be converted to fully polynomial-*time*approximation schemes using*a*scaling technique. ... Bodlaender*for*pointing out to us the equivalence between treewidth bounded graphs and decomposable graphs. We thank*A*. Ramesh*for*bringing [KP+93] to our attention. We also thank Dr. V. ...##
###
Page 7564 of Mathematical Reviews Vol. , Issue 2001J
[page]

2001
*
Mathematical Reviews
*

Finally,
polynomial

*time**algorithms**for*three special cases are derived. ... Properties of an optimal schedule*for*the prob- lems under consideration are presented, and*pseudopolynomial**algorithms*based on dynamic programming are given. ...##
###
Құрылымданбаған деректерді ақпараттық іздеу әдістері

МЕТОДЫ ИНФОРМАЦИОННОГО ПОИСКА НЕСТРУКТУРИРОВАННЫХ ДАННЫХ

2022
*
INTERNATIONAL JOURNAL OF INFORMATION AND COMMUNICATION TECHNOLOGIES
*

МЕТОДЫ ИНФОРМАЦИОННОГО ПОИСКА НЕСТРУКТУРИРОВАННЫХ ДАННЫХ

*A*

*near*-

*linear*

*pseudopolynomial*

*time*

*algorithm*

*for*

*subset*

*sum*. To appear in SODA '17, 2017. //arXiv:1610.04712v2[cs.Ds] 8 Jan 2017.-18p. 5. E. Horowitz, S. Sanni. ...

*A*Faster

*pseudopolynomial*

*time*

*algorithm*

*for*

*subset*

*sum*. To appear in SODA '17, 2017. //arXiv:1610.04712v2[cs.Ds] 8 Jan 2017.-18p. 4. Karl Bringmann. ... To achieve this goal, the new polynomial

*algorithms*are based on the problem of the

*sum*of

*subsets*, which belongs to the NPcomplete class. ...

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