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Worst-case study of local search for MAX-k-SAT

2003
*
Discrete Applied Mathematics
*

Our algorithm

doi:10.1016/s0166-218x(02)00404-3
fatcat:m3cj3kmpgjd33nhfk3v7kjvmnu
*and*its analysis are based on Sch oning's proof of*the*best current worst-case time*bound**for*k-SAT (in: algorithm makes*random*walks of polynomial length. ... Also, it was proved that approximate solutions*for*these*problems*(even beyond inapproximability ratios) can be obtained faster than*exact*solutions. ... Acknowledgements*The*useful comments of three anonymous referees of Discrete Applied Mathematics greatly improved*the*presentation of this paper*and*added*the*last open question. ...##
###
Random assignment problems

2009
*
European Journal of Operational Research
*

electrical engineering, sports,

doi:10.1016/j.ejor.2007.11.062
fatcat:odlsyyktuzanja6ootozuozu7y
*and*others (*for*a comprehensive review of*the*subject of*assignment**problems*, their formulations*and*applications, see,*for*instance, Pardalos*and*Pitsoulis (2000) , Burkard ... Analysis of*random*instances of optimization*problems*is instrumental*for*understanding of*the*behavior*and*properties of problem's solutions, feasible region, optimal values, especially in large-scale ... In this paper we have discussed*the*state-of-*the*art results concerning*the*properties of*random**assignment**problems*, including*the*recent advances in*the*context of*random*linear*assignment**problem*, multidimensional ...##
###
Beyond set disjointness

2014
*
Proceedings of the 2014 ACM symposium on Principles of distributed computing - PODC '14
*

*For*two players, known lower

*bounds*

*for*

*the*easier

*problem*of set disjointness imply our algorithms are optimal up to constant factors in communication

*and*number of rounds. ... Given a protocol

*for*computing

*the*intersection, it can also be used to compute

*the*

*exact*Jaccard similarity,

*the*rarity,

*the*number of distinct elements,

*and*joins between databases. ... This in turn gives

*the*first protocol

*for*computing

*the*

*exact*Jaccard similarity |S∩T | |S∪T | ,

*exact*Hamming distance,

*exact*number of distinct elements,

*and*

*exact*1-rarity

*and*2-rarity [9] . ...

##
###
Faster than classical quantum algorithm for dense formulas of exact satisfiability and occupation problems

2016
*
New Journal of Physics
*

We present an

doi:10.1088/1367-2630/18/7/073003
fatcat:euyz2oq6cngkjmtpecasb66cku
*exact*quantum algorithm*for*solving*the**Exact*Satisfiability (XSAT)*problem*, which belongs to*the*important NP-complete complexity class. ...*The*query complexities*for**the*worst-case are respectively*bounded*by O(√(2^n-M^'))*and*O(2^n-M^'), where n is*the*number of variables*and*M^'*the*number of linearly independent clauses. ... In general,*for*satisfiability*problems*, T (n) is*expected*to be exponential with*the*number of variables n. ...##
###
Tree-Width and the Computational Complexity of MAP Approximations in Bayesian Networks

2015
*
The Journal of Artificial Intelligence Research
*

*The*

*problem*of finding

*the*most probable explanation to a designated set of variables given partial evidence (

*the*MAP

*problem*) is a notoriously intractable

*problem*in Bayesian networks, both to compute ... In this paper we investigate whether

*the*same holds

*for*approximating MAP. ...

*The*author wishes to thank

*the*workshop participants

*and*(both sets of) anonymous reviewers

*for*stimulating discussion

*and*worthwhile suggestions. ...

##
###
Scheduling-LPs bear probabilities randomized approximations for min-sum criteria
[chapter]

1997
*
Lecture Notes in Computer Science
*

*The*crucial idea

*for*these multiple machine

*problems*is not to use standard list scheduling but rather to

*assign*jobs randomly to machines (with probabilities taken from an optimal LP solution)

*and*to ... In

*the*on-line setting, we are scheduling jobs that continually arrive to be processed

*and*,

*for*each time t, we must

*construct*

*the*schedule until time t without any knowledge of

*the*jobs that will arrive ... Acknowledgements:

*The*authors are grateful to Chandra S. Chekuri, Michel X. Goeroans,

*and*David B. Shmoys

*for*helpful comments. ...

##
###
Wavelength Assignment in Optical Networks with Fixed Fiber Capacity
[chapter]

2004
*
Lecture Notes in Computer Science
*

In addition, unless all languages in NP have

doi:10.1007/978-3-540-27836-8_14
fatcat:tzhgv4x35jbg3guy5jhrlbt2je
*randomized*algorithms with*expected*running time O(n polylog(n) ), we show that there is no log γ µ approximation*for*any γ ∈ (0, 1)*and*no log γ m approximation ... We consider*the**problem*of*assigning*wavelengths to demands in an optical network of m links. ... Acknowledgement*The*authors wish to thank Chandra Chekuri, Bruce Shepherd*and**the*anonymous referees*for*many helpful comments. ...##
###
Leveraging belief propagation, backtrack search, and statistics for model counting

2010
*
Annals of Operations Research
*

We consider

doi:10.1007/s10479-009-0680-7
fatcat:7zgswwv5l5gblj6dj7ebngzose
*the**problem*of estimating*the*model count (number of solutions) of Boolean formulas,*and*present two techniques that compute estimates of these counts, as well as either lower or upper*bounds*...*For*upper*bounds*, we perform multiple runs of*the*MiniSat SAT solver with a minor modification,*and*obtain statistical*bounds*on*the*model count based on*the*observation that*the*distribution of a certain ...*The**problem*of finding a truth*assignment**for*which F evaluates to TRUE is known as*the*propositional satisfiability*problem*, or SAT,*and*is*the*canonical NP-complete*problem*. ...##
###
Page 2661 of Mathematical Reviews Vol. , Issue 2001D
[page]

2001
*
Mathematical Reviews
*

(directed) (modified) colored cutwidth, feasible reg- ister

*assignment**and*module allocation*for*graphs of*bounded*pathwidth. ... In addition, as r (*the*ratio of*the*number of clauses to*the*number of variables) increases,*random*k-SAT instances get easier*and*easier to solve,*and**the*base*for**the**expected*number of nodes that is ...##
###
Treewidth and the Computational Complexity of MAP Approximations
[chapter]

2014
*
Lecture Notes in Computer Science
*

*The*

*problem*of finding

*the*most probable explanation to a designated set of variables (

*the*MAP

*problem*) is a notoriously intractable

*problem*in Bayesian networks, both to compute exactly

*and*to approximate ... In this paper we investigate whether

*the*same holds

*for*approximating MAP. ...

*random*joint value

*assignments*to

*the*variables X i

*and*propagating

*the*

*assignments*according to

*the*CPTs of

*the*operator variables T j ) can decide this MAP query with a

*bounded*degree of error. ...

##
###
Solving and Sampling with Many Solutions: Satisfiability and Other Hard Problems
[article]

2017
*
arXiv
*
pre-print

This improves significantly over

arXiv:1708.01122v1
fatcat:dk4o2sovnvhb7anxj7iagu2era
*the*trivial sampling*bound*of*expected*Θ^*(ε^-1),*and*on all previous algorithms whenever ε = Ω(0.708^n). ... We also consider algorithms*for*3-SAT with an ε fraction of satisfying*assignments*,*and*prove that it can be solved in O^*(ε^-2.27) deterministic time,*and*in O^*(ε^-0.936)*randomized*time. ... Acknowledgments We would like to thank Noga Alon*and*József Solymosi*for*discussions on*the**problem*. We also thank*the*reviewers of IPEC 2017*for*valuable remarks that improved*the*exposition. ...##
###
Auctions with Budget Constraints
[chapter]

2004
*
Lecture Notes in Computer Science
*

In this paper we present

doi:10.1007/978-3-540-27810-8_4
fatcat:rf62dxqa7rerzdcxvqkmdrn6ri
*exact**and*approximate algorithms*for*auctions with budget constraints. ... We also present an FPTAS*for**the*case of a constant number of bidders. ...*The*rest of this paper is organized as follows: Section 2 formally defines*the*auction with budget constraints*problem*, Section 3 presents algorithms*for**exact*solutions*and*hardness results,*and*Section ...##
###
An Adaptive, Distribution-Free Algorithm for the Newsvendor Problem with Censored Demands, with Applications to Inventory and Distribution

2001
*
Management science
*

W e consider

doi:10.1287/mnsc.47.8.1101.10231
fatcat:p4ezkstig5defixae6wi6vwyue
*the**problem*of optimizing inventories*for**problems*where*the*demand distribution is unknown,*and*where it does not necessarily follow a standard form such as*the*normal. ... (see Lee*and*Nahmias 1993 , Porteus 1990 ,*and*Khouja 1999*for*thorough reviews of*the*inventory literature). ...*For*both of these*problem*classes, it is not possible to find even good*bounds**for*stochastic versions of*the**problem*. ...##
###
Exact and Heuristic Methods for the Weapon Target Assignment Problem

2003
*
Social Science Research Network
*

There do not exist any

doi:10.2139/ssrn.489802
fatcat:u6eqi6yn4jdbfbhtdnnlaku75i
*exact*methods*for**the*WTA*problem*which can solve even small size*problems*(*for*example, with 20 weapons*and*20 targets). ... In this paper, we suggest linear programming, integer programming,*and*network flow based lower*bounding*methods using which we obtain several branch*and**bound*algorithms*for**the*WTA*problem*. ... Robert Murphey at*the*Air Force Research Laboratory, Eglin Air Force Base to bring this*problem*to our notice*and**for*helpful discussions. ...##
###
Exact and Heuristic Algorithms for the Weapon-Target Assignment Problem

2007
*
Operations Research
*

There do not exist any

doi:10.1287/opre.1070.0440
fatcat:ls7x7ljk7nafldk27ifdpfdqwi
*exact*methods*for**the*WTA*problem*which can solve even small size*problems*(*for*example, with 20 weapons*and*20 targets). ... In this paper, we suggest linear programming, integer programming,*and*network flow based lower*bounding*methods using which we obtain several branch*and**bound*algorithms*for**the*WTA*problem*. ... Robert Murphey at*the*Air Force Research Laboratory, Eglin Air Force Base to bring this*problem*to our notice*and**for*helpful discussions. ...
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