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

Edward A. Hirsch
2003 Discrete Applied Mathematics  
Our algorithm 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.  ... 
doi:10.1016/s0166-218x(02)00404-3 fatcat:m3cj3kmpgjd33nhfk3v7kjvmnu

Random assignment problems

Pavlo A. Krokhmal, Panos M. Pardalos
2009 European Journal of Operational Research  
electrical engineering, sports, 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  ... 
doi:10.1016/j.ejor.2007.11.062 fatcat:odlsyyktuzanja6ootozuozu7y

Beyond set disjointness

Joshua Brody, Amit Chakrabarti, Ranganath Kondapally, David P. Woodruff, Grigory Yaroslavtsev
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] .  ... 
doi:10.1145/2611462.2611501 dblp:conf/podc/BrodyCKWY14 fatcat:dqbpumli7zhrpeukx2lbm7y5qm

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

Salvatore Mandrà, Gian Giacomo Guerreschi, Alán Aspuru-Guzik
2016 New Journal of Physics  
We present an 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.  ... 
doi:10.1088/1367-2630/18/7/073003 fatcat:euyz2oq6cngkjmtpecasb66cku

Tree-Width and the Computational Complexity of MAP Approximations in Bayesian Networks

Johan Kwisthout
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.  ... 
doi:10.1613/jair.4794 fatcat:6z4vmygryfhudf46rmfhlrb67i

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

Andreas S. Schulz, Martin Skutella
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.  ... 
doi:10.1007/3-540-63397-9_32 fatcat:lpmkjeavl5ghvdnbljneml54em

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

Matthew Andrews, Lisa Zhang
2004 Lecture Notes in Computer Science  
In addition, unless all languages in NP have 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.  ... 
doi:10.1007/978-3-540-27836-8_14 fatcat:tzhgv4x35jbg3guy5jhrlbt2je

Leveraging belief propagation, backtrack search, and statistics for model counting

Lukas Kroc, Ashish Sabharwal, Bart Selman
2010 Annals of Operations Research  
We consider 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.  ... 
doi:10.1007/s10479-009-0680-7 fatcat:7zgswwv5l5gblj6dj7ebngzose

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]

Johan Kwisthout
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.  ... 
doi:10.1007/978-3-319-11433-0_18 fatcat:klmitw6wsfg27htqx6uemrbxdu

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

Jean Cardinal, Jerri Nummenpalo, Emo Welzl
2017 arXiv   pre-print
This improves significantly over 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.  ... 
arXiv:1708.01122v1 fatcat:dk4o2sovnvhb7anxj7iagu2era

Auctions with Budget Constraints [chapter]

Nir Andelman, Yishay Mansour
2004 Lecture Notes in Computer Science  
In this paper we present 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  ... 
doi:10.1007/978-3-540-27810-8_4 fatcat:rf62dxqa7rerzdcxvqkmdrn6ri

An Adaptive, Distribution-Free Algorithm for the Newsvendor Problem with Censored Demands, with Applications to Inventory and Distribution

Gregory A. Godfrey, Warren B. Powell
2001 Management science  
W e consider 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.  ... 
doi:10.1287/mnsc.47.8.1101.10231 fatcat:p4ezkstig5defixae6wi6vwyue

Exact and Heuristic Methods for the Weapon Target Assignment Problem

Ravindra K. Ahuja, Arvind Kumar, Krishna Jha, James B. Orlin
2003 Social Science Research Network  
There do not exist any 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.  ... 
doi:10.2139/ssrn.489802 fatcat:u6eqi6yn4jdbfbhtdnnlaku75i

Exact and Heuristic Algorithms for the Weapon-Target Assignment Problem

Ravindra K. Ahuja, Arvind Kumar, Krishna C. Jha, James B. Orlin
2007 Operations Research  
There do not exist any 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.  ... 
doi:10.1287/opre.1070.0440 fatcat:ls7x7ljk7nafldk27ifdpfdqwi
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