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212
Spectral Partitioning of Random Graphs
, 2001
"... Problems such as bisection, graph coloring, and clique are generally believed hard in the worst case. However, they can be solved if the input data is drawn randomly from a distribution over graphs containing acceptable solutions. In this paper we show that a simple spectral algorithm can solve all ..."
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Cited by 156 (2 self)
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Problems such as bisection, graph coloring, and clique are generally believed hard in the worst case. However, they can be solved if the input data is drawn randomly from a distribution over graphs containing acceptable solutions. In this paper we show that a simple spectral algorithm can solve all three problems above in the average case, as well as a more general problem of partitioning graphs based on edge density. In nearly all cases our approach meets or exceeds previous parameters, while introducing substantial generality. We apply spectral techniques, using foremost the observation that in all of these problems, the expected adjacency matrix is a low rank matrix wherein the structure of the solution is evident.
Composing Mappings among Data Sources
 In VLDB
, 2003
"... Semantic mappings between data sources play a key role in several data sharing architectures. Mappings provide the relationships between data stored in different sources, and therefore enable answering queries that require data from other nodes in a data sharing network. Composing mappings is one of ..."
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Cited by 138 (9 self)
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Semantic mappings between data sources play a key role in several data sharing architectures. Mappings provide the relationships between data stored in different sources, and therefore enable answering queries that require data from other nodes in a data sharing network. Composing mappings is one of the core problems that lies at the heart of several optimization methods in data sharing networks, such as caching frequently traversed paths and redundancy analysis.
Inferring Link Weights using EndtoEnd Measurements
 In ACM SIGCOMM Internet Measurement Workshop
, 2002
"... We describe a novel constraintbased approach to approximate ISP link weights using only endtoend measurements. Common routing protocols such as OSPF and ISIS choose leastcost paths using link weights, so inferred weights provide a simple, concise, and useful model of intradomain routing. Our ap ..."
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Cited by 127 (19 self)
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We describe a novel constraintbased approach to approximate ISP link weights using only endtoend measurements. Common routing protocols such as OSPF and ISIS choose leastcost paths using link weights, so inferred weights provide a simple, concise, and useful model of intradomain routing. Our approach extends routerlevel ISP maps, which include only connectivity, with link weights that are consistent with routing. Our inferred weights agree well with observed routing: while our inferred weights fully characterize the set of shortest paths between 8499% of the routerpairs, alternative models based on hop count and latency do so for only 4781% of the pairs.
Global Optimization Algorithms  Theory and Application
, 2011
"... This ebook is devoted to Global Optimization algorithms, which are methods for finding solutions of high quality for an incredible wide range of problems. We introduce the basic concepts of optimization and discuss features which make optimization problems difficult and thus, should be considered ..."
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Cited by 94 (26 self)
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This ebook is devoted to Global Optimization algorithms, which are methods for finding solutions of high quality for an incredible wide range of problems. We introduce the basic concepts of optimization and discuss features which make optimization problems difficult and thus, should be considered when trying to solve them. In this book, we focus on
Model counting: A new strategy for obtaining good bounds
 In 21st AAAI
, 2006
"... Model counting is the classical problem of computing the number of solutions of a given propositional formula. It vastly generalizes the NPcomplete problem of propositional satisfiability, and hence is both highly useful and extremely expensive to solve in practice. We present a new approach to mod ..."
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Cited by 45 (16 self)
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Model counting is the classical problem of computing the number of solutions of a given propositional formula. It vastly generalizes the NPcomplete problem of propositional satisfiability, and hence is both highly useful and extremely expensive to solve in practice. We present a new approach to model counting that is based on adding a carefully chosen number of socalled streamlining constraints to the input formula in order to cut down the size of its solution space in a controlled manner. Each of the additional constraints is a randomly chosen XOR or parity constraint on the problem variables, represented either directly or in the standard CNF form. Inspired by a related yet quite different theoretical study of the properties of XOR constraints, we provide a formal proof that with high probability, the number of XOR constraints added in order to bring the formula to the boundary of being unsatisfiable determines with high precision its model count. Experimentally, we demonstrate that this approach can be used to obtain good bounds on the model counts for formulas that are far beyond the reach of exact counting methods. In fact, we obtain the first nontrivial solution counts for very hard, highly structured combinatorial problem instances. Note that unlike other counting techniques, such as Markov Chain Monte Carlo methods, we are able to provide highconfidence guarantees on the quality of the counts obtained.
Satisfiability Solvers
, 2008
"... The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worstcase exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and h ..."
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Cited by 48 (0 self)
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The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worstcase exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and hardware verification [29–31, 228], automatic test pattern generation [138, 221], planning [129, 197], scheduling [103], and even challenging problems from algebra [238]. Annual SAT competitions have led to the development of dozens of clever implementations of such solvers [e.g. 13,
From sampling to model counting
 In Proc. IJCAI’07
, 2007
"... We introduce a new technique for counting models of Boolean satisfiability problems. Our approach incorporates information obtained from sampling the solution space. Unlike previous approaches, our method does not require uniform or nearuniform samples. It instead converts local search sampling wit ..."
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Cited by 39 (8 self)
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We introduce a new technique for counting models of Boolean satisfiability problems. Our approach incorporates information obtained from sampling the solution space. Unlike previous approaches, our method does not require uniform or nearuniform samples. It instead converts local search sampling without any guarantees into very good bounds on the model count with guarantees. We give a formal analysis and provide experimental results showing the effectiveness of our approach. 1
Algorithm Selection and Scheduling
"... Abstract. Algorithm portfolios aim to increase the robustness of our ability to solve problems efficiently. While recently proposed algorithm selection methods come ever closer to identifying the most appropriate solver given an input instance, they are bound to make wrong and, at times, costly deci ..."
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Cited by 30 (8 self)
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Abstract. Algorithm portfolios aim to increase the robustness of our ability to solve problems efficiently. While recently proposed algorithm selection methods come ever closer to identifying the most appropriate solver given an input instance, they are bound to make wrong and, at times, costly decisions. Solver scheduling has been proposed to boost the performance of algorithm selection. Scheduling tries to allocate time slots to the given solvers in a portfolio so as to maximize, say, the number of solved instances within a given time limit. We show how to solve the corresponding optimization problem at a low computational cost using column generation, resulting in fast and high quality solutions. We integrate this approach with a recently introduced algorithm selector, which we also extend using other techniques. We propose various static as well as dynamic scheduling strategies, and demonstrate that in comparison to pure algorithm selection, our novel combination of scheduling and solver selection can significantly boost performance. 1
NonModelBased Algorithm Portfolios for SAT
"... When tackling a computationally challenging combinatorial problem, one often observes that some solution approaches work well on some instances, while other approaches work better on other instances. This observation has given rise to the idea of building algorithm portfolios [5]. LeytonBrown et al ..."
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Cited by 9 (3 self)
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When tackling a computationally challenging combinatorial problem, one often observes that some solution approaches work well on some instances, while other approaches work better on other instances. This observation has given rise to the idea of building algorithm portfolios [5]. LeytonBrown et al. [1], for instance, proposed to select one of the algorithms in the portfolio based on some features of the instance to be solved. This approach has been blessed with tremendous success in the past. Especially in SAT, the SATzilla portfolios [7] have performed extremely well in past SAT Competitions [6]. We investigate alternate ways of building algorithm portfolios that differ substantially from the way SATzilla assembles a portfolio. The key idea behind SATzilla is to train a runtime prediction model for each constituent solver, based on a number of wellengineered features of SAT instances. Given a new instance, SATzilla predicts the runtime of each candidate solver based on instance features and the trained models, and chooses the solver that is predicted to perform the best. In contrast, we consider nonmodelbased machine learning techniques such
A General NogoodLearning Framework for PseudoBoolean MultiValued SAT (Extended Abstract ⋆)
"... Jain et al. [4] recently introduced a new nogood learning approach for multivalued satisfaction (MVSAT) problems. This approach was shown to infer significantly stronger nogoods than those inferred by a mechanism that is based on a Boolean representation of a multivalued problem as a SAT instanc ..."
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Cited by 1 (0 self)
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Jain et al. [4] recently introduced a new nogood learning approach for multivalued satisfaction (MVSAT) problems. This approach was shown to infer significantly stronger nogoods than those inferred by a mechanism that is based on a Boolean representation of a multivalued problem as a SAT instance. Like earlier methods, the learning approach is based on an implication graph where nodes represent domain events and edges are implications drawn by the clauses in the given problem. One of the novelties of Jain et al. was the sole focus on variable inequations to infer the minimal reasons for a failure. In this work, we investigate why the particular use of inequations results in stronger nogoods and we formulate a general framework for multivalued nogoodlearning that can handle more general constraints, and also different domain representations, such as interval domains, which are commonly used for bounds consistency in constraint programming (CP). This is an essential step towards an integration of pseudoBoolean and multivalued SAT. Stateoftheart SAT and CP methods differ significantly in style and philosophy,
Results 1  10
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212