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23
Probabilistic Databases with MarkoViews
"... Most of the work on query evaluation in probabilistic databases has focused on the simple tupleindependent data model, where all tuples are independent random events. Several efficient query evaluation techniques exists in this setting, such as safe plans, algorithms based on OBDDs, treedecomposit ..."
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Most of the work on query evaluation in probabilistic databases has focused on the simple tupleindependent data model, where all tuples are independent random events. Several efficient query evaluation techniques exists in this setting, such as safe plans, algorithms based on OBDDs, treedecomposition and a variety of approximation algorithms. However, complex data analytics tasks often require complex correlations between tuples, and here query evaluation is significantly more expensive, or more restrictive. In this paper, we propose MVDB as a framework both for representing complex correlations and for efficient query evaluation. An MVDB specifies correlations by views, called MarkoViews, on the probabilistic relations and declaring the weights of the view’s outputs. An MVDB is a (very large) Markov Logic Network. We make two sets of contributions. First, we show that query evaluation on an MVDB is equivalent to evaluating a Union of Conjunctive Query(UCQ) over a tupleindependent database. The translation is exact (thus allowing the techniques developed for tuple independent databases to be carried over to MVDB), yet it is novel and quite nonobvious (some resulting probabilities may be negative!). This translation in itself though may not lead to much gain since the translated query gets complicated as we try to capture more correlations. Our second contribution is to propose a new query evaluation strategy that exploits offline compilation to speed up online query evaluation. Here we utilize and extend our prior work on compilation of UCQ. We validate experimentally our techniques on a large probabilistic database with MarkoViews inferred from the DBLP data. 1.
Determining the number of solutions to binary CSP instances
"... Abstract. Counting the number of solutions to CSP instances has applications in several areas, ranging from statistical physics to artificial intelligence. We give an algorithm for counting the number of solutions to binary CSPs, which works by transforming the problem into a number of 2sat instanc ..."
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Abstract. Counting the number of solutions to CSP instances has applications in several areas, ranging from statistical physics to artificial intelligence. We give an algorithm for counting the number of solutions to binary CSPs, which works by transforming the problem into a number of 2sat instances, where the total number of solutions to these instances is the same as those of the original problem. The algorithm consists of two main cases, depending on whether the domain size d is even, in which case the algorithm runs in O(1.3247 n · (d/2) n) time, or odd, in which case it runs in O(1.3247 n · ((d 2 + d + 2)/4) n/2) if d = 4 · k + 1, and O(1.3247 n · ((d 2 + d)/4) n/2) if d = 4 · k + 3. We also give an algorithm for counting the number of possible 3colourings of a given graph, which runs in O(1.8171 n), an improvement over our general algorithm gained by using problem specific knowledge. 1
New Polynomial Classes for #2SAT Established Via GraphTopological Structure
"... Abstract—We address the problem of designing efficient procedures for counting models of Boolean formulas and, in this task, we establish new classes of instances where #2SAT is solved in polynomial time. Those instances are recognized by the topological structure of the underlying graph of the inst ..."
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Abstract—We address the problem of designing efficient procedures for counting models of Boolean formulas and, in this task, we establish new classes of instances where #2SAT is solved in polynomial time. Those instances are recognized by the topological structure of the underlying graph of the instances. We show that, if the depthsearch over the constrained graph of a formula generates a tree where the set of fundamental cycles are disjointed (there are not common edges between any pair of fundamental cycles), then #2SAT is tractable. This class of instances do not set restrictions on the number of occurrences of a variable in a Boolean formula. Our proposal can be applied to impact directly in the reduction of the complexity time of the algorithms for other counting problems.
Pure Literal Look Ahead: An O(1,497^n) Satisfiability Algorithm (Extended Abstract)
, 1996
"... In this paper we describe and analyse an improved algorithm for solving the 3Satisfiability problem. The algorithm makes use of the concept 'Pure literal look ahead'. If F is a boolean formula in conjunctive normal form with n variables, then we will show that this algorithm solves the 3Satisfiab ..."
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In this paper we describe and analyse an improved algorithm for solving the 3Satisfiability problem. The algorithm makes use of the concept 'Pure literal look ahead'. If F is a boolean formula in conjunctive normal form with n variables, then we will show that this algorithm solves the 3Satisfiability problem in time less than O(1; 497 n ). 1 INTRODUCTION Let V = fv 1 ; v 2 ; : : : ; v n g be a set of boolean variables. For each variable v i there is a positive literal, denoted by v i , and a negative literal, denoted by v i . The literal v i has value true if and only if the variable v i has value true, and the literal v i has value true if and only if the variable v i has value false. The literals v i and v i will be called complemented and L = fv 1 ; v 1 ; v 2 ; v 2 ; : : : ; v n ; v n g is the set of literals corresponding to V . For L 0 ` L we set Lit(L 0 ) := fv; v j v 2 L 0 or v 2 L 0 g. A kclause (k 1) is a subset of k different literals of L. For a literal v...
Pure Literal Look Ahead: An
"... In this paper we describe and analyse an improved algorithm for solving the 3Satisfiability problem. The algorithm makes use of the concept 'Pure literal look ahead'. If F is a boolean formula in conjunctive normal form with n variables, then we will show that this algorithm solves the 3Satisfiab ..."
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In this paper we describe and analyse an improved algorithm for solving the 3Satisfiability problem. The algorithm makes use of the concept 'Pure literal look ahead'. If F is a boolean formula in conjunctive normal form with n variables, then we will show that this algorithm solves the 3Satisfiability problem in time less than O(1; 497 n ). 1 INTRODUCTION Let V = fv 1 ; v 2 ; : : : ; v n g be a set of boolean variables. For each variable v i there is a positive literal, denoted by v i , and a negative literal, denoted by v i . The literal v i has value true if and only if the variable v i has value true, and the literal v i has value true if and only if the variable v i has value false. The literals v i and v i will be called complemented and L = fv 1 ; v 1 ; v 2 ; v 2 ; : : : ; v n ; v n g is the set of literals corresponding to V . For L 0 ` L we set Lit(L 0 ) := fv; v j v 2 L 0 or v 2 L 0 g. A kclause (k 1) is a subset of k different literals of L. For a literal v...
CNF Application in Discrete Optimization
, 2002
"... this paper, firstly, we show that pigeonhole principle gives ability to implement the primal approach with "nontreelike" unsatisfiable CNF's. Secondly, we suggest complementary formulas and a ways of their construction to embody the dual approach ..."
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this paper, firstly, we show that pigeonhole principle gives ability to implement the primal approach with "nontreelike" unsatisfiable CNF's. Secondly, we suggest complementary formulas and a ways of their construction to embody the dual approach
S. Maslov's Iterative Method: 15 Years Later
, 1996
"... In 1981, S. Maslov has proposed a new iterative method for solving propositional satisfiability problems. The 198187 results related to this method were described in the present book. In this chapter, we briefly recall the origins of Maslov's method, and describe further results and ideas relat ..."
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In 1981, S. Maslov has proposed a new iterative method for solving propositional satisfiability problems. The 198187 results related to this method were described in the present book. In this chapter, we briefly recall the origins of Maslov's method, and describe further results and ideas related to this method.
Computing #2SAT of Grids, GridCylinders and GridTori Boolean Formulas
"... We present an adaptation of transfer matrix method for signed grids, gridcylinders and gridtori. We use this adaptation to count the number of satisfying assignments of Boolean Formulas in 2CNF whose corresponding associated graph has such grid topologies. 1 ..."
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We present an adaptation of transfer matrix method for signed grids, gridcylinders and gridtori. We use this adaptation to count the number of satisfying assignments of Boolean Formulas in 2CNF whose corresponding associated graph has such grid topologies. 1
Chapter 35 On the Satisfiability and Maximum Satisfiability of Random 3CNF Formulas
"... We analyze the pure literal rule heuristic for computing a satisfying assignment to a random 3CNF formula with n variables. We show that the pure literal rule by itself finds satisfying assignments for almost all 3CNF formulas with up to 1.63n clauses, but it fails for more than 1.7n clauses. As a ..."
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We analyze the pure literal rule heuristic for computing a satisfying assignment to a random 3CNF formula with n variables. We show that the pure literal rule by itself finds satisfying assignments for almost all 3CNF formulas with up to 1.63n clauses, but it fails for more than 1.7n clauses. As an aside we show that the value of maximum satisfiability for random 3CNF formulas is tightly concentrated around its mean. 1
BOSE–EINSTEIN CONDENSATION IN THE K–SAT PROBLEM Diploma di Licenza
"... 1 k–SAT and Bose–Einstein condensation 2 ..."