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54
Phase Transition is Not Hard for the Hamiltonian Cycle Problem
 Journal of Arti Intelligence Research
, 1998
"... Using an improved backtrack algorithm with sophisticated pruning techniques, we revise previous observations correlating a high frequency of hard to solve Hamiltonian cycle instances with the G n;m phase transition between Hamiltonicity and nonHamiltonicity. Instead all tested graphs of 100 to 1500 ..."
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Cited by 25 (7 self)
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Using an improved backtrack algorithm with sophisticated pruning techniques, we revise previous observations correlating a high frequency of hard to solve Hamiltonian cycle instances with the G n;m phase transition between Hamiltonicity and nonHamiltonicity. Instead all tested graphs of 100 to 1500 vertices are easily solved. When we artificially restrict the degree sequence with a bounded maximum degree, although there is some increase in difficulty, the frequency of hard graphs is still low. When we consider more regular graphs based on a generalization of knight's tours, we observe frequent instances of really hard graphs, but on these the average degree is bounded by a constant. We design a set of graphs with a feature our algorithm is unable to detect and so are very hard for our algorithm, but in these we can vary the average degree from O(1) to O(n). We have so far found no class of graphs correlated with the G n;m phase transition which asymptotically produces a high frequenc...
NoGood Caching for MultiAgent Backtrack Search
"... Multiagent solutions to the distributed constraint satisfaction problem (DCSP) require new types of techniques which accommodate the local autonomy of agents and the difficulties of computing in a network environment. Recently a technique called asynchronous backtracking has been developed to so ..."
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Cited by 23 (1 self)
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Multiagent solutions to the distributed constraint satisfaction problem (DCSP) require new types of techniques which accommodate the local autonomy of agents and the difficulties of computing in a network environment. Recently a technique called asynchronous backtracking has been developed to solve the DCSP. The algorithm works by sending nogood messages among agents to effect intelligent backtracking. One important issue is developing nogood caching schemes which are appropriate to asynchronous backtracking. There has also been recent progress in a sequential algorithm called dynamic backtracking which exhibits a polynomial bound on nogood cache size. In this paper, we show by example that the existing caching scheme used by dynamic backtracking is not appropriate for the multiagent context. We suggest two alternate nogood caching schemes and two caching algorithms based on these schemes. Experimental comparisons of these caching algorithms are forthcoming. Introducti...
Implicates and Prime Implicates in Random 3SAT
 Artificial Intelligence
, 1995
"... It has been observed previously that Random 3SAT exhibits a phase transition at a critical ratio of constraints to variables, where the average frequency of satisfiability falls abruptly from near 1 to near 0. In this paper we look beyond satisfiability to implicates and prime implicates of nonzero ..."
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Cited by 22 (0 self)
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It has been observed previously that Random 3SAT exhibits a phase transition at a critical ratio of constraints to variables, where the average frequency of satisfiability falls abruptly from near 1 to near 0. In this paper we look beyond satisfiability to implicates and prime implicates of nonzero length and show experimentally that, for any given length, these exhibit their own phase transitions. All of these phase transitions appear to share the same critical point as the wellknown satisfiability phase transition. We also find a rich, regular Some of this work was done while the first author was in the Qualitative Reasoning Group at the Artificial Intelligence Laboratory, the University of Texas at Austin, at a time when the Qualitative Reasoning Group was supported in part by NSF grants IRI8904454, IRI9017047, and IRI9216584, and by NASA contracts NCC 2760 and NAG 9665. Some of this work also was done while the first author was at AT&T Bell Laboratories. y The second au...
Comparing subsumption optimizations
 Collected Papers from the International Description Logics Workshop (DL'98
, 1998
"... Effective systems for expressive description logics require a heavilyoptimised subsumption checker incorporating a range of optimisation techniques. Because of the correspondence between description logics and propositional modal logic most of these techniques carry over into propositional modal lo ..."
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Cited by 20 (12 self)
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Effective systems for expressive description logics require a heavilyoptimised subsumption checker incorporating a range of optimisation techniques. Because of the correspondence between description logics and propositional modal logic most of these techniques carry over into propositional modal logic satisfiability checking. Some of the techniques are extremely effective on various test suites for propositional modal satisfiability and others are less effective. Further, the effectiveness of a technique depends on the test performed. Description logic systems spend much of their time computing subsumption relationships between descriptions. If the system is based on an expressive description logic then the
Backtracking Search Algorithms
, 2006
"... There are three main algorithmic techniques for solving constraint satisfaction problems: backtracking search, local search, and dynamic programming. In this chapter, I survey backtracking search algorithms. Algorithms based on dynamic programming [15]— sometimes referred to in the literature as var ..."
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Cited by 19 (2 self)
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There are three main algorithmic techniques for solving constraint satisfaction problems: backtracking search, local search, and dynamic programming. In this chapter, I survey backtracking search algorithms. Algorithms based on dynamic programming [15]— sometimes referred to in the literature as variable elimination, synthesis, or inference algorithms—are the topic of Chapter 7. Local or stochastic search algorithms are the topic of Chapter 5. An algorithm for solving a constraint satisfaction problem (CSP) can be either complete or incomplete. Complete, or systematic algorithms, come with a guarantee that a solution will be found if one exists, and can be used to show that a CSP does not have a solution and to find a provably optimal solution. Backtracking search algorithms and dynamic programming algorithms are, in general, examples of complete algorithms. Incomplete, or nonsystematic algorithms, cannot be used to show a CSP does not have a solution or to find a provably optimal solution. However, such algorithms are often effective at finding a solution if one exists and can be used to find an approximation to an optimal solution. Local or stochastic search algorithms are examples of incomplete algorithms. Of the two
Constraint Satisfaction
 In In the MIT Encyclopedia of the Cognitive Sciences (MITECS
, 1991
"... to A, true to B, false to C and false to D, is a satisfying truth value assignment. The structure of a constraintnetwork is depicted by a constraint graph whose nodes represents the variables and anytwo nodes are connected if the corresponding variables participate in the same constraint. In the k ..."
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to A, true to B, false to C and false to D, is a satisfying truth value assignment. The structure of a constraintnetwork is depicted by a constraint graph whose nodes represents the variables and anytwo nodes are connected if the corresponding variables participate in the same constraint. In the k colorability formulation, the graph to be colored is the constraint graph. In our SAT example the constraint graph has A connected to D and A; B and C are connected to each other. Constraintnetworks haveproven successful in modeling mundane cognitive tasks such as vision, language comprehension, default reasoning, and abduction, as well as in applications suchasscheduling, design, diagnosis, and temporal and spatial reasoning. In general, constraint satisfaction tasks are computationally intractable #NPhard# #see COMPUTATIONAL COMPLEXITY #. Techniques for pr
Computational modal logic
 Handbook of Modal Logic
, 2006
"... 2 Syntax, semantics, and reasoning problems of modal logics........................... 3 3 Translationbased methods........................................... 6 3.1 Local satisfiability in multi modal Kn................................... 6 3.2 Global satisfiability, nonlogical axioms, transitive ..."
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2 Syntax, semantics, and reasoning problems of modal logics........................... 3 3 Translationbased methods........................................... 6 3.1 Local satisfiability in multi modal Kn................................... 6 3.2 Global satisfiability, nonlogical axioms, transitive modalities, and K4n................. 20
Lifted Search Engines for Satisfiability
, 1999
"... There are several powerful solvers for satisfiability (SAT), such as wsat, DavisPutnam, and relsat. However, in practice, the SAT encodings often have so many clauses that we exceed physical memory resources on attempting to solve them. This excessive size often arises because conversion to SAT, ..."
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Cited by 18 (4 self)
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There are several powerful solvers for satisfiability (SAT), such as wsat, DavisPutnam, and relsat. However, in practice, the SAT encodings often have so many clauses that we exceed physical memory resources on attempting to solve them. This excessive size often arises because conversion to SAT, from a more natural encoding using quantifications over domains, requires expanding quantifiers. This suggests that we should "lift" successful SAT solvers. That is, adapt the solvers to use quantified clauses instead of ground clauses. However, it was generally believed that such lifted solvers would be impractical: Partially, because of the overhead of handling the predicates and quantifiers, and partially because lifting would not allow essential indexing and caching schemes. Here we show that, to the contrary, it is not only practical to handle quantified clauses directly, but that lifting can give exponential savings. We do this by identifying certain tasks that are central to...
2way vs dway branching for CSP
 In Proceedings of CP’05
, 2005
"... Abstract. Most CSP algorithms are based on refinements and extensions of backtracking, and employ one of two simple “branching schemes”: 2way branching or dway branching, for domain size d. The schemes are not equivalent, but little is known about their relative power. Here we compare them in term ..."
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Abstract. Most CSP algorithms are based on refinements and extensions of backtracking, and employ one of two simple “branching schemes”: 2way branching or dway branching, for domain size d. The schemes are not equivalent, but little is known about their relative power. Here we compare them in terms of how efficiently they can refute an unsatisfiable instance with optimal branching choices, by studying two variants of the resolution proof system, denoted CRES and NGRES, which model the reasoning of CSP algorithms. The treelike restrictions, treeCRES and treeNGRES, exactly capture the power of backtracking with 2way branching and dway branching, respectively. We give a family instances which require exponential sized search trees for backtracking with dway branching, but have size O(d 2 n) search trees for backtracking with 2way branching. We also give a natural branching strategy with which backtracking with 2way branching finds refutations of these instances in time O(d 2 n 2). The unrestricted variants of CRES and NGRES can simulate the reasoning of algorithms which incorporate learning and kconsistency enforcement. We show exponential separations between CRES and NGRES, as well as between the treelike and unrestricted versions of each system. All separations given are nearly optimal. 1
Applications of Description Logics: State of the Art and Research Challenges
 Proc. of the 13th Int. Conf. on Conceptual Structures (ICCS’05), number 3596 in Lecture Notes in Artificial Intelligence
, 2005
"... Abstract. Description Logics (DLs) are a family of class based knowledge representation formalisms characterised by the use of various constructors to build complex classes from simpler ones, and by an emphasis on the provision of sound, complete and (empirically) tractable reasoning services. They ..."
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Abstract. Description Logics (DLs) are a family of class based knowledge representation formalisms characterised by the use of various constructors to build complex classes from simpler ones, and by an emphasis on the provision of sound, complete and (empirically) tractable reasoning services. They have a range of applications, but are mostly widely known as the basis for ontology languages such as OWL. The increasing use of DL based ontologies in areas such as eScience and the Semantic Web is, however, already stretching the capabilities of existing DL systems, and brings with it a range of challenges for future research. 1