reducts of the random partial order abstract we determine up to the equivalence of first order interdefinability all structures which are first order definable in the random partial order it turns out that there are precisely five such structures we achieve this result by showing that there exist exactly five closed permutation groups which contain the automorphism group of the random partial order and thus expose all symmetries of this structure our result lines up with previous similar classifications for the random graph and the order of the rationals it also provides further evidence for a conjecture due to simon thomas which states that the number of structures definable in a homogeneous structure in a finite relational language is up to first order interdefinability always finite in the proof we use the new technique of canonical functions originally invented in the context of theoretical computer science which allows for a systematic ramsey theoretic analysis of functions acting on the random partial order the technique identifies patterns in arbitrary functions on the random partial order which makes them accessible to finite combinatorial arguments

a solution method for the static constrained stackelberg problem via penalty method this note presents a new solution method for the static constrained stackelberg problem through our approach the stackelberg problem is completely transformed into a one level unconstrained problem such that the newly introduced overall augmented objective function is minimized with repect to the leader s and the follower s variables jointly it can be proved that a sequence of solutions to the transformed problems converges to the solution of the original problem when the penalty parameters are updated

a homotopy method for solving bilevel programming problem abstract a homotopy method for solving bilevel programming problem blpp is proposed the algorithm is based on constructing the homotopy equation for blpp one satisfiable sufficient condition is given to ensure that the point of homotopy path globally converges to a k k t point of blpp numerical results are presented to show the effectiveness of this method

classifying the complexity of constraints using finite algebras many natural combinatorial problems can be expressed as constraint satisfaction problems this class of problems is known to be np complete in general but certain restrictions on the form of the constraints can ensure tractability here we show that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and we explore how the computational complexity of the corresponding constraint satisfaction problem is connected to the properties of this algebra hence we completely translate the problem of classifying the complexity of restricted constraint satisfaction problems into the language of universal algebra we introduce a notion of tractable algebra and investigate how the tractability of an algebra relates to the tractability of the smaller algebras which may be derived from it including its subalgebras and homomorphic images this allows us to reduce significantly the types of algebras which need to be classified using our results we also show that if the decision problem associated with a given collection of constraint types can be solved efficiently then so can the corresponding search problem we then classify all finite strictly simple surjective algebras with respect to tractability obtaining a dichotomy theorem which generalizes schaefer s dichotomy for the generalized satisfiability problem finally we suggest a possible general algebraic criterion for distinguishing the tractable and intractable cases of the constraint satisfaction problem

a class of stability regions for which a kharitonov like theorem holds families of complex polynomials whose coefficients lie within given intervals are discussed in particular the problem of determining if all polynomials in a family have the property that all of their roots lie within a given region is discussed towards this end a notion of a kharitonov region is defined roughly speaking a kharitonov region is a region in the complex plane with the following property given any suitable family of polynomials in order to determine if all polynomials in the family have all of their roots in the region it suffices to check only the vertex polynomials of the family the main result is a sufficient condition for a given region to be a kharitonov region

tractable constraints on ordered domains abstract finding solutions to a constraint satisfaction problem is known to be an np complete problem in general but may be tractable in cases where either the set of allowed constraints or the graph structure is restricted in this paper we identify a restricted set of contraints which gives rise to a class of tractable problems this class generalizes the notion of a horn formula in propositional logic to larger domain sizes we give a polynomial time algorithm for solving such problems and prove that the class of problems generated by any larger set of constraints is np complete

a dichotomy theorem for constraint satisfaction problems on a 3 element set the constraint satisfaction problem csp provides a common framework for many combinatorial problems the general csp is known to be np complete however certain restrictions on a possible form of constraints may affect the complexity and lead to tractable problem classes there is therefore a fundamental research direction aiming to separate those subclasses of the csp that are tractable and those which remain np complete schaefer gave an exhaustive solution of this problem for the csp on a 2 element domain in this article we generalise this result to a classification of the complexity of the csp on a 3 element domain the main result states that every subproblem of the csp is either tractable or np complete and the criterion separating them is that conjectured in bulatov et al 2005 and bulatov and jeavons 2001b we also characterize those subproblems for which standard constraint propagation techniques provide a decision procedure finally we exhibit a polynomial time algorithm which for a given set of allowed constraints outputs if this set gives rise to a tractable problem class to obtain the main result and the algorithm we extensively use the algebraic technique for the csp developed in jeavons 1998b bulatov et al 2005 and bulatov and jeavons 2001b

interval oscillation criteria for a forced second order nonlinear ordinary differential equations with oscillatory potential new oscillation criteria established in the paper for a forced second order nonlinear equation with oscillatory potential p t y t q t f y t g t are different from the most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line our results are of a high degree of generality and sharper than some previous results and handle the cases which are not covered by known results moreover these results can also be applied to the extreme such as t 0 q s ds

point algebras for temporal reasoning algorithms and complexity we investigate the computational complexity of temporal reasoning in different time models such as totally ordered partially ordered and branching time our main result concerns the satisfiability problem for point algebras and point algebras extended with disjunctions for these problems we identify all tractable subclasses we also provide a number of additional results for instance we present a new time model suitable for reasoning about systems with a bounded number of unsynchronized clocks we investigate connections with spatial reasoning and we present improved algorithms for deciding satisfiability of the tractable point algebras

scheduling with and or precedence constraints in many scheduling applications it is required that the processing of some job be postponed until some other job which can be chosen from a pregiven set of alternatives has been completed the traditional concept of precedence constraints fails to model such restrictions therefore the concept has been generalized to so called and or precedence constraints which can cope with this kind of requirement in the context of traditional precedence constraints feasibility transitivity and the computation of earliest start times for jobs are fundamental well studied problems the purpose of this paper is to provide efficient algorithms for these tasks for the more general model of and or precedence constraints we show that feasibility as well as many questions related to transitivity can be solved by applying essentially the same linear time algorithm in order to compute earliest start times we propose two polynomial time algorithms to cope with different classes of time distances between jobs

new kamenev type oscillation criteria for second order nonlinear differential equations with damping abstract some new oscillation criteria are established for the nonlinear damped differential equation r t y p t y q t f y 0 that are different from most known ones in the sense that they are based on a class of new functions t s r defined in the sequel our results are sharper than some previous results which can be seen by the examples at the end of this paper

interval criteria for oscillation of second order linear ordinary differential equations abstract new oscillation criteria are established for the equation py qy 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line our results are more natural according to the sturm separation theorem and sharper than some previous results and can be applied to extreme cases such as t 0 q t dt

twenty one large tractable subclasses of allen s algebra abstract this paper continues nebel and burckert s investigation of allen s interval algebra by presenting nine more maximal tractable subclasses of the algebra provided that p np in addition to their previously reported ord horn subclass furthermore twelve tractable subclasses are identified whose maximality is not decided four of them can express the notion of sequentiality between intervals which is not possible in the ord horn algebra all of the algebras are considerably larger than the ord horn subclass the satisfiability algorithm which is common for all the algebras is shown to be linear furthermore the path consistency algorithm is shown to decide satisfiability of interval networks using any of the algebras

a new computational method for stackelberg and min max problems by use of a penalty method this paper is concerned with the stackelberg problem and the min max problem in competitive systems the stackelberg approach is applied to the optimization of two level systems where the higher level determines the optimal value of its decision variables parameters for the lower level so as to minimize its objective while the lower level minimizes its own objective with respect to the lower level decision variables under the given parameters meanwhile the min max problem is to determine a min max solution such that a function maximized with respect to the maximizer s variables is minimized with respect to the minimizer s variables this problem is also characterized by a parametric approach in a two level scheme new computational methods are proposed here that is a series of nonlinear programming problems approximating the original two level problem by application of a penalty method to a constrained parametric problem in the lower level are solved iteratively it is proved that a sequence of approximated solutions converges to the correct stackelberg solution or the min max solution some numerical examples are presented to illustrate the algorithms

interval oscillation criteria for second order nonlinear differential equations with damping new oscillation criteria are established for the nonlinear damped differential equation ry py qf y 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t0 rather than on the whole half line our results are sharper than some previous results and extend and improve the recent interval criteria of kong and huang and can be applied to extreme cases such as t0 q s ds in particular several examples that dwell upon the sharp conditions of our results are also included

maximal infinite valued constraint languages we systematically investigate the computational complexity of constraint satisfaction problems for constraint languages over an infinite domain in particular we study a generalization of the well established notion of maximal constraint languages from finite to infinite domains if the constraint language can be defined with an w categorical structure then maximal constraint languages are in one to one correspondence to minimal oligomorphic clones based on this correspondence we derive general tractability and hardness criteria for the corresponding constraint satisfaction problems

space time tradeoffs for approximate nearest neighbor searching nearest neighbor searching is the problem of preprocessing a set of n point points in d dimensional space so that given any query point q it is possible to report the closest point to q rapidly in approximate nearest neighbor searching a parameter e 0 is given and a multiplicative error of 1 e is allowed we assume that the dimension d is a constant and treat n and e as asymptotic quantities numerous solutions have been proposed ranging from low space solutions having space o n and query time o log n 1 ed 1 to high space solutions having space roughly o n log n ed and query time o log n e we show that there is a single approach to this fundamental problem which both improves upon existing results and spans the spectrum of space time tradeoffs given a tradeoff parameter where 2 1 e we show that there exists a data structure of space o n d 1 log 1 e that can answer queries in time o log n 1 e d 1 2 when e 2 this yields a data structure of space o n log 1 e that can answer queries in time o log n 1 e d 1 2 when e 1 e it provides a data structure of space o n ed 1 log 1 e that can answer queries in time o log n e our results are based on a data structure called a t e avd which is a hierarchical quadtree based subdivision of space into cells each cell stores up to t representative points of the set such that for any query point q in the cell at least one of these points is an approximate nearest neighbor of q we provide new algorithms for constructing avds and tools for analyzing their total space requirements we also establish lower bounds on the space complexity of avds and show that up to a factor of o log 1 e our space bounds are asymptotically tight in the two extremes e 2 and e 1 e

interval oscillation criteria related to integral averaging technique for certain nonlinear differential equations abstract we present new interval oscillation criteria related to integral averaging technique for certain classes of second order nonlinear differential equations that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line our results are sharper than some previous results and handle the cases which are not covered by known criteria in particular several examples that dwell upon the sharp conditions of our results are also included

reasoning about temporal relations the tractable subalgebras of allen s interval algebra allen s interval algebra is one of the best established formalisms for temporal reasoning this article provides the final step in the classification of complexity for satisfiability problems over constraints expressed in this algebra when the constraints are chosen from the full allen s algebra this form of satisfiability problem is known to be np complete however eighteen tractable subalgebras have previously been identified we show here that these subalgebras include all possible tractable subsets of allen s algebra in other words we show that this algebra contains exactly eighteen maximal tractable subalgebras and reasoning in any fragment not entirely contained in one of these subalgebras is np complete we obtain this dichotomy result by giving a new uniform description of the known maximal tractable subalgebras and then systematically using a general algebraic technique for identifying maximal subalgebras with a given property

closure properties of constraints many combinatorial search problems can be expressed as constraint satisfaction problems and this class of problems is known to be np complete in general in this paper we investigate the subclasses that arise from restricting the possible constraint types we first show that any set of constraints that does not give rise to an np complete class of problems must satisfy a certain type of algebraic closure condition we then investigate all the different possible forms of this algebraic closure property and establish which of these are sufficient to ensure tractability as examples we show that all known classes of tractable constraints over finite domains can be characterized by such an algebraic closure property finally we describe a simple computational procedure that can be used to determine the closure properties of a given set of constraints this procedure involves solving a particular constraint satisfaction problem which we call an indicator problem

building tractable disjunctive constraints many combinatorial search problems can be expressed as constraint satisfaction problems this class of problems is known to be np hard in general but a number of restricted constraint classes have been identified which ensure tractability this paper presents the first general results on combining tractable constraint classes to obtain larger more general tractable classes we give examples to show that many known examples of tractable constraint classes from a wide variety of different contexts can be constructed from simpler tractable classes using a general method we also construct several new tractable classes that have not previously been identified

the complexity of temporal constraint satisfaction problems a temporal constraint language is a set of relations that has a first order definition in q an extended abstract of this article appeared in the proceedings of stoc 08

schaefer s theorem for graphs schaefer s theorem is a complexity classification result for so called boolean constraint satisfaction problems it states that every boolean constraint satisfaction problem is either contained in one out of six classes and can be solved in polynomial time or is np complete we present an analog of this dichotomy result for the propositional logic of graphs instead of boolean logic in this generalization of schaefer s result the input consists of a set w of variables and a conjunction of statements constraints about these variables in the language of graphs where each statement is taken from a fixed finite set of allowed quantifier free first order formulas the question is whether is satisfiable in a graph we prove that either is contained in one out of 17 classes of graph formulas and the corresponding problem can be solved in polynomial time or the problem is np complete this is achieved by a universal algebraic approach which in turn allows us to use structural ramsey theory to apply the universal algebraic approach we formulate the computational problems under consideration as constraint satisfaction problems csps whose templates are first order definable in the countably infinite random graph our method for classifying the computational complexity of those csps is based on a ramsey theoretic analysis of functions acting on the random graph and we develop general tools suitable for such an analysis which are of independent mathematical interest

reasoning about qualitative temporal information abstract representing and reasoning about incomplete and indefinite qualitative temporal information is an essential part of many artificial intelligence tasks an interval based framework and a point based framework have been proposed for representing such temporal information in this paper we address two fundamental reasoning tasks that arise in applications of these frameworks given possibly indefinite and incomplete knowledge of the relationships between some intervals or points i find a scenario that is consistent with the information provided and ii find the feasible relations between all pairs of intervals or points for the point based framework and a restricted version of the interval based framework we give computationally efficient procedures for finding a consistent scenario and for finding the feasible relations our algorithms are marked improvements over the previously known algorithms in particular we develop an o n2 time algorithm for finding one consistent scenario that is an o n improvement over the previously known algorithm where n is the number of intervals or points and we develop an algorithm for finding all the feasible relations that is of far more practical use than the previously known algorithm for the unrestricted version of the interval based framework finding a consistent scenario and finding the feasible relations have been shown to be np complete we show how the results for the point algebra aid in the design of a backtracking algorithm for finding one consistent scenario that is shown to be useful in practice for planning problems

the computational structure of monotone monadic snp and constraint satisfaction a study through datalog and group theory this paper starts with the project of finding a large subclass of np which exhibits a dichotomy the approach is to find this subclass via syntactic prescriptions while the paper does not achieve this goal it does isolate a class of problems specified by monotone monadic snp without inequality which may exhibit this dichotomy we justify the placing of all these restrictions by showing essentially using ladner s theorem that classes obtained by using only two of the above three restrictions do not show this dichotomy we then explore the structure of this class we show that all problems in this class reduce to the seemingly simpler class csp we divide csp into subclasses and try to unify the collection of all known polytime algorithms for csp problems and extract properties that make csp problems np hard this is where the second part of the title a study through datalog and group theory comes in we present conjectures about this class which would end in showing the dichotomy

the projective sumt method for convex programming an algorithm for solving convex programming problems is derived from the differential equation characterizing the trajectory of unconstrained minimizers of the classical logarithmic barrier function convergence of the continuous version of this projective sumt method is proved under minimal assumptions extension of the algorithm to a form which handles linear equality constraints produces a differential equation analogue of karmarkar s method for linear programming the discrete version uses the same method of search and finds the step size by minimizing the logarithmic method of centers function an acceleration procedure based on the nonvanishing of the jacobian of the karush kuhn tucker system at a minimizer is shown to converge quadratically when the problem variables are bounded dual feasible points are available and the algorithm produces at each iteration lower and upper bounds on the global minimum a matrix approximation is given which greatly reduces the traditional problems in inverting the

new oscillation criteria of second order nonlinear differential equations by employing a class of new functions f f t s l and a generalized riccati technique some new oscillation and interval oscillation criteria are established for the second order nonlinear differential equation r t y t q t y t y t 0 the obtained interval oscillation criteria can be applied to equations with forcing term two examples are also included to show the significance of our results

reasoning about temporal relations a maximal tractable subclass of allen s interval algebra we introduce a new subclass of allen s interval algebra we call ord horn subclass which is a strict superset of the pointisable subclass we prove that reasoning in the ord horn subclass is a polynomial time problem and show that the path consistency method is sufficient for deciding satisfiability further using an extensive machine generated case analysis we show that the ord horn subclass is a maximal tractable subclass of the full algebra assuming p np in fact it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations