growth rates and explosions in sandpiles we study the abelian sandpile growth model where n particles are added at the origin on a stable background configuration in zd any site with at least 2d particles then topples by sending one particle to each neighbor we find that with constant background height h 2d 2 the diameter of the set of sites that topple has order n1 d this was previously known only for h d our proof uses a strong form of the least action principle for sandpiles and a novel method of background modification we can extend this diameter bound to certain backgrounds in which an arbitrarily high fraction of sites have height 2d 1 on the other hand we show that if the background height 2d 2 is augmented by 1 at an arbitrarily small fraction of sites chosen independently at random then adding finitely many particles creates an explosion a sandpile that never stabilizes

circuit satisfiability and constraint satisfaction around skolem arithmetic abstract we study interactions between skolem arithmetic and certain classes of circuit satisfiability and constraint satisfaction problems csps we revisit results of glaser et al 1 in the context of csps and settle the major open question from that paper finding a certain satisfiability problem on circuits involving complement intersection union and multiplication to be decidable this we prove using the decidability of skolem arithmetic then we solve a second question left open in 1 by proving a tight upper bound for the similar circuit satisfiability problem involving just intersection union and multiplication we continue by studying first order expansions of skolem arithmetic without constants n as csps we find already here a rich landscape of problems with non trivial instances that are in p as well as those that are np complete

attempt to distinguish electric signals of a dichotomous nature three types of electric signals were analyzed ion current fluctuations in membrane channels icfmc seismic electric signals activities ses and artificial noises an the wavelet transform when applied to the conventional time domain does not allow a classification of these signals but does so in the natural time domain a classification also becomes possible if we study q versus q where chi stands for the natural time for q values approximately between 1 and 2 the signals are classified and icfmc lies between the other two types for q 1 the entropy s identical with ln of icfmc almost equals that of a uniform distribution while the an and ses have larger and smaller s values respectively the recent p varotsos n sarlis and e skordas phys rev e 67 021109 2003 finding that in short time scales both ses and an which are shown to be non markovian result in comparable detrended fluctuation analysis exponents alpha in 1 0 1 5 is revisited even a markovian dichotomous time series in short time scales leads to similar alpha exponents

exact analysis of dodgson elections lewis carroll s 1876 voting system is complete for parallel access to np in 1876 lewis carroll proposed a voting system in which the winner is the candidate who with the fewest changes in voters preferences becomes a condorcet winner a candidate who beats all other candidates in pairwise majority rule elections bartholdi tovey and trick provided a lower bound np hardness on the computational complexity of determining the election winner in carroll s system we provide a stronger lower bound and an upper bound that matches our lower bound in particular determining the winner in carroll s system is complete for parallel access to np that is it is complete for theta 2 p for which it becomes the most natural complete problem known it follows that determining the winner in carroll s elections is not np complete unless the polynomial hierarchy collapses

generalizing constraint satisfaction on trees hybrid tractability and variable elimination the constraint satisfaction problem csp is a central generic problem in artificial intelligence considerable progress has been made in identifying properties which ensure tractability in such problems such as the property of being tree structured in this paper we introduce the broken triangle property which allows us to define a novel tractable class for this problem which significantly generalizes the class of problems with tree structure we show that the broken triangle property is conservative i e it is preserved under domain reduction and hence under arc consistency operations and that there is a polynomial time algorithm to determine an ordering of the variables for which the broken triangle property holds or to determine that no such ordering exists we also present a non conservative extension of the broken triangle property which is also sufficient to ensure tractability and can also be detected in polynomial time we show that both the broken triangle property and its extension can be used to eliminate variables and that both of these properties provide the basis for preprocessing procedures that yield unique closures orthogonal to value elimination by enforcement of consistency finally we also discuss the possibility of using the broken triangle property in variable ordering heuristics

a direct method to predict cyclic steady states of elastoplastic structures the asymptotic steady state behavior of an elastic perfectly plastic structure under cyclic loading may be determined by time consuming incremental time stepping calculations direct methods alternatively have a big computational advantage as they attempt to find the characteristics of the cyclic state right from the start of the calculations most of these methods address an elastic shakedown state through the shakedown theorems and on the basis of mathematical programming algorithms in the present paper a novel direct method that has a more physical basis and may predict any cyclic stress state of a structure under a given loading is presented the method exploits the cyclic nature of the expected residual stress distribution at the steady cycle thus after equilibrating the elastic part of the total stress with the external load the unknown residual stress part is decomposed into fourier series whose coefficients are evaluated iteratively by satisfying compatibility and equilibrium with zero loads at time points inside the cycle and then integrating over the cycle a computationally simple way to account for plasticity is proposed the procedure converges uniformly to the true cyclic residual stress for a loading below the elastic shakedown limit or to an unsafe cyclic total stress which may be used to mark the regions with plastic straining inside the cycle the method then continues to determine whether the applied loading would lead the structure to ratcheting or to regions that alternate plastically the procedure is formulated within the finite element method a von mises yield surface is typically used examples of application of one and two dimensional structures are included

the complexity of manipulative attacks in nearly single peaked electorates many electoral control and manipulation problems which we will refer to in general as manipulative actions problems are np hard in the general case it has recently been noted that many of these problems fall into polynomial time if the electorate is single peaked i e is polarized along some axis issue however real world electorates are not truly single peaked there are usually some mavericks and so real world electorates tend merely to be nearly single peaked this paper studies the complexity of manipulative action algorithms for elections over nearly single peaked electorates we do this for many notions of nearness and for a broad range of election systems we provide instances where even one maverick jumps the manipulative action complexity up to np hardness but we also provide many instances where some number of mavericks can be tolerated without increasing the manipulative action complexity

when are elections with few candidates hard to manipulate in multiagent settings where the agents have different preferences preference aggregation is a central issue voting is a general method for preference aggregation but seminal results have shown that all general voting protocols are manipulable one could try to avoid manipulation by using protocols where determining a beneficial manipulation is hard especially among computational agents it is reasonable to measure this hardness by computational complexity some earlier work has been done in this area but it was assumed that the number of voters and candidates is unbounded such hardness results lose relevance when the number of candidates is small because manipulation algorithms that are exponential only in the number of candidates and only slightly so might be available we give such an algorithm for an individual agent to manipulate the single transferable vote stv protocol which has been shown hard to manipulate in the above sense this motivates the core of this article which derives hardness results for realistic elections where the number of candidates is a small constant but the number of voters can be large the main manipulation question we study is that of coalitional manipulation by weighted voters we show that for simpler manipulation problems manipulation cannot be hard with few candidates we study both constructive manipulation making a given candidate win and destructive manipulation making a given candidate not win we characterize the exact number of candidates for which manipulation becomes hard for the plurality borda stv copeland maximin veto plurality with runoff regular cup and randomized cup protocols we also show that hardness of manipulation in this setting implies hardness of manipulation by an individual in unweighted settings when there is uncertainty about the others votes but not vice versa to our knowledge these are the first results on the hardness of manipulation when there is uncertainty about the others votes

long range correlations in the electric signals that precede rupture further investigations the correlations within the time series of the seismic electric signal ses activities have been studied in a previous paper p varotsos n sarlis and e skordas phys rev e 66 011902 2002 here we analyze the time series of successive high and low level states durations the existence of correlation between the states is investigated by means of hurst and detrended fluctuation analysis dfa the multifractal dfa mf dfa is also employed the results point to a stronger correlation and hence longer memory in the series of the high level states furthermore an analysis in the natural time domain reveals that certain power spectrum characteristics seem to distinguish ses activities from artificial man made electric noises more precisely for natural frequencies 0 f 0 5 the curves of the ses activities and artificial noises lie above and below respectively that of the uniform distribution ud a classification of these two types of electric signals ses activities artificial noises cannot be achieved on the basis of the values of the power law exponents alone if the hurst analysis dfa and mf dfa are applied to the original time series the latter two methods however seem to allow a distinction between the ses activities and artificial noises when treating them not in conventional the time frame but in the natural time domain to further test the techniques a time series produced by another system was examined we chose a signal of ion current fluctuations in membrane channels icfmcs the following conclusions among others have been obtained first the power spectrum analysis in the natural time domain shows that the icfmc curve almost coincides in the range 0 f 0 5 with that of the ud and hence icfmc lies just in the boundary between the ses activities and artificial noises second mf dfa indicates monofractality for the icfmcs with a generalized hurst exponent h 50 8460 03 in the range 7 70 ms

mixed integer programming with convex concave constraints fixed parameter tractability and applications to multicovering and voting abstract a classic result of lenstra math oper res 1983 says that an integer linear program can be solved in fixed parameter tractable fpt time for the parameterization by the number of variables we extend this result by incorporating piecewise linear convex or concave functions to our mixed integer programs this general technique allows us to analyze the parameterized complexity of a number of classic np hard computational problems in particular we prove that weighted set multicover is in fpt when parameterized by the number of elements to cover and that there exists an fpt time approximation scheme for multiset multicover for the same parameter this is our most technical result further we use our general technique to prove that a number of problems from computational social choice e g problems related to bribery and control in elections are in fpt when parameterized by the number of candidates for bribery this resolves a nearly 10 year old family of open problems and for weighted electoral control of approval voting this improves some previously known xp memberships to fpt memberships

long range correlations in the electric signals that precede rupture the smoluchowski chapman kolmogorov functional equation is applied to the electric signals that precede rupture the results suggest a non markovian character of the analyzed data the rescaled range hurst and detrended fluctuation analyses as well as that related with the mean distance a walker spanned lead to power law exponents which are consistent with the existence of long range correlations a universality in the power spectrum characteristics of these signals emerges if an analysis is made not in the conventional time frame but in the natural time domain within this frame it seems that certain power spectrum characteristics of ion current fluctuations in membrane channels distinguish them from the electric signals preceding rupture the latter exhibit a behavior compatible with that expected from a model based on the random field ising hamiltonian at the critical point

hybrid tractability of valued constraint problems the constraint satisfaction problem csp is a central generic problem in computer science and artificial intelligence it provides a common framework for many theoretical problems as well as for many real life applications valued constraint problems are a generalisation of the csp which allow the user to model optimisation problems considerable effort has been made in identifying properties which ensure tractability in such problems in this work we initiate the study of hybrid tractability of valued constraint problems that is properties which guarantee tractability of the given valued constraint problem but which do not depend only on the underlying structure of the instance such as being tree structured or only on the types of valued constraints in the instance such as submodularity we present several novel hybrid classes of valued constraint problems in which all unary constraints are allowed which include a machine scheduling problem constraint problems of arbitrary arities with no overlapping nogoods and the softalldiff constraint with arbitrary unary valued constraints an important tool in our investigation will be the notion of forbidden substructures

termination of rewrite relations on λ terms based on girard s notion of reducibility in this paper we show how to extend the notion of reducibility introduced by girard for proving the termination of reduction in the polymorphic calculus to prove the termination of various kinds of rewrite relations on terms including rewriting modulo some equational theory and rewriting with matching modulo by using the notion of computability closure this provides a powerful termination criterion for various higher order rewriting frameworks including klop s combinatory reductions systems with simple types and nipkow s higher order rewrite systems

the treewidth of proofs abstract so called ordered variants of the classical notions of pathwidth and treewidth are introduced and proposed as proof theoretically meaningful complexity measures for the directed acyclic graphs underlying proofs ordered pathwidth is roughly the same as proof space and the ordered treewidth of a proof is meant to serve as a measure of how far it is from being treelike length space lower bounds for k dnf refutations are generalized to arbitrary infinity axioms and strengthened in that the space measure is relaxed to ordered treewidth

broken triangles a binary csp instance satisfying the broken triangle property btp can be solved in polynomial time unfortunately in practice few instances satisfy the btp we show that a local version of the btp allows the merging of domain values in arbitrary instances of binary csp thus providing a novel polynomial time reduction operation extensive experimental trials on benchmark instances demonstrate a significant decrease in instance size for certain classes of problems we show that btp merging can be generalised to instances with constraints of arbitrary arity and we investigate the theoretical relationship with resolution in sat a directional version of general arity btp merging then allows us to extend the btp tractable class previously defined only for binary csp we investigate the complexity of several related problems including the recognition problem for the general arity btp class when the variable order is unknown finding an optimal order in which to apply btp merges and detecting btp merges in the presence of global constraints such as alldifferent

the tractability frontier of graph like first order query sets the focus of this work is first order model checking by which we refer to the problem of deciding whether or not a given first order sentence is satisfied by a given finite structure in particular we aim to understand on which sets of sentences this problem is tractable in the sense of parameterized complexity theory to this end we define the notion of a graph like sentence set the definition is inspired by previous work on first order model checking wherein the permitted connectives and quantifiers were restricted our main theorem is the complete tractability classification of such graph like sentence sets which is to our knowledge the first complexity classification theorem concerning a class of sentences that has no restriction on the connectives and quantifiers to present and prove our classification we introduce and develop a novel complexity theoretic framework that is built on parameterized complexity and includes new notions of reduction

the power of linear programming for general valued csps let d called the domain be a fixed finite set and let gamma called the valued constraint language be a fixed set of functions of the form f d m to mathbb q cup infty where different functions might have different arity m we study the valued constraint satisfaction problem parametrized by gamma denoted by vcsp gamma these are minimization problems given by n variables and the objective function given by a sum of functions from gamma each depending on a subset of the n variables for example if d 0 1 and gamma contains all ternary 0 infty valued functions vcsp gamma corresponds to 3 sat more generally if gamma contains only 0 infty valued functions vcsp gamma corresponds to csp gamma if d 0 1 and gamma contains all ternary 0 1 valued functions vcsp gamma corresponds to min 3 sat in which the goal is to minimize the number of unsatisfied clauses in a 3 cnf instance finite valued constraint languages contain functions that take on only rational values and not infinite values our main result is a precise algebraic characterization of valued constraint languages whose instances can be solved exactly by the basic linear programming relaxation blp for a valued constraint language gamma blp is a decision procedure for gamma if and only if gamma admits a symmetric fractional polymorphism of every arity for a finite valued constraint language gamma blp is a decision procedure if and only if gamma admits a symmetric fractional polymorphism of some arity or equivalently if gamma admits a symmetric fractional polymorphism of arity 2 using these results we obtain tractability of several novel classes of problems including problems over valued constraint languages that are 1 submodular on arbitrary lattices 2 k submodular on arbitrary finite domains 3 weakly and hence strongly tree submodular on arbitrary trees

shakedown state simulation techniques based on linear elastic solutions abstract the paper extends an iterative method previously applied to the determination of the limit state of a perfectly plastic body 5 to the determination of the shakedown limit state of a body subjected to a cyclic history of mechanical load and temperature a convergence proof is presented for a particular class of problems where the magnitude of a mechanical load at the shakedown limit is found as the limit of a sequence of monotonically reducing upper bounds an implementation of the method in a finite element scheme is discussed and examples of the application of the method to sample problems are presented

domain growth morphology in curvature driven two dimensional coarsening we study the distribution of domain areas areas enclosed by domain boundaries hulls and perimeters for curvature driven two dimensional coarsening employing a combination of exact analysis and numerical studies for various initial conditions we show that the number of hulls per unit area n h a t da with enclosed area in the interval a a da is described for a disordered initial condition by the scaling function n h a t 2 c h a ensuremath lambda h t 2 where c h 1 8 ensuremath pi sqrt 3 ensuremath approx 0 023 is a universal constant and ensuremath lambda h is a material parameter for a critical initial condition the same form is obtained with the same ensuremath lambda h but with c h replaced by c h 2 for the distribution of domain areas we argue that the corresponding scaling function has for random initial conditions the form n d a t 2 c d ensuremath lambda d t ensuremath tau ensuremath ensuremath 2 a ensuremath lambda d t ensuremath tau ensuremath where c d and ensuremath lambda d are numerically very close to c h and ensuremath lambda h respectively and ensuremath tau ensuremath 187 91 ensuremath approx 2 055 for critical initial conditions one replaces c d by c d 2 and the exponent is ensuremath tau 379 187 ensuremath approx 2 027 these results are extended to describe the number density of the length of hulls and domain walls surrounding connected clusters of aligned spins these predictions are supported by extensive numerical simulations we also study numerically the geometric properties of the boundaries and areas

complexity of and algorithms for the manipulation of borda nanson s and baldwin s voting rules we investigate manipulation of the borda voting rule as well as two elimination style voting rules nanson s and baldwin s voting rules which are based on borda voting we argue that these rules have a number of desirable computational properties for unweighted borda voting we prove that it is np hard for a coalition of two manipulators to compute a manipulation this resolves a long standing open problem in the computational complexity of manipulating common voting rules we prove that manipulation of baldwin s and nanson s rules is computationally more difficult than manipulation of borda as it is np hard for a single manipulator to compute a manipulation in addition for baldwin s and nanson s rules with weighted votes we prove that it is np hard for a coalition of manipulators to compute a manipulation with a small number of candidates because of these np hardness results we compute manipulations using heuristic algorithms that attempt to minimise the number of manipulators we propose several new heuristic methods experiments show that these methods significantly outperform the previously best known heuristic method for the borda rule our results suggest that whilst computing a manipulation of the borda rule is np hard computational complexity may provide only a weak barrier against manipulation in practice in contrast to the borda rule our experiments with baldwin s and nanson s rules demonstrate that both of them are often more difficult to manipulate in practice these results suggest that elimination style voting rules deserve further study

tree projections and structural decomposition methods minimality and game theoretic characterization tree projections provide a mathematical framework that encompasses all the various purely structural decomposition methods that have been proposed in the literature to single out classes of nearly acyclic hyper graphs such as the tree decomposition method which is the most powerful decomposition method on graphs and the generalized hypertree decomposition method which is its natural counterpart on arbitrary hypergraphs the paper analyzes this framework by focusing in particular on minimal tree projections that is on tree projections without useless redundancies first it is shown that minimal tree projections enjoy a number of properties that are usually required for normal form decompositions in various structural decomposition methods in particular they enjoy the same kind of connection properties as minimal tree decompositions of graphs with the result being tight in the light of the negative answer that is provided to the open question about whether they enjoy a slightly stronger notion of connection property defined to speed up the computation of hypertree decompositions second it is shown that tree projections admit a natural game theoretic characterization in terms of the robber and captain game in this game as for the robber and cops game characterizing tree decompositions the existence of winning strategies implies the existence of monotone ones as a special case the robber and captain game can be used to characterize the generalized hypertree decomposition method where such a game theoretic characterization was missing and asked for besides their theoretical interest these results have immediate algorithmic applications both for the general setting and for structural decomposition methods that can be recast in terms of tree projections

a quantitative version of the gibbard satterthwaite theorem for three alternatives the gibbard satterthwaite theorem states that every nondictatorial election rule among at least three alternatives can be strategically manipulated we prove a quantitative version of the gibbard satterthwaite theorem a random manipulation by a single random voter will succeed with a nonnegligible probability for any election rule among three alternatives that is far from being a dictatorship and from having only two alternatives in its range

quantified conjunctive queries on partially ordered sets we study the computational problem of checking whether a quantified conjunctive query a first order sentence built using only conjunction as boolean connective is true in a finite poset a reflexive antisymmetric and transitive directed graph we prove that the problem is already np hard on a certain fixed poset and investigate structural properties of posets yielding fixed parameter tractability when the problem is parameterized by the query our main algorithmic result is that model checking quantified conjunctive queries on posets is fixed parameter tractable when parameterized by the sentence and the width of the poset the maximum size of a subset of pairwise incomparable elements we complement our algorithmic result by complexity results with respect to classes of finite posets in a hierarchy of natural poset invariants establishing its tightness in this sense

fixed parameter tractability and completeness i basic results for many fixed parameter problems that are trivially soluable in polynomial time such as k dominating set essentially no better algorithm is presently known than the one which tries all possible solutions other problems such as k feedback vertex set exhibit fixed parameter tractability for each fixed k the problem is soluable in time bounded by a polynomial of degree c where c is a constant independent of k we establish the main results of a completeness program which addresses the apparent fixed parameter intractability of many parameterized problems in particular we define a hierarchy of classes of parameterized problems fpt subseteq w 1 subseteq w 2 subseteq cdots subseteq w sat subseteq w p and identify natural complete problems for w t for t geq 2 in other papers we have shown many problems complete for w 1 dominating set is shown to be complete for w 2 and thus is not fixed parameter tractable unless independent set clique irredundant set and many other natural problems in w 2 are also fixed parameter tractable we also give a compendium of currently known hardness results as an appendix

limit state solutions based upon linear elastic solutions with a spatially varying elastic modulus abstract the paper describes an iterative method of determining the limit state of a perfectly plastic body for the von mises yield condition a sequence of incompressible linear elastic solutions are defined with a spatially varying shear modulus which provide a sequence of upper bounds to the limit load which monotonically reduce and converge to the limit state solution for a discretized solution generated by a rayleigh ritz method the sequence converges to the least upper bound associated with the class of displacement fields an example of a finite element implementation method is given and applied to the limit state of a cracked body a method for accelerated convergence is described for problems where the plastic region forms a small proportion of the total volume of the body

parameterized computational complexity of control problems in voting systems voting systems are common tools in a variety of areas this paper studies parameterized computational complexity of control of plurality condorcet and approval voting systems respectively the types of controls considered include adding or deleting candidates or voters under constructive or destructive setting we obtain the following results 1 constructive control by adding candidates in plurality voting is w 2 hard with respect to the parameter number of added candidates 2 destructive control by adding candidates in plurality voting is w 2 hard with respect to the parameter number of added candidates 3 constructive control by adding voters in condorcet voting is w 1 hard with respect to the parameter number of added voters 4 constructive control by deleting voters in condorcet voting is w 1 hard with respect to the parameter number of deleted voters 5 constructive control by adding voters in approval voting is w 1 hard with respect to the parameter number of added voters and 6 constructive control by deleting voters in approval voting is w 2 hard with respect to the parameter number of deleted voters

exact algorithms for weighted and unweighted borda manipulation problems we derive exact combinatorial algorithms for both weighed and unweighted borda manipulation problems we derive an fpt algorithm for the unweighted borda manipulation problem with respect to the number of candidates we prove that borda manipulation with two manipulators is polynomial time solvable in single peaked elections we propose o m 2 m t 1 time and o t m 1 t t 1 m time algorithms for the weighted and the unweighted borda manipulation problems respectively where t is the number of manipulators and m is the number of candidates in particular for t 2 our algorithm for the unweighted case runs in o 3 m time affirmatively resolving one open problem posed by betzler et al 2 as a byproduct of our results we show that the unweighted borda manipulation problem admits an algorithm with running time o 2 9 m 2 log m based on an integer linear programming technique finally we prove that the unweighted borda manipulation problem is polynomial time solvable in single peaked elections in contrast to the np hardness in the general case

scaling of waves in the bak tang wiesenfeld sandpile model n with aen ae0 n a similar ansatzes should according to this view hold for the number of topplings s which difiers from a because sites can topple more than once in an avalanche and for the radius and duration of avalanches but recent inves tigations 10 12 show that the two dimensional btw model may be characterized by a multifractal behavior where difierent moments of a are governed by exponents aen which are not linear in n and are indeed not related to each other for difierent n difierent reasons for this have been proposed in 10 11 and in 12 notice that multi fractality of avalanches can be proven for certain variants of the 1 d sandpile model 14 deviations from pure power laws had been seen already in early simulations but were usually interpreted as fl nite size efiects due to avalanches which touch the bound ary of the lattice to illustrate that this is most likely not true and that there is a real problem with simple scaling we show in fig 1 the ratio ps x l pa x l of the integrated distributions ps x l r 1 x dx 0 ps x 0 l for d 2 and for difierent values of l in these simula tions cylindrical boundary conditions were used open at y l 2 and periodic at x 0 l and data were col lected only for avalanches starting at y 0 in this way we hope to have minimized boundary efiects also since we do not make separate flts to ps x l and pa x l we have none of the uncertainties inherent in such flts due

on the evaluation of election outcomes under uncertainty we investigate the extent to which it is possible to compute the probability of a particular candidate winning an election given imperfect information about the preferences of the electorate we assume that for each voter we have a probability distribution over a set of preference orderings thus for each voter we have a number of possible preference orderings we do not know which of these orderings actually represents the preferences of the voter but for each ordering we know the probability that it does for the case where the number of candidates is a constant we are able to give a polynomial time algorithm to compute the probability that a given candidate will win we present experimental results obtained with an implementation of the algorithm illustrating how the email protected s performance in practice is better than its predicted theoretical bound however when the number of candidates is not bounded we prove that the problem becomes p hard for the plurality k approval borda copeland and bucklin voting rules we further show that even evaluating if a candidate has any chance of winning is np complete for the plurality voting rule in the case where voters may have different weights with unweighted voters we give a polynomial algorithm for plurality and show that the problem is hard for many other voting rules finally we give a monte carlo approximation algorithm for computing the probability of a candidate winning in any settings with an error that is as small as desired

dynamic range majority data structures given a set p of n coloured points on the real line we study the problem of answering range majority or heavy hitter queries on p more specifically for a query range q we want to return each colour that is assigned to more than an fraction of the points contained in q we present a new data structure for answering range majority queries on a dynamic set of points where 0 1 our data structure uses o n space supports queries in o lg n time and updates in o lg n amortized time if the coordinates of the points are integers then the query time can be improved to o lg n lg lg n for constant values of this improved query time matches an existing lower bound for any data structure with polylogarithmic update time we also generalize our data structure to handle sets of points in d dimensions for d 2 as well as dynamic arrays in which each entry is a colour

the learnability of voting rules scoring rules and voting trees are two broad and concisely representable classes of voting rules scoring rules award points to alternatives according to their position in the preferences of the voters while voting trees are iterative procedures that select an alternative based on pairwise comparisons in this paper we investigate the pac learnability of these classes of rules we demonstrate that the class of scoring rules as functions from preferences into alternatives is efficiently learnable in the pac model with respect to voting trees while in general a learning algorithm would require an exponential number of samples we show that if the number of leaves is polynomial in the size of the set of alternatives then a polynomial training set suffices we apply these results in an emerging theory automated design of voting rules by learning

the complexity of conservative valued csps we study the complexity of valued constraint satisfaction problems vcsps parametrized by a constraint language a fixed set of cost functions over a finite domain an instance of the problem is specified by a sum of cost functions from the language and the goal is to minimize the sum under the unique games conjecture the approximability of finite valued vcsps is well understood see raghavendra 2008 however there is no characterization of finite valued vcsps let alone general valued vcsps that can be solved exactly in polynomial time thus giving insights from a combinatorial optimization perspective we consider the case of languages containing all possible unary cost functions in the case of languages consisting of only 0 valued cost functions i e relations such languages have been called conservative and studied by bulatov 2003 2011 and recently by barto 2011 since we study valued languages we call a language conservative if it contains all finite valued unary cost functions the computational complexity of conservative valued languages has been studied by cohen et al 2006 for languages over boolean domains by deineko et al 2008 for 0 1 valued languages a k a max csp and by takhanov 2010a for 0 valued languages containing all finite valued unary cost functions a k a min cost hom we prove a schaefer like dichotomy theorem for conservative valued languages if all cost functions in the language satisfy a certain condition specified by a complementary combination of stp and mjn multimorphisms then any instance can be solved in polynomial time via a new algorithm developed in this article otherwise the language is np hard this is the first complete complexity classification of general valued constraint languages over non boolean domains it is a common phenomenon that complexity classifications of problems over non boolean domains are significantly harder than the boolean cases the polynomial time algorithm we present for the tractable cases is a generalization of the submodular minimization problem and a result of cohen et al 2008 our results generalize previous results by takhanov 2010a and a subset of results by cohen et al 2006 and deineko et al 2008 moreover our results do not rely on any computer assisted search as in deineko et al 2008 and provide a powerful tool for proving hardness of finite valued and general valued languages

non equilibrium relaxation and interface energy of the ising model abstract from the non equilibrium critical relaxation study of the two dimensional ising model the dynamical critical exponent z is estimated to be 2 165 0 010 for this model the relaxation in the ordered phase of this model is consistent with exp t behavior the interface energy of the three dimensional ising model is studied and the critical exponent of the correlation length and the critical amplitude of the surface tension 0 are estimated to be 0 6250 0 0025 and 1 42 0 04 respectively a dynamic monte carlo renormalization group method is successfully applied to the equilibrium properties of the three dimensional ising model

a note on linear function approximation using random projections linear function approximations based on random projections are proposed and justified for a class of fixed point and minimization problems

binary constraint satisfaction problems defined by excluded topological minors abstract the binary constraint satisfaction problem csp is to decide whether there exists an assignment to a set of variables which satisfies specified constraints between pairs of variables a binary csp instance can be presented as a labelled graph encoding both the forms of the constraints and where they are imposed we consider subproblems defined by restricting the allowed form of this graph one type of restriction is to forbid certain specified substructures patterns this captures some tractable classes of the csp but does not capture classes defined by language restrictions or the well known structural property of acyclicity we extend the notion of pattern and introduce the notion of a topological minor of a binary csp instance by forbidding a finite set of patterns from occurring as topological minors we obtain a compact mechanism for expressing novel tractable subproblems of the csp including new generalisations of the class of acyclic instances

locally constrained homomorphisms on graphs of bounded treewidth and bounded degree a homomorphism from a graph g to a graph h is locally bijective surjective or injective if its restriction to the neighborhood of every vertex of g is bijective surjective or injective respectively we prove that the problems of testing whether a given graph g allows a homomorphism to a given graph h that is locally bijective surjective or injective respectively are np complete even when g has pathwidth at most 5 4 or 2 respectively or when both g and h have maximum degree 3 we complement these hardness results by showing that the three problems are polynomial time solvable if g has bounded treewidth and in addition g or h has bounded maximum degree

the complexity of homomorphism and constraint satisfaction problems seen from the other side we give a complexity theoretic classification of homomorphism problems for graphs and more generally relational structures obtained by restricting the left hand side structure in a homomorphism for every class c of structures let hom c be the problem of deciding whether a given structure a c has a homomorphism to a given arbitrary structure s we prove that under some complexity theoretic assumption from parameterized complexity theory hom c is in polynomial time if and only if c has bounded tree width modulo homomorphic equivalence translated into the language of constraint satisfaction problems our result yields a characterization of the tractable structural restrictions of constraint satisfaction problems translated into the language of database theory it implies a characterization of the tractable instances of the evaluation problem for conjunctive queries over relational databases

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

natural time analysis of critical phenomena a quantity exists by which one can identify the approach of a dynamical system to the state of criticality which is hard to identify otherwise this quantity is the variance of natural time where and pk is the normalized energy released during the kth event of which the natural time is defined as k k n and n stands for the total number of events then we show that 1 becomes equal to 0 070 at the critical state for a variety of dynamical systems this holds for criticality models such as 2d ising and the bak tang wiesenfeld sandpile which is the standard example of self organized criticality this condition of 1 0 070 holds for experimental results of critical phenomena such as growth of rice piles seismic electric signals and the subsequent seismicity before the associated main shock

control of condorcet voting complexity and a relation algebraic approach abstract we study the constructive variant of the control problem for condorcet voting where control is done by deleting voters we prove that this problem remains np hard if instead of condorcet winners the alternatives in the uncovered set win furthermore we present a relation algebraic model of condorcet voting and relation algebraic specifications of the dominance relation and the solutions of the control problem all our relation algebraic specifications immediately can be translated into the programming language of the obdd based computer system relview our approach is very flexible and especially appropriate for prototyping and experimentation and as such very instructive for educational purposes it can easily be applied to other voting rules and control problems

parameterized complexity of candidate control in elections and related digraph problems there are different ways for an external agent to influence the outcome of an election we concentrate on control by adding or deleting candidates our main focus is to investigate the parameterized complexity of various control problems for different voting systems to this end we introduce natural digraph problems that may be of independent interest they help in determining the parameterized complexity of control for different voting systems including llull copeland and plurality voting devising several parameterized reductions we provide an overview of the parameterized complexity of the digraph and control problems with respect to natural parameters such as adding deleting only a bounded number of candidates or having only few voters

a generalised method for ratchet analysis of structures undergoing arbitrary thermo mechanical load histories a novel approach is presented based upon the linear matching method framework in order to directly calculate the ratchet limit of structures subjected to arbitrary thermo mechanical load histories traditionally ratchet analysis methods have been based upon the fundamental premise of decomposing the cyclic load history into cyclic and constant components respectively in order to assess the magnitude of additional constant loading a structure may accommodate before ratcheting occurs the method proposed in this paper for the first time accurately and efficiently calculates the ratchet limit with respect to a proportional variation between the cyclic primary and secondary loads as opposed to an additional primary load only the method is a strain based approach and utilises a novel convergence scheme in order to calculate an approximate ratchet boundary based upon a predefined target magnitude of ratchet strain per cycle the ratcheting failure mechanism evaluated by the method leads to less conservative ratchet boundaries compared to the traditional bree solution the method yields the total and plastic strain ranges as well as the ratchet strains for various levels of loading between the ratchet and limit load boundaries two example problems have been utilised in order to verify the proposed methodology

predictability of the coherent noise model and its applications we study the threshold distribution function of the coherent noise model for the case of infinite number of agents this function is piecewise constant with a finite number of steps n the latter exhibits a 1 f behavior as a function of the order of occurrence of an avalanche and hence versus natural time an analytic expression of the expectation value mathcal e s for the size s of the next avalanche is obtained and used for the prediction of the next avalanche apart from mathcal e s the number of steps n can also serve for this purpose this enables the construction of a similar prediction scheme which can be applied to real earthquake aftershock data

new limits of treewidth based tractability in optimization sparse structures are frequently sought when pursuing tractability in optimization problems they are exploited from both theoretical and computational perspectives to handle complex problems that become manageable when sparsity is present an example of this type of structure is given by treewidth a graph theoretical parameter that measures how tree like a graph is this parameter has been used for decades for analyzing the complexity of various optimization problems and for obtaining tractable algorithms for problems where this parameter is bounded the goal of this work is to contribute to the understanding of the limits of the treewidth based tractability in optimization our results are as follows first we prove that in a certain sense the already known positive results on extension complexity based on low treewidth are the best possible secondly under mild assumptions we prove that treewidth is the only graph theoretical parameter that yields tractability for a wide class of optimization problems a fact well known in graphical models in machine learning and in constraint satisfaction problems which here we extend to an approximation setting in optimization

the complexity of finite valued csps we study the computational complexity of exact minimization of rational valued discrete functions let be a set of rational valued functions on a fixed finite domain such a set is called a finite valued constraint language the valued constraint satisfaction problem vcsp is the problem of minimizing a function given as a sum of functions from we establish a dichotomy theorem with respect to exact solvability for all finite valued constraint languages defined on domains of arbitrary finite size we show that every constraint language either admits a binary symmetric fractional polymorphism in which case the basic linear programming relaxation solves any instance of vcsp exactly or satisfies a simple hardness condition that allows for a polynomial time reduction from max cut to vcsp

parameterized computational complexity of dodgson and young elections abstract we show that the two np complete problems of dodgson score and young score have differing computational complexities when the winner is close to being a condorcet winner on the one hand we present an efficient fixed parameter algorithm for determining a condorcet winner in dodgson elections by a minimum number of switches in the votes on the other hand we prove that the corresponding problem for young elections where one has to delete votes instead of performing switches is w 2 complete in addition we study dodgson elections that allow ties between the candidates and give fixed parameter tractability as well as w 2 completeness results depending on the cost model for switching ties

attempt to distinguish long range temporal correlations from the statistics of the increments by natural time analysis most probable value of 1 of the shuffled data is found to be approximately equal to that of the original data the difference most likely arising from temporal correlation finally it is found that the differential entropy associated with the probability p1 maximizes for around 1 6 1 7 which is comparable to the value determined experimentally in diverse phenomena e g solar flares icequakes dislocation glide in stressed single crystals of ice etc it also agrees with the b value in the gutenberg richter law of earthquakes in addition the case of multiplicative cascades is studied in the natural time domain

constructing np intermediate problems by blowing holes with parameters of various properties the search for natural np intermediate problems is one of the holy grails within computational complexity ladner s original diagonalization technique for generating np intermediate problems blowing holes has a serious shortcoming it creates problems with a highly artificial structure by arbitrarily removing certain problem instances in this article we limit this problem by generalizing ladner s method to use parameters with various characteristics this allows one to define more fine grained parameters resulting in np intermediate problems where we only blow holes in a controlled subset of the problem we begin by fully characterizing the problems that admit np intermediate subproblems for a broad and natural class of parameterizations and extend the result further such that structural csp restrictions based on parameters that are hard to compute such as tree width are covered thereby generalizing a result by grohe for studying certain classes of problems including csps parameterized by constraint languages we consider more powerful parameterizations first we identify a new method for obtaining constraint languages such that csp are np intermediate the sets can have very different properties compared to previous constructions by for instance bodirsky grohe and provides insights into the algebraic approach for studying the complexity of infinite domain csps second we prove that the propositional abduction problem parameterized by constraint languages admits np intermediate problems this settles an open question posed by nordh zanuttini we provide a framework to obtain np intermediate problems based on diagonalization we categorize different types of parameters that are usable in our framework we construct np intermediate constraint satisfaction problems we resolve the open question whether boolean abduction admits intermediate problems

tractable hypergraph properties for constraint satisfaction and conjunctive queries an important question in the study of constraint satisfaction problems csp is understanding how the graph or hypergraph describing the incidence structure of the constraints influences the complexity of the problem for binary csp instances that is where each constraint involves only two variables the situation is well understood the complexity of the problem essentially depends on the treewidth of the graph of the constraints grohe 2007 marx 2010b however this is not the correct answer if constraints with unbounded number of variables are allowed and in particular for csp instances arising from query evaluation problems in database theory formally if h is a class of hypergraphs then let csp h be csp restricted to instances whose hypergraph is in h our goal is to characterize those classes of hypergraphs for which csp h is polynomial time solvable or fixed parameter tractable parameterized by the number of variables note that in the applications related to database query evaluation we usually assume that the number of variables is much smaller than the size of the instance thus parameterization by the number of variables is a meaningful question the most general known property of h that makes csp h polynomial time solvable is bounded fractional hypertree width here we introduce a new hypergraph measure called submodular width and show that bounded submodular width of h which is a strictly more general property than bounded fractional hypertree width implies that csp h is fixed parameter tractable in a matching hardness result we show that if h has unbounded submodular width then csp h is not fixed parameter tractable and hence not polynomial time solvable unless the exponential time hypothesis eth fails the algorithmic result uses tree decompositions in a novel way instead of using a single decomposition depending on the hypergraph the instance is split into a set of instances all on the same set of variables as the original instance and then the new instances are solved by choosing a different tree decomposition for each of them the reason why this strategy works is that the splitting can be done in such a way that the new instances are uniform with respect to the number extensions of partial solutions and therefore the number of partial solutions can be described by a submodular function for the hardness result we prove via a series of combinatorial results that if a hypergraph h has large submodular width then a 3sat instance can be efficiently simulated by a csp instance whose hypergraph is h to prove these combinatorial results we need to develop a theory of multicommodity flows on hypergraphs and vertex separators in the case when the function b s defining the cost of separator s is submodular which can be of independent interest

tight lower bounds on graph embedding problems we prove that unless the exponential time hypothesis eth fails deciding if there is a homomorphism from graph g to graph h cannot be done in time vv h vo vv g v we also show an exponential time reduction from graph homomorphism to subgraph isomorphism this rules out subject to eth a possibility of vv h vo vv h v time algorithm deciding if graph g is a subgraph of h for both problems our lower bounds asymptotically match the running time of brute force algorithms trying all possible mappings of one graph into another thus our work closes the gap in the known complexity of these fundamental problems moreover as a consequence of our reductions conditional lower bounds follow for other related problems such as locally injective homomorphism graph minors topological graph minors minimum distortion embedding and quadratic assignment problem

ranking chain sum orders ranking information is an important topic in information sciences internet searching voting systems and sports in the full information approach a ranking is a total order of the candidates we compare two rankings by pairwise comparisons under the nearest neighbor kendall tau distance and study the distance and rank aggregation problems in many settings the information is incomplete and a ranking is given by a partial order a bucket order is obtained if a ranking allows ties and treats tied candidates as equivalent then the distance and rank aggregation problems can be solved efficiently in almost linear time a chain sum order is complementary to a bucket order and consists of a set of disjoint total orders its width and height is the number and the maximum size of the total orders respectively we show that the distance and rank aggregation problems of a total order and a chain sum order of bounded width or of height at most two can be solved in polynomial time and are np complete for a total and a chain sum order of height at least 12 both problems remain np complete for a total and a heap order which is the partial order obtained from a single elimination tournament in sports however the problems are fixed parameter tractable with respect to the distance and the ulam distance but are fixed parameter intractable with respect to the order dimension

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 complexity of counting homomorphisms seen from the other side for every class of relational structures c let hom c be the problem of deciding whether a structure a c has a homomorphism to a given arbitrary structure b grohe has proved that under a certain complexity theoretic assumption hom c is solvable in polynomial time if and only if the cores of all structures in c have bounded tree width we prove under a weaker complexity theoretic assumption that the corresponding counting problem hom c is solvable in polynomial time if and only if all structures in c have bounded tree width this answers an open question posed by grohe

a bisimulation like proof method for contextual properties in untyped λ calculus with references and deallocation we develop a general method for proving properties of programs under arbitrary contexts including but not limited to observational equivalence space improvement and a form of memory safety of the programs in untyped call by value l calculus with first class dynamically allocated higher order references and deallocation the method generalizes sumii et al s environmental bisimulation technique and gives a sound and complete characterization of each proved property in the sense that the bisimilarity the largest set satisfying the bisimulation like conditions equals the set of terms with the property to be proved we give examples of contextual properties concerning typical data structures such as linked lists binary search trees and directed acyclic graphs with reference counts all with deletion operations that release memory this shows the scalability of the environmental approach from contextual equivalence to other binary relations such as space improvement and unary predicates such as memory safety as well as to languages with non monotone store

query evaluation via tree decompositions a number of efficient methods for evaluating first order and monadic second order queries on finite relational structures are based on tree decompositions of structures or queries we systematically study these methods in the first part of the article we consider arbitrary formulas on tree like structures we generalize a theorem of courcelle 1990 by showing that on structures of bounded tree width a monadic second order formula with free first and second order variables can be evaluated in time linear in the structure size plus the size of the output in the second part we study tree like formulas on arbitrary structures we generalize the notions of acyclicity and bounded tree width from conjunctive queries to arbitrary first order formulas in a straightforward way and analyze the complexity of evaluating formulas of these fragments moreover we show that the acyclic and bounded tree width fragments have the same expressive power as the well known guarded fragment and the finite variable fragments of first order logic respectively

fixed parameter tractability and completeness ii on completeness for w 1 abstract for many fixed parameter problems that are trivially solvable in polynomial time such as k dominating set essentially no better algorithm is presently known than the one which tries all possible solutions other problems such as feedback vertex set exhibit fixed parameter tractability for each fixed k the problem is solvable in time bounded by a polynomial of degree c where c is a constant independent of k in a previous paper the w hierarchy of parameterized problems was defined and complete problems were identified for the classes w t for t 2 our main result shows that independent set is complete for w 1

theoretical studies of self organized criticality these notes are intended to provide a pedagogical introduction to the abelian sandpile model of self organized criticality and its related models the abelian group the algebra of particle addition operators the burning test for recurrent states equivalence to the spanning trees problem are described the exact solution of the directed version of the model in any dimension is explained the model s equivalence to scheidegger s model of river basins takayasu s aggregation model and the voter model is discussed for the undirected case the solution for one dimensional lattices and the bethe lattice is briefly described known results about the two dimensional case are summarized generalization to the abelian distributed processors model is discussed time dependent properties and the universality of critical behavior in sandpiles are briefly discussed i conclude by listing some still unsolved problems

fixed parameter tractability definability and model checking in this article we study parameterized complexity theory from the perspective of logic or more specifically descriptive complexity theory we propose to consider parameterized model checking problems for various fragments of first order logic as generic parameterized problems and show how this approach can be useful in studying both fixed parameter tractability and intractability for example we establish the equivalence between the model checking for existential first order logic the homomorphism problem for relational structures and the substructure isomorphism problem our main tractability result shows that model checking for first order formulas is fixed parameter tractable when restricted to a class of input structures with an excluded minor on the intractability side for every t ge 0 we prove an equivalence between model checking for first order formulas with t quantifier alternations and the parameterized halting problem for alternating turing machines with t alternations we discuss the close connection between this alternation hierarchy and downey and fellows w hierarchy on a more abstract level we consider two forms of definability called fagin definability and slicewise definability that are appropriate for describing parameterized problems we give a characterization of the class fpt of all fixed parameter tractable problems in terms of slicewise definability in finite variable least fixed point logic which is reminiscent of the immerman vardi theorem characterizing the class ptime in terms of definability in least fixed point logic

algorithms for the coalitional manipulation problem we investigate the problem of coalitional manipulation in elections which is known to be hard in a variety of voting rules we put forward efficient algorithms for the problem in borda maximin and plurality with runoff and analyze their windows of error specifically given an instance on which an algorithm fails we bound the additional power the manipulators need in order to succeed we finally discuss the implications of our results with respect to the popular approach of employing computational hardness to preclude manipulation