Algebraic Properties of Valued Constraint Satisfaction Problem

The paper presents an algebraic framework for optimization problems expressible as Valued Constraint Satisfaction Problems. Our results generalize the algebraic framework for the decision version (CSPs) provided by Bulatov et al. [SICOMP 2005]. We introduce the notions of weighted algebras and varieties and use the Galois connection due to Cohen et al. [SICOMP 2013] to link VCSP languages to weighted algebras. We show that the difficulty of VCSP depends only on the weighted variety generated by the associated weighted algebra. Paralleling the results for CSPs we exhibit a reduction to cores and rigid cores which allows us to focus on idempotent weighted varieties. Further, we propose an analogue of the Algebraic CSP Dichotomy Conjecture; prove the hardness direction and verify that it agrees with known results for VCSPs on two-element sets [Cohen et al. 2006], finite-valued VCSPs [Thapper and Zivny 2013] and conservative VCSPs [Kolmogorov and Zivny 2013].Comment: arXiv admin note: text overlap with arXiv:1207.6692 by other author

Faster Existential FO Model Checking on Posets

We prove that the model checking problem for the existential fragment of first-order (FO) logic on partially ordered sets is fixed-parameter tractable (FPT) with respect to the formula and the width of a poset (the maximum size of an antichain). While there is a long line of research into FO model checking on graphs, the study of this problem on posets has been initiated just recently by Bova, Ganian and Szeider (CSL-LICS 2014), who proved that the existential fragment of FO has an FPT algorithm for a poset of fixed width. We improve upon their result in two ways: (1) the runtime of our algorithm is O(f(|{\phi}|,w).n^2) on n-element posets of width w, compared to O(g(|{\phi}|). n^{h(w)}) of Bova et al., and (2) our proofs are simpler and easier to follow. We complement this result by showing that, under a certain complexity-theoretical assumption, the existential FO model checking problem does not have a polynomial kernel.Comment: Paper as accepted to the LMCS journal. An extended abstract of an earlier version of this paper has appeared at ISAAC'14. Main changes to the previous version are improvements in the Multicoloured Clique part (Section 4

Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis

Obtaining lower bounds for NP-hard problems has for a long time been an active area of research. Recent algebraic techniques introduced by Jonsson et al. (SODA 2013) show that the time complexity of the parameterized SAT($\cdot$) problem correlates to the lattice of strong partial clones. With this ordering they isolated a relation $R$ such that SAT($R$) can be solved at least as fast as any other NP-hard SAT($\cdot$) problem. In this paper we extend this method and show that such languages also exist for the max ones problem (MaxOnes($\Gamma$)) and the Boolean valued constraint satisfaction problem over finite-valued constraint languages (VCSP($\Delta$)). With the help of these languages we relate MaxOnes and VCSP to the exponential time hypothesis in several different ways.Comment: This is an extended version of Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis, appearing in Proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science MFCS 2014 Budapest, August 25-29, 201

Reasoning about temporal relations : the maximal 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

Regulation strength and technology creep play key roles in global long-term projections of wild capture fisheries

Unidad de excelencia María de Maeztu CEX2019-000940-MIdentificadors digitals: Digital object identifier for the 'European Research Council' (http://dx.doi.org/10.13039/501100000781) Digital object identifier for 'Horizon 2020' (http://dx.doi.org/10.13039/501100007601) - BIGSEA projectMany studies have shown that the global fish catch can only be sustained with effective regulation that restrains overfishing. However, the persistence of weak or ineffective regulation in many parts of the world, coupled with changing technologies and additional stressors like climate change, renders the future of global catches uncertain. Here, we use a spatially resolved, bio-economic size-spectrum model to shed light on the interactive impacts of three globally important drivers over multidecadal timescales: imperfect regulation, technology-driven catchability increase, and climate change. We implement regulation as the adjustment of fishing towards a target level with some degree of effectiveness and project a range of possible trajectories for global fisheries. We find that if technological progress continues apace, increasingly effective regulation is required to prevent overfishing, akin to a Red Queen race. Climate change reduces the possible upper bound for global catches, but its economic impacts can be offset by strong regulation. Ominously, technological progress under weak regulation masks a progressive erosion of fish biomass by boosting profits and generating a temporary stabilization of global catches. Our study illustrates the large degree to which the long-term outlook of global fisheries can be improved by continually strengthening fisheries regulation, despite the negative impacts of climate change

The STAR MAPS-based PiXeL detector

The PiXeL detector (PXL) for the Heavy Flavor Tracker (HFT) of the STAR experiment at RHIC is the first application of the state-of-the-art thin Monolithic Active Pixel Sensors (MAPS) technology in a collider environment. Custom built pixel sensors, their readout electronics and the detector mechanical structure are described in detail. Selected detector design aspects and production steps are presented. The detector operations during the three years of data taking (2014-2016) and the overall performance exceeding the design specifications are discussed in the conclusive sections of this paper

Perspectives for Positron Emission Tomography with RPCs

In this study we address the feasibility and main properties of a positron emission tomograph (PET) based on RPCs. The concept, making use of the converter-plate principle, takes advantage of the intrinsic layered structure of RPCs and its simple and economic construction. The extremely good time and position resolutions of RPCs also allow the TOF-PET imaging technique to be considered. Monte-Carlo simulations, supported by experimental data, are presented and the main advantages and drawbacks for applications of potential interest are discussed.Comment: Presented at "RPC2001-VI Workshop on Resistive Plate Chambers and Related Detectors", Coimbra, Portugal, 26-27 November 2001 (5 pages

Solving order constraints in logarithmic space.

We combine methods of order theory, finite model theory, and universal algebra to study, within the constraint satisfaction framework, the complexity of some well-known combinatorial problems connected with a finite poset. We identify some conditions on a poset which guarantee solvability of the problems in (deterministic, symmetric, or non-deterministic) logarithmic space. On the example of order constraints we study how a certain algebraic invariance property is related to solvability of a constraint satisfaction problem in non-deterministic logarithmic space

A maximal tractable class of soft constraints

Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which associates some measure of desirability with each possible combination of values for those variables. However, the crucial question of the computational complexity of finding the optimal solution to a collection of soft constraints has so far received very little attention. In this paper we identify a class of soft binary constraints for which the problem of finding the optimal solution is tractable. In other words, we show that for any given set of such constraints, there exists a polynomial time algorithm to determine the assignment having the best overall combined measure of desirability. This tractable class includes many commonly-occurring soft constraints, such as 'as near as possible' or 'as soon as possible after', as well as crisp constraints such as 'greater than'. Finally, we show that this tractable class is maximal, in the sense that adding any other form of soft binary constraint which is not in the class gives rise to a class of problems which is NP-hard

Tropically convex constraint satisfaction

A semilinear relation S is max-closed if it is preserved by taking the componentwise maximum. The constraint satisfaction problem for max-closed semilinear constraints is at least as hard as determining the winner in Mean Payoff Games, a notorious problem of open computational complexity. Mean Payoff Games are known to be in the intersection of NP and co-NP, which is not known for max-closed semilinear constraints. Semilinear relations that are max-closed and additionally closed under translations have been called tropically convex in the literature. One of our main results is a new duality for open tropically convex relations, which puts the CSP for tropically convex semilinaer constraints in general into NP intersected co-NP. This extends the corresponding complexity result for scheduling under and-or precedence constraints, or equivalently the max-atoms problem. To this end, we present a characterization of max-closed semilinear relations in terms of syntactically restricted first-order logic, and another characterization in terms of a finite set of relations L that allow primitive positive definitions of all other relations in the class. We also present a subclass of max-closed constraints where the CSP is in P; this class generalizes the class of max-closed constraints over finite domains, and the feasibility problem for max-closed linear inequalities. Finally, we show that the class of max-closed semilinear constraints is maximal in the sense that as soon as a single relation that is not max-closed is added to L, the CSP becomes NP-hard.Comment: 29 pages, 2 figure