Solving Infinite-Domain CSPs Using the Patchwork Property

Dabrowski, Konrad K.; Jönsson, Peter; Ordyniak, Sebastian; Osipov, George

doi:10.1609/aaai.v35i5.16488

Cited by 4 publications

(3 citation statements)

References 59 publications

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“…On the one hand, they are solvable in 2 O(n 2 ) time or 2 O(n•log n) time in certain cases [20], but we can currently only rule out subexponential 2 o(n) algorithms under ETH [23]. On the other hand, despite the immense success of parameterized complexity, there is a lack of natural FPT algorithms for qualitative reasoning, and we are only aware of a handful of less surprising examples such as tree-width [6,10].…”

Section: Introductionmentioning

confidence: 99%

A Multivariate Complexity Analysis of Qualitative Reasoning Problems

Hikima

Akagi

Marumo

et al. 2022

Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence

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Online bipartite matching has attracted much attention due to its importance in various applications such as advertising, ride-sharing, and crowdsourcing. In most online matching problems, the rewards and node arrival probabilities are given in advance and are not controllable. However, many real-world matching services require them to be controllable and the decision-maker faces a non-trivial problem of optimizing them. In this study, we formulate a new optimization problem, Online Matching with Controllable Rewards and Arrival probabilities (OM-CRA), to simultaneously determine not only the matching strategy but also the rewards and arrival probabilities. Even though our problem is more complex than the existing ones, we propose a fast 1/2-approximation algorithm for OM-CRA. The proposed approach transforms OM-CRA to a saddle-point problem by approximating the objective function, and then solves it by the Primal-Dual Hybrid Gradient (PDHG) method with acceleration through the use of the problem structure. In simulations on real data from crowdsourcing and ride-sharing platforms, we show that the proposed algorithm can find solutions with high total rewards in practical times.

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Section: Introductionmentioning

confidence: 99%

A Multivariate Complexity Analysis of Qualitative Reasoning Problems

Hikima

Akagi

Marumo

et al. 2022

Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence

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show abstract

“…In contrast to this, we present an XP algorithm for CSP(D ∞,k ) when k ∈ N. Additionally, we prove that CSP(D 2,k ) for 1 ≤ k < ∞, is not in FPT (under standard complexity-theoretic assumptions), thus showing that significantly faster algorithms for DTP are unlikely. Problems such as Allen's Algebra and RCC8 are in FPT (Dabrowski et al 2021) so DTP is in fact a substantially harder problem. We complement all of these results by showing that CSP(D 2,∞ ) is pNP-hard, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…The polynomial-time solvability of CSP(D 2,0 ) follows from the fact that the relations in D 2,0 equal the point algebra (Vilain and Kautz 1986). It is well known that CSP(D k,0 ) for k ≥ 3 is NP-hard (this follows, for instance, from an easy reduction from the BE-TWEENNESS problem (Garey and Johnson 1979)) and re- sults by Dabrowski et al (2021) show that these problems are in FPT.…”

Section: Introductionmentioning

confidence: 99%

Disjunctive Temporal Problems under Structural Restrictions

Dabrowski

Jönsson

Ordyniak

et al. 2021

AAAI

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The disjunctive temporal problem (DTP) is an expressive temporal formalism that extends Dechter et al.'s simple temporal problem. The DTP is well studied in the literature and has many important applications. It is known that deciding satisfiability of DTPs is NP-hard and that, in many cases, single-exponential algorithms (running in O(c^n) time) do not exist under the Exponential-Time Hypothesis. The computational hardness makes it worthwhile to identify restricted problems that are efficiently solvable. One way of doing this is to restrict the interactions of variables and constraints. We show that instances of DTP of any arity with integers bounded by poly(n) can be solved in n^{f(w)} time, where n denotes the problem size, w is the treewidth of the incidence graph and f is a computable function; in other words, this problem is in the complexity class XP and it can be solved in polynomial time whenever w is fixed. We complement this result by showing that binary DTPs that only involve the integers 0 and 1 are not fixed-parameter tractable with respect to treewidth, i.e. they do not admit a f(w)poly(n)$ time algorithm for any computable function f, under standard complexity assumptions. For instances with unbounded integers, we show that even binary DTPs parameterized by treewidth cannot be in XP, unless P = NP.

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Using Model Theory to Find Decidable and Tractable Description Logics with Concrete Domains

Baader

Rydval

2022

J Autom Reasoning

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Concrete domains have been introduced in the area of Description Logic to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons) when defining concepts. Unfortunately, in the presence of general concept inclusions (GCIs), which are supported by all modern DL systems, adding concrete domains may easily lead to undecidability. To regain decidability of the DL $$\mathcal {ALC}$$ ALC in the presence of GCIs, quite strong restrictions, in sum called $$\omega $$ ω -admissibility, were imposed on the concrete domain. On the one hand, we generalize the notion of $$\omega $$ ω -admissibility from concrete domains with only binary predicates to concrete domains with predicates of arbitrary arity. On the other hand, we relate $$\omega $$ ω -admissibility to well-known notions from model theory. In particular, we show that finitely bounded homogeneous structures yield $$\omega $$ ω -admissible concrete domains. This allows us to show $$\omega $$ ω -admissibility of concrete domains using existing results from model theory. When integrating concrete domains into lightweight DLs of the $$\mathcal {EL}$$ EL family, achieving decidability is not enough. One wants reasoning in the resulting DL to be tractable. This can be achieved by using so-called p-admissible concrete domains and restricting the interaction between the DL and the concrete domain. We investigate p-admissibility from an algebraic point of view. Again, this yields strong algebraic tools for demonstrating p-admissibility. In particular, we obtain an expressive numerical p-admissible concrete domain based on the rational numbers. Although $$\omega $$ ω -admissibility and p-admissibility are orthogonal conditions that are almost exclusive, our algebraic characterizations of these two properties allow us to locate an infinite class of p-admissible concrete domains whose integration into $$\mathcal {ALC}$$ ALC yields decidable DLs.

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Solving Infinite-Domain CSPs Using the Patchwork Property

Cited by 4 publications

References 59 publications

A Multivariate Complexity Analysis of Qualitative Reasoning Problems

A Multivariate Complexity Analysis of Qualitative Reasoning Problems

Disjunctive Temporal Problems under Structural Restrictions

Using Model Theory to Find Decidable and Tractable Description Logics with Concrete Domains

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