scholarly journals Bag Query Containment and Information Theory

2021 ◽  
Vol 46 (3) ◽  
pp. 1-39
Author(s):  
Mahmoud Abo Khamis ◽  
Phokion G. Kolaitis ◽  
Hung Q. Ngo ◽  
Dan Suciu
Keyword(s):  
Information Theory ◽  
Time Algorithm ◽  
Algorithmic Problem ◽  
Conjunctive Query ◽  
Exponential Time ◽  
Containment Problem ◽  
Information Inequalities ◽  
Query Containment ◽  
Open Question ◽  
Exponential Time Algorithm

The query containment problem is a fundamental algorithmic problem in data management. While this problem is well understood under set semantics, it is by far less understood under bag semantics. In particular, it is a long-standing open question whether or not the conjunctive query containment problem under bag semantics is decidable. We unveil tight connections between information theory and the conjunctive query containment under bag semantics. These connections are established using information inequalities, which are considered to be the laws of information theory. Our first main result asserts that deciding the validity of a generalization of information inequalities is many-one equivalent to the restricted case of conjunctive query containment in which the containing query is acyclic; thus, either both these problems are decidable or both are undecidable. Our second main result identifies a new decidable case of the conjunctive query containment problem under bag semantics. Specifically, we give an exponential-time algorithm for conjunctive query containment under bag semantics, provided the containing query is chordal and admits a simple junction tree.

An Exact Exponential Time Algorithm for Power Dominating Set

Algorithmica ◽  
2011 ◽  
Vol 63 (1-2) ◽  
pp. 323-346 ◽  
Author(s):  
Daniel Binkele-Raible ◽  
Henning Fernau
Keyword(s):  
Dominating Set ◽  
Time Algorithm ◽  
Exponential Time ◽  
Exponential Time Algorithm

An improved exponential-time algorithm for k -SAT

2005 ◽  
Vol 52 (3) ◽  
pp. 337-364 ◽  
Author(s):  
Ramamohan Paturi ◽  
Pavel Pudlák ◽  
Michael E. Saks ◽  
Francis Zane
Keyword(s):  
Time Algorithm ◽  
Exponential Time ◽  
Exponential Time Algorithm

scholarly journals Bounded homomorphisms and finitely generated fiber products of lattices

2020 ◽  
Vol 30 (04) ◽  
pp. 693-710
Author(s):  
William DeMeo ◽  
Peter Mayr ◽  
Nik Ruškuc
Keyword(s):  
Word Problem ◽  
Time Algorithm ◽  
Finitely Generated ◽  
Bounded Lattice ◽  
Exponential Time ◽  
Unpublished Result ◽  
Lattice Homomorphisms ◽  
Finitely Presented ◽  
Exponential Time Algorithm

We investigate when fiber products of lattices are finitely generated and obtain a new characterization of bounded lattice homomorphisms onto lattices satisfying a property we call Dean’s condition (D) which arises from Dean’s solution to the word problem for finitely presented lattices. In particular, all finitely presented lattices and those satisfying Whitman’s condition satisfy (D). For lattice epimorphisms [Formula: see text], [Formula: see text], where [Formula: see text], [Formula: see text] are finitely generated and [Formula: see text] satisfies (D), we show the following: If [Formula: see text] and [Formula: see text] are bounded, then their fiber product (pullback) [Formula: see text] is finitely generated. While the converse is not true in general, it does hold when [Formula: see text] and [Formula: see text] are free. As a consequence, we obtain an (exponential time) algorithm to decide boundedness for finitely presented lattices and their finitely generated sublattices satisfying (D). This generalizes an unpublished result of Freese and Nation.

scholarly journals Pessimistic Leader-Follower Equilibria with Multiple Followers

2017 ◽  
Author(s):  
Stefano Coniglio ◽  
Nicola Gatti ◽  
Alberto Marchesi
Keyword(s):  
Nash Equilibrium ◽  
Normal Form ◽  
Scientific Literature ◽  
Time Algorithm ◽  
Exponential Time ◽  
Normal Form Games ◽  
Opposite Case ◽  
Pure Strategies ◽  
Multiple Followers ◽  
Exponential Time Algorithm

The problem of computing the strategy to commit to has been widely investigated in the scientific literature for the case where a single-follower is present. In the multi-follower setting though, results are only sporadic. In this paper, we address the multi-follower case for normal-form games, assuming that, after observing the leader’s commitment, the followers play pure strategies and reach a Nash equilibrium. We focus on the pessimistic case where, among many equilibria, one minimizing the leader’s utility is chosen (the opposite case is computationally trivial). We show that the problem is NP-hard even with only two followers, and propose an exact exponential-time algorithm which, for any number of followers, either finds an equilibrium when the game admits a finite one or, if not, an α-approximation of the supremum of the leader’ utility, for any α > 0.

scholarly journals Matching Cut in Graphs with Large Minimum Degree

Algorithmica ◽  
2020 ◽  
Author(s):  
Chi-Yeh Chen ◽  
Sun-Yuan Hsieh ◽  
Hoang-Oanh Le ◽  
Van Bang Le ◽  
Sheng-Lung Peng
Keyword(s):  
Polynomial Time ◽  
Minimum Degree ◽  
Positive Root ◽  
Time Algorithm ◽  
Bipartite Graphs ◽  
Exponential Time ◽  
Running Time ◽  
Subexponential Time ◽  
Exponential Time Hypothesis ◽  
Exponential Time Algorithm

AbstractIn a graph, a matching cut is an edge cut that is a matching. Matching Cut is the problem of deciding whether or not a given graph has a matching cut, which is known to be $${\mathsf {NP}}$$ NP -complete. While Matching Cut is trivial for graphs with minimum degree at most one, it is $${\mathsf {NP}}$$ NP -complete on graphs with minimum degree two. In this paper, we show that, for any given constant $$c>1$$ c > 1 , Matching Cut is $${\mathsf {NP}}$$ NP -complete in the class of graphs with minimum degree c and this restriction of Matching Cut has no subexponential-time algorithm in the number of vertices unless the Exponential-Time Hypothesis fails. We also show that, for any given constant $$\epsilon >0$$ ϵ > 0 , Matching Cut remains $${\mathsf {NP}}$$ NP -complete in the class of n-vertex (bipartite) graphs with unbounded minimum degree $$\delta >n^{1-\epsilon }$$ δ > n 1 - ϵ . We give an exact branching algorithm to solve Matching Cut for graphs with minimum degree $$\delta \ge 3$$ δ ≥ 3 in $$O^*(\lambda ^n)$$ O ∗ ( λ n ) time, where $$\lambda$$ λ is the positive root of the polynomial $$x^{\delta +1}-x^{\delta }-1$$ x δ + 1 - x δ - 1 . Despite the hardness results, this is a very fast exact exponential-time algorithm for Matching Cut on graphs with large minimum degree; for instance, the running time is $$O^*(1.0099^n)$$ O ∗ ( 1 . 0099 n ) on graphs with minimum degree $$\delta \ge 469$$ δ ≥ 469 . Complementing our hardness results, we show that, for any two fixed constants $$1< c <4$$ 1 < c < 4 and $$c^{\prime }\ge 0$$ c ′ ≥ 0 , Matching Cut is solvable in polynomial time for graphs with large minimum degree $$\delta \ge \frac{1}{c}n-c^{\prime }$$ δ ≥ 1 c n - c ′ .

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