exponential time
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2021 ◽  
Author(s):  
Katie Steele

According to Craig Callender (2020), the “received view” across the social sciences is that, when it comes to time and preference, only exponential time discounting is rational. Callender argues that this view is false, even pernicious. Here I endorse what I take to be Callender’s main argument, but only insofar as the received view is understood in a particular way. I go on to propose a different way of understanding the received view that makes it true. In short: When time discounting is suitably conceived, the exponential form of the discounting function is indeed uniquely rational.


Algorithmica ◽  
2021 ◽  
Author(s):  
Julian Dörfler ◽  
Marc Roth ◽  
Johannes Schmitt ◽  
Philip Wellnitz

AbstractWe study the problem $$\#\textsc {IndSub}(\varPhi )$$ # I N D S U B ( Φ ) of counting all induced subgraphs of size k in a graph G that satisfy the property $$\varPhi $$ Φ . It is shown that, given any graph property $$\varPhi $$ Φ that distinguishes independent sets from bicliques, $$\#\textsc {IndSub}(\varPhi )$$ # I N D S U B ( Φ ) is hard for the class $$\#\mathsf {W[1]}$$ # W [ 1 ] , i.e., the parameterized counting equivalent of $${{\mathsf {N}}}{{\mathsf {P}}}$$ N P . Under additional suitable density conditions on $$\varPhi $$ Φ , satisfied e.g. by non-trivial monotone properties on bipartite graphs, we strengthen $$\#\mathsf {W[1]}$$ # W [ 1 ] -hardness by establishing that $$\#\textsc {IndSub}(\varPhi )$$ # I N D S U B ( Φ ) cannot be solved in time $$f(k)\cdot n^{o(k)}$$ f ( k ) · n o ( k ) for any computable function f, unless the Exponential Time Hypothesis fails. Finally, we observe that our results remain true even if the input graph G is restricted to be bipartite and counting is done modulo a fixed prime.


Algorithmica ◽  
2021 ◽  
Author(s):  
Lars Jaffke ◽  
Paloma T. Lima ◽  
Geevarghese Philip

AbstractA clique coloring of a graph is an assignment of colors to its vertices such that no maximal clique is monochromatic. We initiate the study of structural parameterizations of the Clique Coloring problem which asks whether a given graph has a clique coloring with q colors. For fixed $$q \ge 2$$ q ≥ 2 , we give an $$\mathscr {O}^{\star }(q^{{\mathsf {tw}}})$$ O ⋆ ( q tw ) -time algorithm when the input graph is given together with one of its tree decompositions of width $${\mathsf {tw}} $$ tw . We complement this result with a matching lower bound under the Strong Exponential Time Hypothesis. We furthermore show that (when the number of colors is unbounded) Clique Coloring is $$\mathsf {XP}$$ XP parameterized by clique-width.


2021 ◽  
Vol 46 (3) ◽  
pp. 1-39
Author(s):  
Mahmoud Abo Khamis ◽  
Phokion G. Kolaitis ◽  
Hung Q. Ngo ◽  
Dan Suciu

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.


2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Noufe H. Aljahdaly ◽  
H. A. Ashi

This paper addresses a first numerical simulation to the nonlinear dynamic system of equations that describes the prey-predator model at the predator mating period. Some male species accompany the females during the mating period. In this case, both male and female feed on the same prey. The presented work shows the numerical solution for this specific case of the prey-predator mathematical model via an exponential time differencing method. In addition, the paper provides the biological implication of the solution.


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