scholarly journals Exponential-time approximation of weighted set cover

2009 ◽  
Vol 109 (16) ◽  
pp. 957-961 ◽  
Author(s):  
Marek Cygan ◽  
Łukasz Kowalik ◽  
Mateusz Wykurz
Keyword(s):  
Set Cover ◽  
Exponential Time ◽  
Time Approximation

Exponential Time Approximation Scheme for TSP

2019 ◽  
pp. 121-128
Author(s):  
Zhixiang Chen ◽  
Qilong Feng ◽  
Bin Fu ◽  
Mugang Lin ◽  
Jianxin Wang
Keyword(s):  
Approximation Scheme ◽  
Exponential Time ◽  
Time Approximation

scholarly journals Chamberlin--Courant Rule with Approval Ballots: Approximating the MaxCover Problem with Bounded Frequencies in FPT Time

2017 ◽  
Vol 60 ◽  
pp. 687-716 ◽  
Author(s):  
Piotr Skowron ◽  
Piotr Faliszewski
Keyword(s):  
Approximation Algorithm ◽  
Exact Algorithms ◽  
The Other ◽  
Winner Determination ◽  
Exponential Time ◽  
Time Approximation ◽  
Polynomial Time Approximation Algorithm ◽  
Voting Rule ◽  
Np Complete ◽  
Better Than

We consider the problem of winner determination under Chamberlin--Courant's multiwinner voting rule with approval utilities. This problem is equivalent to the well-known NP-complete MaxCover problem and, so, the best polynomial-time approximation algorithm for it has approximation ratio 1 - 1/e. We show exponential-time/FPT approximation algorithms that, on one hand, achieve arbitrarily good approximation ratios and, on the other hand, have running times much better than known exact algorithms. We focus on the cases where the voters have to approve of at most/at least a given number of candidates.

scholarly journals New Tools and Connections for Exponential-Time Approximation

Algorithmica ◽  
2018 ◽  
Vol 81 (10) ◽  
pp. 3993-4009 ◽  
Author(s):  
Nikhil Bansal ◽  
Parinya Chalermsook ◽  
Bundit Laekhanukit ◽  
Danupon Nanongkai ◽  
Jesper Nederlof
Keyword(s):  
Exponential Time ◽  
Time Approximation

scholarly journals Combinatorial Dominance Guarantees for Heuristic Algorithms

2007 ◽  
Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽  
Author(s):  
Daniel Berend ◽  
Steven S. Skiena ◽  
Yochai Twitto
Keyword(s):  
Polynomial Time ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Vertex Cover ◽  
Approximation Schemes ◽  
Set Cover ◽  
Time Approximation ◽  
Analysis Techniques ◽  
Wide Range ◽  
International Audience

International audience An $f(n)$ $\textit{dominance bound}$ on a heuristic for some problem is a guarantee that the heuristic always returns a solution not worse than at least $f(n)$ solutions. In this paper, we analyze several heuristics for $\textit{Vertex Cover}$, $\textit{Set Cover}$, and $\textit{Knapsack}$ for dominance bounds. In particular, we show that the well-known $\textit{maximal matching}$ heuristic of $\textit{Vertex Cover}$ provides an excellent dominance bound. We introduce new general analysis techniques which apply to a wide range of problems and heuristics for this measure. Certain general results relating approximation ratio and combinatorial dominance guarantees for optimization problems over subsets are established. We prove certain limitations on the combinatorial dominance guarantees of polynomial-time approximation schemes (PTAS), and give inapproximability results for the problems above.

The Structure and Photochromism of 2,4,4,6-Tetraphenyl-4H-thiopyran

1992 ◽  
Vol 57 (6) ◽  
pp. 1326-1334 ◽  
Author(s):  
Jaroslav Vojtěchovský ◽  
Jindřich Hašek ◽  
Stanislav Nešpůrek ◽  
Mojmír Adamec
Keyword(s):  
Solid State ◽  
Uv Light ◽  
Order Reaction ◽  
Boat Conformation ◽  
X Rays ◽  
Exponential Time ◽  
First Order ◽  
Double Plane ◽  
The Mean ◽  
Independent Molecules

2,4,4,6-Tetraphenyl-4H-thiopyran, C29H22S, orthorhombic, Pna21, a = 17.980(4), b = 6.956(2), c = 34.562(11) Å, V = 4323(2) Å3, Z = 8, Dx = 1.237 g cm-3, F(000) = 1696, λ(CuKα) = 1.54184 A, μ = 1.372 mm-2, T = 294 K. The final R was 0.050 for the unique set of 3103 observed reflections. The central 4H-thiopyran ring forms a boat conformation for both symmetrically independent molecules with average boat angles 4.4(3) and 6.8(3)° at S and C(sp3), respectively. The mean planes of phenyls at the position 2 and 6 are turned from the double plane of 4H-thiopyran by 42.5(5) and 35.8(3)°, respectively. The investigated material undergoes a photochromic change in the solid state after irradiation with UV light or X-rays. The maximum of the new absorption band is situated at 564 nm. The non-exponential time dependence of photochromic bleaching is analysed in terms of a dispersive first-order reaction.

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