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 Inapproximability and Polynomial-Time Approximation Algorithm for UET Tasks on Structured Processor Networks

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
M. Bouznif ◽  
R. Giroudeau
Keyword(s):  
Approximation Algorithm ◽  
Large Class ◽  
Bipartite Graph ◽  
Polynomial Time ◽  
Performance Guarantee ◽  
Makespan Minimization ◽  
Time Approximation ◽  
Polynomial Time Approximation Algorithm ◽  
Precedence Graph ◽  
Polynomial Time Approximation

We investigate complexity and approximation results on a processor networks where the communication delay depends on the distance between the processors performing tasks. We then prove that there is no heuristic with a performance guarantee smaller than 4/3 for makespan minimization for precedence graph on a large class of processor networks like hypercube, grid, torus, and so forth, with a fixed diameter . We extend complexity results when the precedence graph is a bipartite graph. We also design an efficient polynomial-time -approximation algorithm for the makespan minimization on processor networks with diameter .

COMPUTING THE RUPTURE DEGREE IN COMPOSITE GRAPHS

2010 ◽  
Vol 21 (03) ◽  
pp. 311-319 ◽  
Author(s):  
AYSUN AYTAC ◽  
ZEYNEP NIHAN ODABAS
Keyword(s):  
Complete Graph ◽  
Connected Graph ◽  
The Other ◽  
Trade Off ◽  
Number Of Components ◽  
Np Complete ◽  
Work Done ◽  
Better Than

The rupture degree of an incomplete connected graph G is defined by [Formula: see text] where w(G - S) is the number of components of G - S and m(G - S) is the order of a largest component of G - S. For the complete graph Kn, rupture degree is defined as 1 - n. This parameter can be used to measure the vulnerability of a graph. Rupture degree can reflect the vulnerability of graphs better than or independent of the other parameters. To some extent, it represents a trade-off between the amount of work done to damage the network and how badly the network is damaged. Computing the rupture degree of a graph is NP-complete. In this paper, we give formulas for the rupture degree of composition of some special graphs and we consider the relationships between the rupture degree and other vulnerability parameters.

scholarly journals A Polynomial-Time Approximation Algorithm for a Geometric Dispersion Problem

2006 ◽  
pp. 166-175
Author(s):  
Marc Benkert ◽  
Joachim Gudmundsson ◽  
Christian Knauer ◽  
Esther Moet ◽  
René van Oostrum ◽  
...  
Keyword(s):  
Approximation Algorithm ◽  
Polynomial Time ◽  
Time Approximation ◽  
Polynomial Time Approximation Algorithm ◽  
Dispersion Problem ◽  
Polynomial Time Approximation

APPROXIMATION ALGORITHMS FOR SCHEDULING MALLEABLE TASKS UNDER PRECEDENCE CONSTRAINTS

2002 ◽  
Vol 13 (04) ◽  
pp. 613-627 ◽  
Author(s):  
RENAUD LEPÈRE ◽  
DENIS TRYSTRAM ◽  
GERHARD J. WOEGINGER
Keyword(s):  
Approximation Algorithms ◽  
Approximation Algorithm ◽  
Polynomial Time ◽  
Precedence Constraints ◽  
Performance Guarantee ◽  
Time Approximation ◽  
Polynomial Time Approximation Algorithm ◽  
Special Cases ◽  
Special Case ◽  
Polynomial Time Approximation

This work presents approximation algorithms for scheduling the tasks of a parallel application that are subject to precedence constraints. The considered tasks are malleable which means that they may be executed on a varying number of processors in parallel. The considered objective criterion is the makespan, i.e., the largest task completion time. We demonstrate a close relationship between this scheduling problem and one of its subproblems, the allotment problem. By exploiting this relationship, we design a polynomial time approximation algorithm with performance guarantee arbitrarily close to [Formula: see text] for the special case of series parallel precedence constraints and for the special case of precedence constraints of bounded width. These special cases cover the important situation of tree structured precedence constraints. For arbitrary precedence constraints, we give a polynomial time approximation algorithm with performance guarantee [Formula: see text].

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