scholarly journals On a Greedy Approach for Genome Scaffolding

2021 ◽  
Author(s):  
Tom Davot ◽  
Annie Chateau ◽  
Rohan Fossé ◽  
Rodolphe Giroudeau ◽  
Mathias Weller
Keyword(s):  
Approximation Algorithm ◽  
Relative Position ◽  
Complete Graphs ◽  
Assembly Process ◽  
Contig Assembly ◽  
Time Approximation ◽  
Genome Scaffolding ◽  
Polynomial Time Approximation Algorithm ◽  
Cover Problem ◽  
Position And Orientation

Abstract Background: Scaffolding is a bioinformatics problem aimed at completing the contig assembly process by determining the relative position and orientation of these contigs. It can be seen as a paths and cycles cover problem of a particular graph called the “scaffold graph”.Results: We provide some NP-hardness and inapproximability results on this problem. We also adapt a greedy approximation algorithm on complete graphs so that it works on a special class aiming to be close to real instances. The described algorithm is the first polynomial-time approximation algorithm designed for this problem on non-complete graphs.Conclusion: Tests on a set of simulated instances show that our algorithm provides better results than the version on complete graphs.

scholarly journals Tight Approximation for Proportional Approval Voting

2020 ◽  
Author(s):  
Szymon Dudycz ◽  
Pasin Manurangsi ◽  
Jan Marcinkowski ◽  
Krzysztof Sornat
Keyword(s):  
Lower Bound ◽  
Approximation Algorithm ◽  
Approval Voting ◽  
Voting Rules ◽  
Natural Class ◽  
Total Utility ◽  
Time Approximation ◽  
Polynomial Time Approximation Algorithm ◽  
Dominant Weights ◽  
Cover Problem

In approval-based multiwinner elections, we are given a set of voters, a set of candidates, and, for each voter, a set of candidates approved by the voter. The goal is to find a committee of size k that maximizes the total utility of the voters. In this paper, we study approximability of Thiele rules, which are known to be NP-hard to solve exactly. We provide a tight polynomial time approximation algorithm for a natural class of geometrically dominant weights that includes such voting rules as Proportional Approval Voting or p-Geometric. The algorithm is relatively simple: first we solve a linear program and then we round a solution by employing a framework called pipage rounding due to Ageev and Sviridenko (2004) and Calinescu et al. (2011). We provide a matching lower bound via a reduction from the Label Cover problem. Moreover, assuming a conjecture called Gap-ETH, we show that better approximation ratio cannot be obtained even in time f(k)*pow(n,o(k)).

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 .

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.

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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