scholarly journals A Polynomial-Time Algorithm for Computing Shortest Paths of Bounded Curvature Amidst Moderate Obstacles

2003 ◽  
Vol 13 (03) ◽  
pp. 189-229 ◽  
Author(s):  
Jean-Daniel Boissonnat ◽  
Sylvain Lazard
Keyword(s):  
Polynomial Time ◽  
Shortest Paths ◽  
Exact Algorithm ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Radius Of Curvature ◽  
Bounded Curvature

In this paper, we consider the problem of computing shortest paths of bounded curvature amidst obstacles in the plane. More precisely, given two prescribed initial and final configurations (specifying the location and the direction of travel) and a set of obstacles in the plane, we want to compute a shortest C1 path joining those two configurations, avoiding the obstacles, and with the further constraint that, on each C2 piece, the radius of curvature is at least 1. In this paper, we consider the case of moderate obstacles and present a polynomial-time exact algorithm to solve this problem.

A Pseudo-Polynomial Time Algorithm for a Special Multiobjective Order Picking Problem

2015 ◽  
Vol 14 (05) ◽  
pp. 1111-1128 ◽  
Author(s):  
Özgür Özpeynirci ◽  
Cansu Kandemir
Keyword(s):  
Polynomial Time ◽  
Exact Algorithm ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Order Picking ◽  
Special Design ◽  
Nondominated Points ◽  
Polynomially Solvable ◽  
Nondominated Point ◽  
Special Case

In this study, we work on the order picking problem (OPP) in a specially designed warehouse with a single picker. Ratliff and Rosenthal [Operations Research31(3) (1983) 507–521] show that the special design of the warehouse and use of one picker lead to a polynomially solvable case. We address the multiobjective version of this special case and investigate the properties of the nondominated points. We develop an exact algorithm that finds any nondominated point and present an illustrative example. Finally we conduct a computational test and report the results.

scholarly journals An efficient exact algorithm for computing all pairwise distances between reconciliations in the duplication-transfer-loss model

2019 ◽  
Vol 20 (S20) ◽  
Author(s):  
Santi Santichaivekin ◽  
Ross Mawhorter ◽  
Ran Libeskind-Hadas
Keyword(s):  
Polynomial Time ◽  
Maximum Parsimony ◽  
Exact Algorithm ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Distance Metrics ◽  
Worst Case ◽  
Loss Model ◽  
Biological Dataset ◽  
Wide Range

Abstract Background Maximum parsimony reconciliation in the duplication-transfer-loss model is widely used in studying the evolutionary histories of genes and species and in studying coevolution of parasites and their hosts and pairs of symbionts. While efficient algorithms are known for finding maximum parsimony reconciliations, the number of reconciliations can grow exponentially in the size of the trees. An understanding of the space of maximum parsimony reconciliations is necessary to determine whether a single reconciliation can adequately represent the space or whether multiple representative reconciliations are needed. Results We show that for any instance of the reconciliation problem, the distribution of pairwise distances can be computed exactly by an efficient polynomial-time algorithm with respect to several different distance metrics. We describe the algorithm, analyze its asymptotic worst-case running time, and demonstrate its utility and viability on a large biological dataset. Conclusions This result provides new insights into the structure of the space of maximum parsimony reconciliations. These insights are likely to be useful in the wide range of applications that employ reconciliation methods.

Learning Importance of Preferences

10.29007/v68w ◽  
2018 ◽  
Author(s):  
Ying Zhu ◽  
Mirek Truszczynski
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Scoring Rules ◽  
Np Hard ◽  
Individual Preferences

We study the problem of learning the importance of preferences in preference profiles in two important cases: when individual preferences are aggregated by the ranked Pareto rule, and when they are aggregated by positional scoring rules. For the ranked Pareto rule, we provide a polynomial-time algorithm that finds a ranking of preferences such that the ranked profile correctly decides all the examples, whenever such a ranking exists. We also show that the problem to learn a ranking maximizing the number of correctly decided examples (also under the ranked Pareto rule) is NP-hard. We obtain similar results for the case of weighted profiles when positional scoring rules are used for aggregation.

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