Polynomial time algorithms for two special classes of the proportionate multiprocessor open shop

2010 ◽  
Vol 201 (3) ◽  
pp. 720-728 ◽  
Author(s):  
Marie E. Matta ◽  
Salah E. Elmaghraby
Keyword(s):  
Polynomial Time ◽  
Open Shop ◽  
Polynomial Time Algorithms ◽  
Multiprocessor Open Shop ◽  
Special Classes

SHORTEST DESCENDING PATHS: TOWARDS AN EXACT ALGORITHM

2011 ◽  
Vol 21 (04) ◽  
pp. 431-466 ◽  
Author(s):  
MUSTAQ AHMED ◽  
ANNA LUBIW
Keyword(s):  
Approximation Algorithms ◽  
Polynomial Time ◽  
Shortest Path ◽  
Exact Algorithm ◽  
Full Characterization ◽  
Polynomial Time Algorithms ◽  
Straight Line ◽  
Bend Angles ◽  
Special Classes

A path from s to t on a polyhedral terrain is descending if the height of a point p never increases while we move p along the path from s to t. Although a shortest path on a terrain unfolds to a straight line, a shortest descending path (SDP) does not. We give a full characterization of the bend angles of an SDP, showing that they follow a generalized form of Snell's law of refraction of light. The complexity of finding SDPs is open—only approximation algorithms are known. We reduce the SDP problem to the problem of finding an SDP through a given sequence of faces. We give polynomial time algorithms for SDPs on two special classes of terrains, but argue that the general case will be difficult.

Multiprocessor open shop problem: literature review and future directions

2020 ◽  
Vol 40 (2) ◽  
pp. 547-569
Author(s):  
Zeynep Adak ◽  
Mahmure Övül Arıoğlu Akan ◽  
Serol Bulkan
Keyword(s):  
Literature Review ◽  
Open Shop ◽  
Future Directions ◽  
Open Shop Problem ◽  
Multiprocessor Open Shop

scholarly journals An Overview of Algorithms for Network Survivability

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
F. A. Kuipers
Keyword(s):  
Polynomial Time ◽  
Network Connectivity ◽  
Network Survivability ◽  
Disjoint Paths ◽  
Polynomial Time Algorithms ◽  
Concise Overview ◽  
Main Components

Network survivability—the ability to maintain operation when one or a few network components fail—is indispensable for present-day networks. In this paper, we characterize three main components in establishing network survivability for an existing network, namely, (1) determining network connectivity, (2) augmenting the network, and (3) finding disjoint paths. We present a concise overview of network survivability algorithms, where we focus on presenting a few polynomial-time algorithms that could be implemented by practitioners and give references to more involved algorithms.

scholarly journals Reconstruction of score sets

2014 ◽  
Vol 6 (2) ◽  
pp. 210-229
Author(s):  
Antal Iványi
Keyword(s):  
Polynomial Time ◽  
Constructive Proof ◽  
Construction Algorithm ◽  
Polynomial Time Algorithms ◽  
General Polynomial ◽  
Degree Set ◽  
New Algorithms

Abstract The score set of a tournament is defined as the set of its different outdegrees. In 1978 Reid [15] published the conjecture that for any set of nonnegative integers D there exists a tournament T whose degree set is D. Reid proved the conjecture for tournaments containing n = 1, 2, and 3 vertices. In 1986 Hager [4] published a constructive proof of the conjecture for n = 4 and 5 vertices. In 1989 Yao [18] presented an arithmetical proof of the conjecture, but general polynomial construction algorithm is not known. In [6] we described polynomial time algorithms which reconstruct the score sets containing only elements less than 7. In [5] we improved this bound to 9. In this paper we present and analyze new algorithms Hole-Map, Hole-Pairs, Hole-Max, Hole-Shift, Fill-All, Prefix-Deletion, and using them improve the above bound to 12, giving a constructive partial proof of Reid’s conjecture.

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