scholarly journals Polynomial-time algorithms for scheduling problem for coupled-tasks in presence of treatment tasks

2010 ◽  
Vol 36 ◽  
pp. 647-654 ◽  
Author(s):  
G. Simonin ◽  
R. Giroudeau ◽  
J.-C. König
Keyword(s):  
Polynomial Time ◽  
Scheduling Problem ◽  
Polynomial Time Algorithms ◽  
Coupled Tasks

scholarly journals Cable tree wiring - benchmarking solvers on a real-world scheduling problem with a variety of precedence constraints

Constraints ◽  
2021 ◽  
Author(s):  
Jana Koehler ◽  
Josef Bürgler ◽  
Urs Fontana ◽  
Etienne Fux ◽  
Florian Herzog ◽  
...  
Keyword(s):  
State Of The Art ◽  
Precedence Constraints ◽  
Traveling Salesman ◽  
Mixed Integer ◽  
Automated Manufacturing ◽  
Scheduling Problem ◽  
Tasks Scheduling ◽  
Optimization Modulo Theories ◽  
Coupled Tasks ◽  
Np Hardness

AbstractCable trees are used in industrial products to transmit energy and information between different product parts. To this date, they are mostly assembled by humans and only few automated manufacturing solutions exist using complex robotic machines. For these machines, the wiring plan has to be translated into a wiring sequence of cable plugging operations to be followed by the machine. In this paper, we study and formalize the problem of deriving the optimal wiring sequence for a given layout of a cable tree. We summarize our investigations to model this cable tree wiring problem (CTW). as a traveling salesman problem with atomic, soft atomic, and disjunctive precedence constraints as well as tour-dependent edge costs such that it can be solved by state-of-the-art constraint programming (CP), Optimization Modulo Theories (OMT), and mixed-integer programming (MIP). solvers. It is further shown, how the CTW problem can be viewed as a soft version of the coupled tasks scheduling problem. We discuss various modeling variants for the problem, prove its NP-hardness, and empirically compare CP, OMT, and MIP solvers on a benchmark set of 278 instances. The complete benchmark set with all models and instance data is available on github and was included in the MiniZinc challenge 2020.

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.

scholarly journals The Complexity Landscape of Resource-Constrained Scheduling

2020 ◽  
Author(s):  
Robert Ganian ◽  
Thekla Hamm ◽  
Guillaume Mescoff
Keyword(s):  
Artificial Intelligence ◽  
Polynomial Time ◽  
Project Scheduling ◽  
Scheduling Problem ◽  
Comprehensive Understanding ◽  
Resource Constrained ◽  
Special Cases ◽  
Project Scheduling Problem ◽  
Np Complete ◽  
New Algorithms

The Resource-Constrained Project Scheduling Problem (RCPSP) and its extension via activity modes (MRCPSP) are well-established scheduling frameworks that have found numerous applications in a broad range of settings related to artificial intelligence. Unsurprisingly, the problem of finding a suitable schedule in these frameworks is known to be NP-complete; however, aside from a few results for special cases, we have lacked an in-depth and comprehensive understanding of the complexity of the problems from the viewpoint of natural restrictions of the considered instances. In the first part of our paper, we develop new algorithms and give hardness-proofs in order to obtain a detailed complexity map of (M)RCPSP that settles the complexity of all 1024 considered variants of the problem defined in terms of explicit restrictions of natural parameters of instances. In the second part, we turn to implicit structural restrictions defined in terms of the complexity of interactions between individual activities. In particular, we show that if the treewidth of a graph which captures such interactions is bounded by a constant, then we can solve MRCPSP in polynomial time.

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