Optimal Polynomial Time Algorithm for Restoring Multicast Cloud Services

2016 ◽  
Vol 20 (8) ◽  
pp. 1543-1546 ◽  
Author(s):  
Sara Ayoubi ◽  
Chadi Assi ◽  
Lata Narayanan ◽  
Khaled Shaban
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Cloud Services ◽  
Optimal Polynomial

THE PROBLEM OF PARTITIONING WITH DUPLICATIONS AND ITS APPLICATIONS

1994 ◽  
Vol 03 (03) ◽  
pp. 395-405
Author(s):  
J. HARALAMBIDES ◽  
S. TRAGOUDAS
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Vlsi Layout ◽  
Optimal Polynomial ◽  
Partitioning Problem ◽  
Polynomially Solvable ◽  
The Cost ◽  
Parallel Graph ◽  
Special Case

The problem of partitioning the elements of a graph G=(V, E) into two equal size sets A and B that share at most d elements such that the total number of edges (u, v), u∈A−B, v∈B−A is minimized, arises in the areas of Hypermedia Organization, Network Integrity, and VLSI Layout. We formulate the problem in terms of element duplication, where each element c∈A∩B is substituted by two copies c′∈A and c″∈B As a result, edges incident to c′ or c″ need not count in the cost of the partition. We show that this partitioning problem is NP-hard in general, and we present a solution which utilizes an optimal polynomial time algorithm for the special case where G is a series-parallel graph. We also discuss special other cases where the partitioning problem or variations are polynomially solvable.

Supply Chain Scheduling on a Single Machine with Availability Constraint

2013 ◽  
Vol 380-384 ◽  
pp. 4736-4739 ◽  
Author(s):  
Jing Fan
Keyword(s):  
Supply Chain ◽  
Polynomial Time ◽  
Single Machine ◽  
Arrival Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Supply Chain Scheduling ◽  
Delivery Cost ◽  
Availability Constraint ◽  
Optimal Polynomial

In the actual industrial engineering, the machine may be checked to ensure that they can work efficiently. Thus, the machine has an unavailable interval so that the job could be interrupted. When the machine becomes available again, the job can be resumed processing. When the job is completed, it can be delivered in batches to one customer by vehicles with capacity constraint. Our goal is to minimize the sum of arrival time of batches and the total delivery cost. We develop an optimal polynomial time algorithm and give an instance to verify the algorithm.

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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