On the Size of Systems of Sets Every t of which Have an SDR, with an Application to the Worst-Case Ratio of Heuristics for Packing Problems

1989 ◽  
Vol 2 (1) ◽  
pp. 68-72 ◽  
Author(s):  
C. A. J. Hurkens ◽  
A. Schrijver
Keyword(s):  
Worst Case ◽  
Packing Problems ◽  
Worst Case Ratio

scholarly journals Parallel Machine Scheduling with Batch Delivery to Two Customers

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Xueling Zhong ◽  
Dakui Jiang
Keyword(s):  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Variable Cost ◽  
Worst Case ◽  
Batch Delivery ◽  
Worst Case Ratio ◽  
Processing Facility ◽  
Production And Distribution ◽  
Distribution Cost

In some make-to-order supply chains, the manufacturer needs to process and deliver products for customers at different locations. To coordinate production and distribution operations at the detailed scheduling level, we study a parallel machine scheduling model with batch delivery to two customers by vehicle routing method. In this model, the supply chain consists of a processing facility withmparallel machines and two customers. A set of jobs containingn1jobs from customer 1 andn2jobs from customer 2 are first processed in the processing facility and then delivered to the customers directly without intermediate inventory. The problem is to find a joint schedule of production and distribution such that the tradeoff between maximum arrival time of the jobs and total distribution cost is minimized. The distribution cost of a delivery shipment consists of a fixed charge and a variable cost proportional to the total distance of the route taken by the shipment. We provide polynomial time heuristics with worst-case performance analysis for the problem. Ifm=2and(n1-b)(n2-b)<0, we propose a heuristic with worst-case ratio bound of 3/2, wherebis the capacity of the delivery shipment. Otherwise, the worst-case ratio bound of the heuristic we propose is2-2/(m+1).

SCHEDULING FILE TRANSFERS UNDER PORT AND CHANNEL CONSTRAINTS

1993 ◽  
Vol 04 (02) ◽  
pp. 101-115 ◽  
Author(s):  
SHIN-ICHI NAKANO ◽  
TAKAO NISHIZEKI
Keyword(s):  
Communication Channel ◽  
Edge Coloring ◽  
Large Collection ◽  
File Transfer ◽  
Worst Case ◽  
File Transfers ◽  
Worst Case Ratio ◽  
Efficient Approximation Algorithm ◽  
New Type ◽  
Efficient Approximation

The file transfer scheduling problem was introduced and studied by Coffman, Garey, Johnson and LaPaugh. The problem is to schedule transfers of a large collection of files between various nodes of a network under port constraint so as to minimize the overall finishing time. This paper extends their model to include communication channel constraint in addition to port constraint. We formulate the problem with both port and channel constraints as a new type of edge-coloring of multigraphs, called an fg-edge-coloring, and give an efficient approximation algorithm with absolute worst-case ratio 3/2.

scholarly journals Optimal Computer Crash Performance Precaution

2012 ◽  
Vol Vol. 14 no. 1 (Distributed Computing and...) ◽  
Author(s):  
Efraim Laksman ◽  
Hakan Lennerstad ◽  
Lars Lundberg
Keyword(s):  
Completion Time ◽  
Optimal Allocation ◽  
Parallel Program ◽  
Parallel Computer ◽  
Upper And Lower Bounds ◽  
Worst Case ◽  
Worst Case Ratio ◽  
International Audience ◽  
Computer Crash ◽  
The Cost

Distributed Computing and Networking International audience For a parallel computer system with m identical computers, we study optimal performance precaution for one possible computer crash. We want to calculate the cost of crash precaution in the case of no crash. We thus define a tolerance level r meaning that we only tolerate that the completion time of a parallel program after a crash is at most a factor r + 1 larger than if we use optimal allocation on m - 1 computers. This is an r-dependent restriction of the set of allocations of a program. Then, what is the worst-case ratio of the optimal r-dependent completion time in the case of no crash and the unrestricted optimal completion time of the same parallel program? We denote the maximal ratio of completion times f(r, m) - i.e., the ratio for worst-case programs. In the paper we establish upper and lower bounds of the worst-case cost function f (r, m) and characterize worst-case programs.

GENERALIZED FIRST-FIT ALGORITHMS IN TWO AND THREE DIMENSIONS

1990 ◽  
Vol 01 (02) ◽  
pp. 131-150 ◽  
Author(s):  
KEQIN LI ◽  
KAM-HOI CHENG
Keyword(s):  
Bin Packing ◽  
Three Dimensional ◽  
Packing Problem ◽  
Three Dimensions ◽  
Performance Ratio ◽  
Dimensional Case ◽  
Performance Bound ◽  
Worst Case ◽  
Packing Problems ◽  
The One

We investigate the two and three dimensional bin packing problems, i.e., packing a list of rectangles (boxes) into unit square (cube) bins so that the number of bins used is a minimum. A simple on-line packing algorithm for the one dimensional bin packing problem, the First-Fit algorithm, is generalized to two and three dimensions. We first give an algorithm for the two dimensional case and show that its asymptotic worse case performance ratio is [Formula: see text]. The algorithm is then generalized to the three dimensional case and its performance ratio [Formula: see text]. The second algorithm takes a parameter and we prove that by choosing the parameter properly, it has an asymptotic worst case performance bound which can be made as close as desired to 1.72=2.89 and 1.73=4.913 respectively in two and three dimensions.

scholarly journals Theoretical Expectation versus Practical Performance of Jackson’s Heuristic

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Nodari Vakhania ◽  
Dante Pérez ◽  
Lester Carballo
Keyword(s):  
Problem Instance ◽  
Due Dates ◽  
Solution Quality ◽  
Worst Case ◽  
Release Times ◽  
Worst Case Ratio ◽  
Practical Performance ◽  
Approximation Heuristic ◽  
Relationship Of

A basic 2-approximation heuristic was suggested by Jackson in early 50s last century for scheduling jobs with release times and due dates to minimize the maximum job lateness. The theoretical worst-case bound of 2 helps a little in practice, when the solution quality is important. The quality of the solution delivered by Jackson’s heuristic is closely related to the maximum job processing timepmax  that occurs in a given problem instance and with the resultant interference with other jobs that such a long job may cause. We use the relationship ofpmaxwith the optimal objective value to obtain more accurate approximation ratio, which may drastically outperform the earlier known worst-case ratio of 2. This is proved, in practice, by our computational experiments.

A Note on "An On-Line Scheduling Heuristic with Better Worst Case Ratio than Graham's List Scheduling"

1997 ◽  
Vol 26 (3) ◽  
pp. 870-872 ◽  
Author(s):  
R. Chandrasekaran ◽  
Bo Chen ◽  
Gábor Galambos ◽  
P. R. Narayanan ◽  
André Van Vliet ◽  
...  
Keyword(s):  
List Scheduling ◽  
Worst Case ◽  
Worst Case Ratio ◽  
On Line ◽  
Scheduling Heuristic

SINGLE-MACHINE SCHEDULING WITH PROPORTIONALLY DETERIORATING JOBS SUBJECT TO AVAILABILITY CONSTRAINTS

2012 ◽  
Vol 29 (04) ◽  
pp. 1250019 ◽  
Author(s):  
SHISHENG LI ◽  
BAOQIANG FAN
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Deteriorating Jobs ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Single Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Worst Case ◽  
Availability Constraints ◽  
Worst Case Ratio

We address the nonresumable version of the scheduling problem with proportionally deteriorating jobs on a single machine subject to availability constraints. The objective is to minimize the total weighted completion time. We show that there exists no polynomial-time algorithm with a constant worst-case ratio for the problem with two nonavailability intervals unless [Formula: see text]. Furthermore, we propose a pseudo-polynomial-time algorithm and a fully polynomial-time approximation scheme for the problem with a single nonavailability interval.

A Note on Limited Preemption

1998 ◽  
Vol 08 (01) ◽  
pp. 3-6 ◽  
Author(s):  
E. G. Coffman ◽  
S. Even
Keyword(s):  
Worst Case ◽  
Worst Case Ratio

The concept of limited preemption is introduced, where a task can be preempted, but can not be moved from one processor to another. For optimal makespan scheduling on two processors, the worst case ratio of the makespan with no preemption to that with limited preemption is shown to be 4/3, while the worst case ratio of the makespan with limited preemption to that with unlimited preemption is 4/3 as well.

EFFECTS OF SYMMETRY ON GLOBALIZING SEPARATED MONOPOLIES TO A NASH-COURNOT OLIGOPOLY

2012 ◽  
Vol 14 (02) ◽  
pp. 1250009 ◽  
Author(s):  
HISAO KAMEDA ◽  
TAKASHI UI
Keyword(s):  
Consumer Surplus ◽  
The Other ◽  
Production Functions ◽  
Noncooperative Game ◽  
Cournot Oligopoly ◽  
Worst Case ◽  
Oligopolistic Market ◽  
Complete Symmetry ◽  
Worst Case Ratio ◽  
Linear Demand

The effects of uniting separated markets, each monopolized by a producer, into a globalized oligopolistic market, which is regarded as a noncooperative game, or as a Cournot oligopoly game, are investigated. The cases where such globalization degrades the profits of all producers coincidently, are examined. Linear demand and production functions are considered. It is shown that in complete symmetry, the degree of such coincident profit degradation is strongest (the worst-case ratio), where the degree means the most modest ratio of the profit degradation among all producers. The system is in complete symmetry when the values of parameters describing all producers and markets are identical. On the other hand, in producer symmetry, the degree of coincident consumer surplus improvement is highest (the best-case ratio), where the degree means the lowest of the ratios of consumer surplus improvement among all (previously separated) markets. The system is in producer symmetry when the values of parameters describing all producers are identical.

scholarly journals Two Parallel Machines Scheduling with Two-Vehicle Job Delivery to Minimize Makespan

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Lisi Cao ◽  
Jianhong Hao ◽  
Dakui Jiang
Keyword(s):  
Parallel Machines ◽  
Parallel Machine Scheduling ◽  
Performance Ratio ◽  
Identical Parallel Machines ◽  
Worst Case ◽  
Worst Case Ratio ◽  
Parallel Machines Scheduling ◽  
Np Hard Problem ◽  
Worst Case Performance Ratio ◽  
Job Delivery

A problem of parallel machine scheduling with coordinated job deliveries is handled to minimize the makespan. Different jobs call for dissimilar sizes of storing space in the process of transportation. A range of jobs of one customer in the problem have priority to be processed on two identical parallel machines without preemption and then delivered to the customer by two vehicles in batches. For this NP-hard problem, we first prove that it is impossible to have a polynomial heuristic with a worst-case performance ratio bound less than 2 unless P = NP. Thereafter, we develop a polynomial heuristic for this problem, the worst-case ratio of which is bounded by 2.

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