Approximation algorithms for the m-dimensional 0–1 knapsack problem: Worst-case and probabilistic analyses

1984 ◽  
Vol 15 (1) ◽  
pp. 100-109 ◽  
Author(s):  
A.M. Frieze ◽  
M.R.B. Clarke
Keyword(s):  
Approximation Algorithms ◽  
Knapsack Problem ◽  
Worst Case

APPROXIMATION ALGORITHMS FOR A VARIANT OF DISCRETE PIERCING SET PROBLEM FOR UNIT DISKS

2013 ◽  
Vol 23 (06) ◽  
pp. 461-477 ◽  
Author(s):  
MINATI DE ◽  
GAUTAM K. DAS ◽  
PAZ CARMI ◽  
SUBHAS C. NANDY
Keyword(s):  
Approximation Algorithms ◽  
Simple Algorithm ◽  
Constant Factor ◽  
Performance Ratio ◽  
Approximation Result ◽  
Worst Case ◽  
Approximation Factor ◽  
Minimum Number ◽  
Unit Disks ◽  
Set Of Points

In this paper, we consider constant factor approximation algorithms for a variant of the discrete piercing set problem for unit disks. Here a set of points P is given; the objective is to choose minimum number of points in P to pierce the unit disks centered at all the points in P. We first propose a very simple algorithm that produces 12-approximation result in O(n log n) time. Next, we improve the approximation factor to 4 and then to 3. The worst case running time of these algorithms are O(n8 log n) and O(n15 log n) respectively. Apart from the space required for storing the input, the extra work-space requirement for each of these algorithms is O(1). Finally, we propose a PTAS for the same problem. Given a positive integer k, it can produce a solution with performance ratio [Formula: see text] in nO(k) time.

WORST-CASE PERFORMANCE EVALUATION ON MULTIPROCESSOR TASK SCHEDULING WITH RESOURCE AUGMENTATION

2011 ◽  
Vol 22 (04) ◽  
pp. 971-982
Author(s):  
DESHI YE ◽  
QINMING HE
Keyword(s):  
Approximation Algorithms ◽  
Task Scheduling ◽  
Processing Time ◽  
Time Algorithm ◽  
Resource Augmentation ◽  
Worst Case ◽  
Multiprocessor Task Scheduling ◽  
Lpt Algorithm ◽  
On Line ◽  
The Greedy Algorithm

We study the worst-case performance of approximation algorithms for the problem of multiprocessor task scheduling on m identical processors with resource augmentation, whose objective is to minimize the makespan. In this case, the approximation algorithms are given k (k ≥ 0) extra processors than the optimal off-line algorithm. For on-line algorithms, the Greedy algorithm and shelf algorithms are studied. For off-line algorithm, we consider the LPT (longest processing time) algorithm. Particularly, we prove that the schedule produced by the LPT algorithm is no longer than the optimal off-line algorithm if and only if k ≥ m - 2.

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