scholarly journals Efficient Approximation Schemes for Stochastic Probing and Prophet Problems

2021 ◽  
Author(s):  
Danny Segev ◽  
Sahil Singla
Keyword(s):  
Approximation Schemes ◽  
Efficient Approximation

EFFICIENT APPROXIMATION ALGORITHMS FOR TWO-LABEL POINT LABELING

2001 ◽  
Vol 11 (04) ◽  
pp. 455-464 ◽  
Author(s):  
BINHAI ZHU ◽  
C. K. POON
Keyword(s):  
Approximation Algorithms ◽  
Mild Condition ◽  
Distinct Point ◽  
Constant Factor ◽  
Approximation Schemes ◽  
Uniform Size ◽  
Map Labeling ◽  
Label Point ◽  
Efficient Approximation

In this paper we propose and study two practical variations of the map labeling problem: Given a set S of n distinct (point) sites in the plane, label each site with: (1) a pair of non-intersecting squares of maximum possible size, (2) a pair of non-intersecting circles of maximum possible size (all the squares and circles are topologically open and are of uniform size). Almost nothing has been done before in this aspect, i.e., multi-label map labeling. We obtain constant-factor approximation algorithms for these problems. We also study bicriteria approximation schemes for these problems under a mild condition.

scholarly journals APPLICATION PLACEMENT ON A CLUSTER OF SERVERS

2007 ◽  
Vol 18 (05) ◽  
pp. 1023-1041 ◽  
Author(s):  
BHUVAN URGAONKAR ◽  
ARNOLD L. ROSENBERG ◽  
PRASHANT SHENOY
Keyword(s):  
Approximation Algorithms ◽  
Resource Availability ◽  
Distributed Applications ◽  
Approximation Schemes ◽  
Business Relationship ◽  
Placement Problem ◽  
Time Approximation ◽  
Resource Requirements ◽  
Application Placement ◽  
Efficient Approximation

The APPLICATION PLACEMENT PROBLEM (APP, for short) arises in hosting platforms: clusters of servers that are used for hosting large, distributed applications such as Internet services. Hosting platforms imply a business relationship between an entity called the platform provider and a number of entities called the application providers. The latter pay the former for the resources on the hosting platform, in return for which, the former provides guarantees on resource availability for the applications. This implies that a hosting platform should host only applications for which it has sufficient resources. The objective of the APP is to maximize the number of applications that can be hosted on the platform while satisfying their resource requirements. The complexity of the APP is studied here, with the following results. The general APP is NP-hard; indeed, even restricted versions of the APP may not admit polynomial-time approximation schemes. However, several significant variants of the online version of the APP admit efficient approximation algorithms.

scholarly journals Near-linear Time Approximation Schemes for Clustering in Doubling Metrics

2021 ◽  
Vol 68 (6) ◽  
pp. 1-34
Author(s):  
Vincent Cohen-Addad ◽  
Andreas Emil Feldmann ◽  
David Saulpic
Keyword(s):  
Facility Location ◽  
Metric Spaces ◽  
State Of The Art ◽  
Linear Time ◽  
The State ◽  
Approximation Schemes ◽  
Time Approximation ◽  
Prize Collecting ◽  
Doubling Metrics ◽  
Efficient Approximation

We consider the classic Facility Location, k -Median, and k -Means problems in metric spaces of doubling dimension d . We give nearly linear-time approximation schemes for each problem. The complexity of our algorithms is Õ(2 (1/ε) O(d2) n) , making a significant improvement over the state-of-the-art algorithms that run in time n (d/ε) O(d) . Moreover, we show how to extend the techniques used to get the first efficient approximation schemes for the problems of prize-collecting k -Median and k -Means and efficient bicriteria approximation schemes for k -Median with outliers, k -Means with outliers and k -Center.

scholarly journals Approximation Schemes for Two Non-Linear Knapsack Problems and Their Applications in Alternating Current Electric Systems

2017 ◽  
Vol 33 (2) ◽  
pp. 165-179
Author(s):  
Thanh Nguyen
Keyword(s):  
Objective Function ◽  
Polynomial Time ◽  
Alternating Current ◽  
Knapsack Problems ◽  
Approximation Schemes ◽  
Programming Approach ◽  
Approximation Factor ◽  
Electrical Systems ◽  
Non Linear ◽  
Efficient Approximation

The purpose of this paper is to study the approximability of two non-linear Knapsack problems, which are motivated by important applications in alternating current electrical systems. The first problem is to maximize a nonnegative linear objective function subject to a quadratic constraint, whilst the second problem is a dual version of the first one, where an objective function is minimized. Both problems are $\np$-hard since they generalize the unbounded Knapsack problem, and it is unlikely to obtain polynomial-time algorithms for them, unless $\p=\np$. It is therefore of great interest to know whether or not there exist efficient approximation algorithms which can return an approximate solution in polynomial time with a reasonable approximation factor. Our contribution of this paper is to present polynomial-time approximation schemes (PTASs) and this is the best possible result one can hope for the studied problems. Our technique is based on the linear-programming approach which seems to be more simple and efficient than the previous one.

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