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 A Unified Model and Algorithms for Temporal Map Labeling

Algorithmica ◽  
2020 ◽  
Vol 82 (10) ◽  
pp. 2709-2736
Author(s):  
Andreas Gemsa ◽  
Benjamin Niedermann ◽  
Martin Nöllenburg
Keyword(s):  
Approximation Algorithms ◽  
Traffic Control ◽  
Constant Factor ◽  
Maximization Problem ◽  
Fixed Position ◽  
Time Intervals ◽  
Map Labeling ◽  
Polynomial Time Algorithms ◽  
Dynamic Map ◽  
Flexible Model

Abstract We consider map labeling for the case that a map undergoes a sequence of operations such as rotation, zoom and translation over a specified time span. We unify and generalize several previous models for dynamic map labeling into one versatile and flexible model. In contrast to previous research, we completely abstract from the particular operations and express the labeling problem as a set of time intervals representing the labels’ presences, activities and conflicts. One of the model’s strength is manifested in its simplicity and broad range of applications. In particular, it supports label selection both for map features with fixed position as well as for moving entities (e.g., for tracking vehicles in logistics or air traffic control). We study the active range maximization problem in this model. We prove that the problem is -complete and [1]-hard, and present constant-factor approximation algorithms. In the restricted, yet practically relevant case that no more than k labels can be active at any time, we give polynomial-time algorithms as well as constant-factor approximation algorithms.

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.

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.

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