Different Approximation Algorithms for Channel Scheduling in Wireless Networks

We introduce a new two-side approximation method for the channel scheduling problem, which controls the accuracy of approximation in two sides by a pair of parameters f , g . We present a series of simple and practical-for-implementation greedy algorithms which give constant factor approximation in both sides. First, we propose four approximation algorithms for the weighted channel allocation problem: 1. a greedy algorithm for the multichannel with fixed interference radius scheduling problem is proposed and an one side O 1 -IS-approximation is obtained; 2. a greedy O 1 , O 1 -approximation algorithm for single channel with fixed interference radius scheduling problem is presented; 3. we improve the existing algorithm for the multichannel scheduling and show an E O d / ε time 1 − ϵ -approximation algorithm; 4. we speed up the polynomial time approximation scheme for single-channel scheduling through merging two algorithms and show a 1 − ϵ , O 1 -approximation algorithm. Next, we study two polynomial time constant factor greedy approximation algorithms for the unweighted channel allocation with variate interference radius. A greedy O 1 -approximation algorithm for the multichannel scheduling problem and an O 1 , O 1 -approximation algorithm for single-channel scheduling problem are developed. At last, we do some experiments to verify the effectiveness of our proposed methods.

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APPROXIMATION ALGORITHMS FOR SCHEDULING MALLEABLE TASKS UNDER PRECEDENCE CONSTRAINTS

International Journal of Foundations of Computer Science ◽

10.1142/s0129054102001308 ◽

2002 ◽

Vol 13 (04) ◽

pp. 613-627 ◽

Cited By ~ 34

Author(s):

RENAUD LEPÈRE ◽

DENIS TRYSTRAM ◽

GERHARD J. WOEGINGER

Keyword(s):

Approximation Algorithms ◽

Approximation Algorithm ◽

Polynomial Time ◽

Precedence Constraints ◽

Performance Guarantee ◽

Time Approximation ◽

Polynomial Time Approximation Algorithm ◽

Special Cases ◽

Special Case ◽

Polynomial Time Approximation

This work presents approximation algorithms for scheduling the tasks of a parallel application that are subject to precedence constraints. The considered tasks are malleable which means that they may be executed on a varying number of processors in parallel. The considered objective criterion is the makespan, i.e., the largest task completion time. We demonstrate a close relationship between this scheduling problem and one of its subproblems, the allotment problem. By exploiting this relationship, we design a polynomial time approximation algorithm with performance guarantee arbitrarily close to [Formula: see text] for the special case of series parallel precedence constraints and for the special case of precedence constraints of bounded width. These special cases cover the important situation of tree structured precedence constraints. For arbitrary precedence constraints, we give a polynomial time approximation algorithm with performance guarantee [Formula: see text].

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Adding Edges for Maximizing Weighted Reachability

Algorithms ◽

10.3390/a13030068 ◽

2020 ◽

Vol 13 (3) ◽

pp. 68 ◽

Cited By ~ 1

Author(s):

Federico Corò ◽

Gianlorenzo D'Angelo ◽

Cristina M. Pinotti

Keyword(s):

Polynomial Time ◽

Greedy Algorithms ◽

Dynamic Programming Algorithm ◽

Directed Acyclic Graphs ◽

Constant Factor ◽

Programming Algorithm ◽

Single Source ◽

Graph Augmentation ◽

Set Size ◽

Acyclic Graphs

In this paper, we consider the problem of improving the reachability of a graph. We approach the problem from a graph augmentation perspective, in which a limited set size of edges is added to the graph to increase the overall number of reachable nodes. We call this new problem the Maximum Connectivity Improvement (MCI) problem. We first show that, for the purpose of solve solving MCI, we can focus on Directed Acyclic Graphs (DAG) only. We show that approximating the MCI problem on DAG to within any constant factor greater than 1 − 1 / e is NP -hard even if we restrict to graphs with a single source or a single sink, and the problem remains NP -complete if we further restrict to unitary weights. Finally, this paper presents a dynamic programming algorithm for the MCI problem on trees with a single source that produces optimal solutions in polynomial time. Then, we propose two polynomial-time greedy algorithms that guarantee ( 1 − 1 / e ) -approximation ratio on DAGs with a single source, a single sink or two sources.

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CUTTING OUT POLYGONS WITH LINES AND RAYS

International Journal of Computational Geometry & Applications ◽

10.1142/s0218195906002014 ◽

2006 ◽

Vol 16 (02n03) ◽

pp. 227-248 ◽

Cited By ~ 11

Author(s):

OVIDIU DAESCU ◽

JUN LUO

Keyword(s):

Approximation Algorithms ◽

Approximation Algorithm ◽

Convex Polygon ◽

Linear Time ◽

Constant Factor ◽

Open Problems ◽

Cutting Out ◽

Cutting Sequence

We present approximation algorithms for cutting out a polygon P with n vertices from another convex polygon Q with m vertices by line cuts and ray cuts. For line cuts we require both P and Q are convex while for ray cuts we require Q is convex and P is ray cuttable. Our results answer a number of open problems and are either the first solutions or significantly improve over previously known solutions. For the line cutting version, we prove a key property that leads to a simple, constant factor approximation algorithm. For the ray cutting version, we prove it is possible to compute in almost linear time a cutting sequence that is an O( log 2 n)-factor approximation of an optimal cutting sequence. No algorithms were previously known for the ray cutting version.

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Approximation Algorithms for Energy, Reliability, and Makespan Optimization Problems

Parallel Processing Letters ◽

10.1142/s0129626416500018 ◽

2016 ◽

Vol 26 (01) ◽

pp. 1650001 ◽

Cited By ~ 1

Author(s):

Guillaume Aupy ◽

Anne Benoit

Keyword(s):

Energy Consumption ◽

Approximation Algorithms ◽

Approximation Algorithm ◽

Optimization Problems ◽

Linear Chain ◽

Constant Factor ◽

Task Graph ◽

Linear Chains ◽

Energy Reliability ◽

Independent Tasks

We consider the problem of scheduling an application on a parallel computational platform. The application is a particular task graph, either a linear chain of tasks, or a set of independent tasks. The platform is made of identical processors, whose speed can be dynamically modified. It is also subject to failures: if a processor is slowed down to decrease the energy consumption, it has a higher chance to fail. Therefore, the scheduling problem requires us to re-execute or replicate tasks (i.e., execute twice the same task, either on the same processor, or on two distinct processors), in order to increase the reliability. It is a tri-criteria problem: the goal is to minimize the energy consumption, while enforcing a bound on the total execution time (the makespan), and a constraint on the reliability of each task. Our main contribution is to propose approximation algorithms for linear chains of tasks and independent tasks. For linear chains, we design a fully polynomial-time approximation scheme. However, we show that there exists no constant factor approximation algorithm for independent tasks, unless P=NP, and we propose in this case an approximation algorithm with a relaxation on the makespan constraint.

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On the Performance of a Simple Approximation Algorithm for the Longest Path Problem

Journal of Computer Science and Cybernetics ◽

10.15625/1813-9663/35/1/12935 ◽

2019 ◽

Vol 35 (1) ◽

pp. 57-68

Author(s):

Nguyen Thi Phuong ◽

Tran Vinh Duc ◽

Le Cong Thanh

Keyword(s):

Approximation Algorithms ◽

Approximation Algorithm ◽

Polynomial Time ◽

Undirected Graph ◽

Simple Algorithm ◽

Performance Ratio ◽

Constant Ratio ◽

Time Approximation ◽

Longest Path ◽

Longest Path Problem

The longest path problem is known to be NP-hard. Moreover, they cannot be approximated within a constant ratio, unless ${\rm P=NP}$. The best known polynomial time approximation algorithms for this problem essentially find a path of length that is the logarithm of the optimum.In this paper we investigate the performance of an approximation algorithm for this problem in almost every case. We show that a simple algorithm, based on depth-first search, finds on almost every undirected graph $G=(V,E)$ a path of length more than $|V|-3\sqrt{|V| \log |V|}$ and so has performance ratio less than $1+4\sqrt{\log |V|/|V|}$.\

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On polynomial-time approximation algorithms for the variable length scheduling problem

Theoretical Computer Science ◽

10.1016/s0304-3975(03)00141-5 ◽

2003 ◽

Vol 302 (1-3) ◽

pp. 489-495

Author(s):

Artur Czumaj ◽

Leszek Ga̧sieniec ◽

Daya Ram Gaur ◽

Ramesh Krishnamurti ◽

Wojciech Rytter ◽

...

Keyword(s):

Approximation Algorithms ◽

Polynomial Time ◽

Variable Length ◽

Scheduling Problem ◽

Time Approximation ◽

Polynomial Time Approximation

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Weighted Maxmin Fair Share Allocation of Indivisible Chores

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2019/7 ◽

2019 ◽

Cited By ~ 1

Author(s):

Haris Aziz ◽

Hau Chan ◽

Bo Li

Keyword(s):

Approximation Algorithms ◽

Approximation Algorithm ◽

Time Constant ◽

Polynomial Time ◽

Natural Generalization ◽

Linear Program ◽

Fair Share ◽

Special Cases

We initiate the study of indivisible chore allocation for agents with asymmetric shares. The fairness concept we focus on is the weighted natural generalization of maxmin share: WMMS fairness and OWMMS fairness. We first highlight the fact that commonly-used algorithms that work well for allocation of goods to asymmetric agents, and even for chores to symmetric agents do not provide good approximations for allocation of chores to asymmetric agents under WMMS. As a consequence, we present a novel polynomial-time constant-approximation algorithm, via linear program, for OWMMS. For two special cases: the binary valuation case and the 2-agent case, we provide exact or better constant-approximation algorithms.

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A General Framework for Approximating Min Sum Ordering Problems

INFORMS Journal on Computing ◽

10.1287/ijoc.2021.1124 ◽

2021 ◽

Author(s):

Felix Happach ◽

Lisa Hellerstein ◽

Thomas Lidbetter

Keyword(s):

Approximation Algorithm ◽

Boolean Function ◽

Polynomial Time ◽

General Framework ◽

Large Family ◽

Constant Factor ◽

Theoretical Computer Science ◽

Set Cover ◽

Function Evaluation ◽

Finite Set

We consider a large family of problems in which an ordering (or, more precisely, a chain of subsets) of a finite set must be chosen to minimize some weighted sum of costs. This family includes variations of min sum set cover, several scheduling and search problems, and problems in Boolean function evaluation. We define a new problem, called the min sum ordering problem (MSOP), which generalizes all these problems using a cost and a weight function defined on subsets of a finite set. Assuming a polynomial time α-approximation algorithm for the problem of finding a subset whose ratio of weight to cost is maximal, we show that under very minimal assumptions, there is a polynomial time [Formula: see text]-approximation algorithm for MSOP. This approximation result generalizes a proof technique used for several distinct problems in the literature. We apply this to obtain a number of new approximation results. Summary of Contribution: This paper provides a general framework for min sum ordering problems. Within the realm of theoretical computer science, these problems include min sum set cover and its generalizations, as well as problems in Boolean function evaluation. On the operations research side, they include problems in search theory and scheduling. We present and analyze a very general algorithm for these problems, unifying several previous results on various min sum ordering problems and resulting in new constant factor guarantees for others.

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