scholarly journals 3/2-approximation algorithm for a single machine scheduling problem

2021 ◽  
Vol 17 (3) ◽  
pp. 240-253
Author(s):  
Natalia S. Grigoreva ◽  
Keyword(s):  
Approximation Algorithm ◽  
Optimization Problem ◽  
Single Machine Scheduling ◽  
Release Time ◽  
Scheduling Problem ◽  
Delivery Time ◽  
Scheduling Problems ◽  
Delivery Times ◽  
Jobshop Scheduling ◽  
Single Processor

The problem of minimizing the maximum delivery times while scheduling tasks on a single processor is a classical combinatorial optimization problem. Each task ui must be processed without interruption for t(ui) time units on the machine, which can process at most one task at time. Each task uw; has a release time r(ui), when the task is ready for processing, and a delivery time g(ui). Its delivery begins immediately after processing has been completed. The objective is to minimize the time, by which all jobs are delivered. In the Graham notation this problem is denoted by 1|rj,qi|Cmax, it has many applications and it is NP-hard in a strong sense. The problem is useful in solving owshop and jobshop scheduling problems. The goal of this article is to propose a new 3/2-approximation algorithm, which runs in O(n log n) times for scheduling problem 1|rj.qi|Cmax. An example is provided which shows that the bound of 3/2 is accurate. To compare the effectiveness of proposed algorithms, random generated problems of up to 5000 tasks were tested.

Multiple Decisional Query Optimization in Big Data Warehouse

2018 ◽  
Vol 14 (3) ◽  
pp. 22-43
Author(s):  
Ratsimbazafy Rado ◽  
Omar Boussaid
Keyword(s):  
Big Data ◽  
Data Warehouse ◽  
Query Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Distributed Environment ◽  
Shared Data ◽  
Multiple Query Optimization ◽  
Execution Engine ◽  
Multiple Query

Data warehousing (DW) area has always motivated a plethora of hard optimization problem that cannot be solved in polynomial time. Those optimization problems are more complex and interesting when it comes to multiple OLAP queries. In this article, the authors explore the potential of distributed environment for an established data warehouse, database-related optimization problem, the problem of Multiple Query Optimization (MQO). In traditional DW materializing views is an optimization technic to solve such problem by storing pre-computed join or frequently asked queries. In this era of big data this kind of view materialization is not suitable due to the data size. In this article, the authors tackle the problem of MQO on distributed DW by using a multiple, small, shared and easy to maintain shared data. The evaluation shows that, compared to available default execution engine, the authors' approach consumes on average 20% less memory in the Map-scan task and it is 12% faster regarding the execution time of interactive and reporting queries from TPC-DS.

scholarly journals An approximation algorithm for multi-objective optimization problems using a box-coverage

2021 ◽  
Author(s):  
Gabriele Eichfelder ◽  
Leo Warnow
Keyword(s):  
Approximation Algorithm ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Nondominated Set ◽  
Common Technique ◽  
Nondominated Points ◽  
Nondominated Point ◽  
Do So

AbstractFor a continuous multi-objective optimization problem, it is usually not a practical approach to compute all its nondominated points because there are infinitely many of them. For this reason, a typical approach is to compute an approximation of the nondominated set. A common technique for this approach is to generate a polyhedron which contains the nondominated set. However, often these approximations are used for further evaluations. For those applications a polyhedron is a structure that is not easy to handle. In this paper, we introduce an approximation with a simpler structure respecting the natural ordering. In particular, we compute a box-coverage of the nondominated set. To do so, we use an approach that, in general, allows us to update not only one but several boxes whenever a new nondominated point is found. The algorithm is guaranteed to stop with a finite number of boxes, each being sufficiently thin.

A Progressive Approximation Approach for the Exact Solution of Sparse Large-Scale Binary Interdiction Games

2021 ◽  
Author(s):  
Claudio Contardo ◽  
Jorge A. Sefair
Keyword(s):  
Exact Solution ◽  
Approximation Algorithm ◽  
Facility Location ◽  
Shortest Path ◽  
Large Scale ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Solution Space ◽  
Decision Variables ◽  
Algorithmic Framework

We present a progressive approximation algorithm for the exact solution of several classes of interdiction games in which two noncooperative players (namely an attacker and a follower) interact sequentially. The follower must solve an optimization problem that has been previously perturbed by means of a series of attacking actions led by the attacker. These attacking actions aim at augmenting the cost of the decision variables of the follower’s optimization problem. The objective, from the attacker’s viewpoint, is that of choosing an attacking strategy that reduces as much as possible the quality of the optimal solution attainable by the follower. The progressive approximation mechanism consists of the iterative solution of an interdiction problem in which the attacker actions are restricted to a subset of the whole solution space and a pricing subproblem invoked with the objective of proving the optimality of the attacking strategy. This scheme is especially useful when the optimal solutions to the follower’s subproblem intersect with the decision space of the attacker only in a small number of decision variables. In such cases, the progressive approximation method can solve interdiction games otherwise intractable for classical methods. We illustrate the efficiency of our approach on the shortest path, 0-1 knapsack and facility location interdiction games. Summary of Contribution: In this article, we present a progressive approximation algorithm for the exact solution of several classes of interdiction games in which two noncooperative players (namely an attacker and a follower) interact sequentially. We exploit the discrete nature of this interdiction game to design an effective algorithmic framework that improves the performance of general-purpose solvers. Our algorithm combines elements from mathematical programming and computer science, including a metaheuristic algorithm, a binary search procedure, a cutting-planes algorithm, and supervalid inequalities. Although we illustrate our results on three specific problems (shortest path, 0-1 knapsack, and facility location), our algorithmic framework can be extended to a broader class of interdiction problems.

Scheduling a Pipelined Operator Graph of Bounded Treewidth

2011 ◽  
Vol 467-469 ◽  
pp. 1102-1107
Author(s):  
Shu Guang Li ◽  
Xiao Xin
Keyword(s):  
Approximation Algorithm ◽  
Query Optimization ◽  
Bounded Treewidth ◽  
Parallel Query ◽  
Processor Load

Pipelined operator graph (POG) scheduling is an important problem in the area of parallel query optimization. A POG is a graph with vertices representing query operators that can run in parallel and edges representing communication between adjacent operators. The problem is to assign operators to processors so as to minimize the maximum processor load. We present a 2-approximation algorithm for the case where the operator graph has bounded treewidth.

scholarly journals Simple and Efficient Budget Feasible Mechanisms for Monotone Submodular Valuations

2021 ◽  
Vol 9 (1) ◽  
pp. 1-20
Author(s):  
Pooya Jalaly ◽  
Éva Tardos
Keyword(s):  
Approximation Algorithm ◽  
Mechanism Design ◽  
Design Problem ◽  
Optimization Problem ◽  
Submodular Function ◽  
Individual Item ◽  
Large Market ◽  
Total Budget ◽  
Approximation Guarantee ◽  
Budget Feasible

We study the problem of a budget limited buyer who wants to buy a set of items, each from a different seller, to maximize her value. The budget feasible mechanism design problem requires the design a mechanism that incentivizes the sellers to truthfully report their cost and maximizes the buyer’s value while guaranteeing that the total payment does not exceed her budget. Such budget feasible mechanisms can model a buyer in a crowdsourcing market interested in recruiting a set of workers (sellers) to accomplish a task for her. This budget feasible mechanism design problem was introduced by Singer in 2010. We consider the general case where the buyer’s valuation is a monotone submodular function. There are a number of truthful mechanisms known for this problem. We offer two general frameworks for simple mechanisms, and by combining these frameworks, we significantly improve on the best known results, while also simplifying the analysis. For example, we improve the approximation guarantee for the general monotone submodular case from 7.91 to 5 and for the case of large markets (where each individual item has negligible value) from 3 to 2.58. More generally, given an r approximation algorithm for the optimization problem (ignoring incentives), our mechanism is a r + 1 approximation mechanism for large markets, an improvement from 2 r 2 . We also provide a mechanism without the large market assumption, where we achieve a 4 r + 1 approximation guarantee. We also show how our results can be used for the problem of a principal hiring in a Crowdsourcing Market to select a set of tasks subject to a total budget.

MULTI COVER OF A POLYGON MINIMIZING THE SUM OF AREAS

2011 ◽  
Vol 21 (06) ◽  
pp. 685-698 ◽  
Author(s):  
A. KARIM ABU-AFFASH ◽  
PAZ CARMI ◽  
MATTHEW J. KATZ ◽  
GILA MORGENSTERN
Keyword(s):  
Approximation Algorithm ◽  
Network Design ◽  
Sensor Network ◽  
Polynomial Time ◽  
Optimization Problem ◽  
Geometric Optimization ◽  
Discrete Version ◽  
Sensing Range ◽  
Sensor Network Design ◽  
The Cost

We consider a geometric optimization problem that arises in sensor network design. Given a polygon P (possibly with holes) with n vertices, a set Y of m points representing sensors, and an integer k, 1 ≤ k ≤ m. The goal is to assign a sensing range, ri, to each of the sensors yi ∈ Y, such that each point p ∈ P is covered by at least k sensors, and the cost, [Formula: see text], of the assignment is minimized, where α is a constant. In this paper, we assume that α = 2, that is, find a set of disks centered at points of Y, such that (i) each point in P is covered by at least k disks, and (ii) the sum of the areas of the disks is minimized. We present, for any constant k ≥ 1, a polynomial-time c1-approximation algorithm for this problem, where c1 = c1(k) is a constant. The discrete version, where one has to cover a given set of n points, X, by disks centered at points of Y, arises as a subproblem. We present a polynomial-time c2-approximation algorithm for this problem, where c2 = c2(k) is a constant.

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