scholarly journals Streaming Algorithms for Bin Packing and Vector Scheduling

2020 ◽  
Author(s):  
Graham Cormode ◽  
Pavel Veselý
Keyword(s):  
Combinatorial Optimization ◽  
Bin Packing ◽  
Streaming Algorithms ◽  
Small Space ◽  
Model Of Computation ◽  
Identical Machines ◽  
The Cost

AbstractProblems involving the efficient arrangement of simple objects, as captured by bin packing and makespan scheduling, are fundamental tasks in combinatorial optimization. These are well understood in the traditional online and offline cases, but have been less well-studied when the volume of the input is truly massive, and cannot even be read into memory. This is captured by the streaming model of computation, where the aim is to approximate the cost of the solution in one pass over the data, using small space. As a result, streaming algorithms produce concise input summaries that approximately preserve the optimum value. We design the first efficient streaming algorithms for these fundamental problems in combinatorial optimization. For Bin Packing, we provide a streaming asymptotic (1 + ε)-approximation with $\widetilde {O}$ O ~ $\left (\frac {1}{\varepsilon }\right )$ 1 ε , where $\widetilde {{{O}}}$ O ~ hides logarithmic factors. Moreover, such a space bound is essentially optimal. Our algorithm implies a streaming (d + ε)-approximation for Vector Bin Packing in d dimensions, running in space $\widetilde {{{O}}}\left (\frac {d}{\varepsilon }\right )$ O ~ d ε . For the related Vector Scheduling problem, we show how to construct an input summary in space $\widetilde {{{O}}}(d^{2}\cdot m / \varepsilon ^{2})$ O ~ ( d 2 ⋅ m / ε 2 ) that preserves the optimum value up to a factor of $2 - \frac {1}{m} +\varepsilon $ 2 − 1 m + ε , where m is the number of identical machines.

scholarly journals Investigation of the technology of mutual navigation and orientation of small space vehicles flying in formation

2019 ◽  
Vol 18 (1) ◽  
pp. 88-93
Author(s):  
A. V. Nebylov ◽  
V. V. Perliouk ◽  
T. S. Leontieva
Keyword(s):  
Video Camera ◽  
Space Vehicles ◽  
Radio Communication ◽  
Small Space ◽  
Modeling Simulation ◽  
Ground Station ◽  
Bench Experiment ◽  
Radio Communication System ◽  
The Cost ◽  
Orbital Constellation

The paper presents the problem of ensuring support of the flight of a group of small spacecraft (microsatellites) taking into account the small mutual distances between them. The purpose of using the orbital constellation specified is to create a radio communication system to control remote objects like unmanned aerial vehicles and ground robots located in hard-to-reach areas of the Earth from the Central ground station. To reduce the cost of microsatellite design, it was decided to rigidly fix the receiving and transmitting antennas on their housings and use the spatial orientation of the entire apparatus for antenna guidance. This seriously complicated the tasks of navigation and orientation of microsatellites in a formation and required the development of a new method for determining the orientation of a single microsatellite. The essence of the method is to process the image obtained by means of a video camera mounted on a nearby microsatellite. We used methods of computer vision. The results of mathematical modeling simulation, as well as the results of full-scale bench experiment confirming the efficiency of the proposed method are presented.

STM investigation of cobalt silicide nanostructures’ growth on Si(111)-(√19 × √19) substrate

Open Physics ◽  
2009 ◽  
Vol 7 (2) ◽  
Author(s):  
Maciej Cegiel ◽  
Maciej Bazarnik ◽  
Ryszard Czajka
Keyword(s):  
Thin Films ◽  
Surface Reconstruction ◽  
Electronic Devices ◽  
Small Space ◽  
Post Deposition Annealing ◽  
Ni Doping ◽  
Crystal Sample ◽  
Metal Silicides ◽  
The Cost ◽  
Post Deposition

AbstractContinuing miniaturization of electronic devices necessarily requires assembly of several different objects or devices in a small space. Therefore, besides thin films growth, the possibility of fabricating wires and dots [1, 2] at the nanometre scale composed of metal silicides is of the top interest. This report is about the STM/STS investigation of cobalt silicides’ nanostructures created on Si(111)-(√19 × √19) substrates via Co evaporation and post deposition annealing. This (√19 × √19) reconstruction was induced by Ni doping. Less than 1ML of Co on surface was obtained. Surface reconstruction induced growth of agglomerates of clusters rather than an uniform layer. The post deposition annealing of a crystal sample (up to 670 K, 770 K, 870 K, 970 K, 1070 K and 1170 K) led to creation of silicides’ nanostructures. Measurements showed that coalescence of Co nanoislands begun around 970 K. Annealing above 1070 K led to alloying of a Co, Ni and Si. As a consequence the Si(111)-(7×7) reconstruction occurred at the cost of Si(111)-(√19 × √19).

scholarly journals A novel bottom-left packing genetic algorithm for analog module placement

2003 ◽  
Vol 1 ◽  
pp. 191-196 ◽  
Author(s):  
L. Zhang ◽  
U. Kleine
Keyword(s):  
Genetic Algorithm ◽  
Integrated Circuits ◽  
Cost Function ◽  
Bin Packing ◽  
Optimal Parameter ◽  
Packing Problem ◽  
Fractional Factorial ◽  
Genetic Encoding ◽  
The Cost ◽  
Parameter Values

Abstract. This paper presents a novel genetic algorithm for analog module placement. It is based on a generalization of the two-dimensional bin packing problem. The genetic encoding and operators assures that all constraints of the problem are always satisfied. Thus the potential problems of adding penalty terms to the cost function are eliminated, so that the search configuration space decreases drastically. The dedicated cost function covers the special requirements of analog integrated circuits. A fractional factorial experiment was conducted using an orthogonal array to study the algorithm parameters. A meta-GA was applied to determine the optimal parameter values. The algorithm has been tested with several local benchmark circuits. The experimental results show this promising algorithm makes the better performance than simulated annealing approach with the satisfactory results comparable to manual placement.

scholarly journals New Directions in Streaming Algorithms

2020 ◽  
Author(s):  
Ali Vakilian
Keyword(s):  
Machine Learning ◽  
Combinatorial Optimization ◽  
Design Theory ◽  
Large Scale ◽  
Computational Models ◽  
Optimization Problems ◽  
Low Rank ◽  
Set Cover ◽  
Streaming Algorithms ◽  
Combinatorial Optimization Problems

Large volumes of available data have led to the emergence of new computational models for data analysis. One such model is captured by the notion of streaming algorithms: given a sequence of N items, the goal is to compute the value of a given function of the input items by a small number of passes and using a sublinear amount of space in N. Streaming algorithms have applications in many areas such as networking and large scale machine learning. Despite a huge amount of work on this area over the last two decades, there are multiple aspects of streaming algorithms that remained poorly understood, such as (a) streaming algorithms for combinatorial optimization problems and (b) incorporating modern machine learningtechniques in the design of streaming algorithms. In the first part of this thesis, we will describe (essentially) optimal streaming algorithms for set cover and maximum coverage, two classic problems in combinatorial optimization. Next, in the second part, we will show how to augment classic streaming algorithms of the frequency estimation and low-rank approximation problems with machine learning oracles in order to improve their space-accuracy tradeoffs. The new algorithms combine the benefits of machine learning with the formal guarantees available through algorithm design theory.

Acyclic Mechanism Design for Freight Consolidation

2021 ◽  
Author(s):  
Wentao Zhang ◽  
Nelson A. Uhan ◽  
Maged Dessouky ◽  
Alejandro Toriello
Keyword(s):  
Cost Sharing ◽  
Bin Packing ◽  
Noncooperative Game ◽  
Budget Balance ◽  
Freight Consolidation ◽  
Shipping Cost ◽  
Empirical Tests ◽  
Effectiveness And Efficiency ◽  
The Cost ◽  
Better Than

Freight consolidation is a logistics practice that improves the cost-effectiveness and efficiency of transportation operations, and also reduces energy consumption and carbon footprint. A “fair” shipping cost-sharing scheme is indispensable to help establish and sustain the cooperation of a group of suppliers in freight consolidation. In this paper, we design a truthful acyclic mechanism to solve the cost-sharing problem in a freight consolidation system with one consolidation center and one common destination. Applying the acyclic mechanism, the consolidation center decides which suppliers’ demands ship via the consolidation center and their corresponding cost shares based on their willingness to pay for the service. The proposed acyclic mechanism is designed based on bin packing solutions that are also strong Nash equilibria for a related noncooperative game. We study the budget-balance of the mechanism both theoretically and numerically. We prove a 2-budget-balance guarantee for the mechanism in general and better budget-balance guarantees under specific problem settings. Empirical tests on budget-balance show that our mechanism performs much better than the guaranteed budget-balance ratio. We also study the economic efficiency of our mechanism numerically to investigate its impact on social welfare under different conditions.

ON DYNAMIC TASK SCHEDULING FOR FPGA-BASED SYSTEMS

2001 ◽  
Vol 12 (05) ◽  
pp. 645-669 ◽  
Author(s):  
OLIVER DIESSEL ◽  
HOSSAM ELGINDY
Keyword(s):  
Time Complexity ◽  
High Performance ◽  
Bin Packing ◽  
Computational Effort ◽  
Future Research ◽  
Dynamic Task ◽  
Np Complete ◽  
The Cost ◽  
Task Sets ◽  
Dynamic Task Scheduling

The development of FPGAs that can be programmed to implement custom circuits by modifying memory has inspired researchers to investigate how FPGAs can be used as a computational resource in systems designed for high performance applications. When such FPGA–based systems are composed of arrays of chips or chips that can be partially reconfigured, the programmable array space can be partitioned among several concurrently executing tasks. If partition sizes are adapted to the needs of tasks, then array resources become fragmented as tasks with varying requirements are processed. Tasks may end up waiting despite their being sufficient, albeit fragmented resources available. We examine the problem of repartitioning the system (rearranging a subset of the executing tasks) at run–time in order to allow waiting tasks to enter the system sooner. In this paper, we introduce the problems of identifying and scheduling feasible task rearrangements when tasks are moved by reloading. It is shown that both problems are NP–complete. We develop two very different heuristic approaches to finding and scheduling suitable rearrangements. The first method, known as Local Repacking, attempts to minimize the size of the subarray needing rearrangement. Candidate subarrays are repacked using known bin packing algorithms. Task movements are scheduled so as to minimize delays to their execution. The second approach, called Ordered Compaction, constrains the movements of tasks in order to efficiently identify and schedule feasible rearrangements. The heuristics are compared by time complexity and resulting system performance on simulated task sets. The results indicate that considerable scheduling advantages are to be gained for acceptable computational effort. However, the benefits may be jeopardized by delays to moving tasks when the average cost of reloading tasks becomes significant relative to task service periods. We indicate directions for future research to mitigate the cost of moving executing tasks.

Prices of Anarchy of Selfish 2D Bin Packing Games

2019 ◽  
Vol 30 (03) ◽  
pp. 355-374
Author(s):  
Cristina G. Fernandes ◽  
Carlos E. Ferreira ◽  
Flávio K. Miyazawa ◽  
Yoshiko Wakabayashi
Keyword(s):  
Nash Equilibrium ◽  
Bin Packing ◽  
Price Of Anarchy ◽  
Dimensional Case ◽  
Theoretical Problem ◽  
Single Item ◽  
Strong Nash Equilibrium ◽  
Square Packing ◽  
The Cost

We consider a game-theoretical problem called selfish 2-dimensional bin packing game, a generalization of the 1-dimensional case already treated in the literature. In this game, the items to be packed are rectangles, and the bins are unit squares. The game starts with a set of items arbitrarily packed in bins. The cost of an item is defined as the ratio between its area and the total occupied area of the respective bin. Each item is a selfish player that wants to minimize its cost. A migration of an item to another bin is allowed only when its cost is decreased. We show that this game always converges to a Nash equilibrium (a stable packing where no single item can decrease its cost by migrating to another bin). We show that the pure price of anarchy of this game is unbounded, so we address the particular case where all items are squares. We show that the pure price of anarchy of the selfish square packing game is at least [Formula: see text] and at most [Formula: see text]. We also present analogous results for the strong Nash equilibrium (a stable packing where no nonempty set of items can simultaneously migrate to another common bin and decrease the cost of each item in the set). We show that the strong price of anarchy when all items are squares is at least [Formula: see text] and at most [Formula: see text].

A bin packing game with cardinality constraints under the best cost rule

2019 ◽  
Vol 11 (02) ◽  
pp. 1950022
Author(s):  
Qingqin Nong ◽  
Jiapeng Wang ◽  
Suning Gong ◽  
Saijun Guo
Keyword(s):  
Cooperative Game ◽  
Bin Packing ◽  
Social Cost ◽  
Price Of Anarchy ◽  
Packing Problem ◽  
Cardinality Constraints ◽  
Bin Packing Problem ◽  
The Social ◽  
The Cost

We consider the bin packing problem with cardinality constraints in a non-cooperative game setting. In the game, there are a set of items with sizes between 0 and 1, and a number of bins each of which has a capacity of 1. Each bin can pack at most [Formula: see text] items, for a given integer parameter [Formula: see text]. The social cost is the number of bins used in the packing. Each item tries to be packed into one of the bins so as to minimize its cost. The selfish behaviors of the items result in some kind of equilibrium, which greatly depends on the cost rule in the game. We say a cost rule encourages sharing if for an item, compared with sharing a bin with some other items, staying in a bin alone does not decrease its cost. In this paper, we first show that for any bin packing game with cardinality constraints under an encourage-sharing cost rule, the price of anarchy of it is at least [Formula: see text]. We then propose a cost rule and show that the price of anarchy of the bin packing game under the rule is [Formula: see text] when [Formula: see text].

scholarly journals The integrated uncapacitated lot sizing and bin packing problem

2021 ◽  
Author(s):  
Natã Goulart ◽  
Thiago Ferreira de Noronha ◽  
Martin Gomez Ravetti ◽  
Mauricio Cardoso de Souza
Keyword(s):  
Bin Packing ◽  
Lot Sizing ◽  
Packing Problem ◽  
Planning Horizon ◽  
Mixed Integer ◽  
Holding Costs ◽  
Bin Packing Problem ◽  
Combinatorial Relaxation ◽  
The Cost ◽  
Inventory Holding

In the integrated uncapacitated lot sizing and bin packing problem, we have to couple lot sizing decisions of replenishment from single product suppliers with bin packing decisions in the delivery of client orders. A client order is composed of quantities of each product, and the quantities of such an order must be delivered all together no later than a given period. The quantities of an order must all be packed in the same bin, and may be delivered in advance if it is advantageous in terms of costs. We assume a large enough set of homogeneous bins available at each period. The costs involved are setup and inventory holding costs and the cost to use a bin as well. All costs are variable in the planning horizon, and the objective is to minimize the total cost incurred. We propose mixed integer linear programming formulations and a combinatorial relaxation where it is no longer necessary to keep track of the specific bin where each order is packed. An aggregate delivering capacity is computed instead. We also propose heuristics using different strategies to couple the lot sizing and the bin packing subproblems. Computational experiments on instances with different configurations showed that the proposed methods are efficient ways to obtain small optimality gaps in reduced computational times.

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