Tight Bounds for Online Vector Bin Packing Ilan Cohen Joint work with : Yossi Azar,Bruce Shepherd, Seny Kamara.

Slides:

Advertisements

Similar presentations

Coordination Mechanisms for Unrelated Machine Scheduling Yossi Azar joint work with Kamal Jain Vahab Mirrokni.

Advertisements

Tight Bounds for Online Class- constrained Packing Hadas Shachnai Bell Labs and The Technion IIT Tami Tamir The Technion IIT.

Class-constrained Packing Problems with Application to Storage Management in Multimedia Systems Tami Tamir Department of Computer Science The Technion.

1 SOFSEM 2007 Weighted Nearest Neighbor Algorithms for the Graph Exploration Problem on Cycles Eiji Miyano Kyushu Institute of Technology, Japan Joint.

Branch and Bound Example. Initial lower bound Jrpd Use 1 machine preemptive schedule as lower bound Job 2 has a lateness of 5,

Fast Convergence of Selfish Re-Routing Eyal Even-Dar, Tel-Aviv University Yishay Mansour, Tel-Aviv University.

Combinatorial Algorithms

Online Scheduling with Known Arrival Times Nicholas G Hall (Ohio State University) Marc E Posner (Ohio State University) Chris N Potts (University of Southampton)

Bicriteria Approximation Tradeoff for the Node-Cost Budget Problem Yuval Rabani (Technion) Gabriel Scalosub (Tel Aviv University)

2007/3/6 1 Online Chasing Problems for Regular n-gons Hiroshi Fujiwara* Kazuo Iwama Kouki Yonezawa.

1 Better Scalable Algorithms for Broadcast Scheduling Ravishankar Krishnaswamy Carnegie Mellon University Joint work with Nikhil Bansal and Viswanath Nagarajan.

Online Algorithms – II Amrinder Arora Permalink:

Approximating complete partitions Guy Kortsarz Joint work with J. Radhakrishnan and S.Sivasubramanian.

Job Scheduling Lecture 19: March 19. Job Scheduling: Unrelated Multiple Machines There are n jobs, each job has: a processing time p(i,j) (the time to.

Ecole Polytechnique, Nov 11, List Scheduling on Related Machines processors Related machines: machines may have different speeds  0.25 

Grid Load Balancing Scheduling Algorithm Based on Statistics Thinking The 9th International Conference for Young Computer Scientists Bin Lu, Hongbin Zhang.

On sparse Ramsey graphs Torsten Mütze, ETH Zürich Joint work with Ueli Peter (ETH Zürich) TexPoint fonts used in EMF. Read the TexPoint manual before you.

Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs Xiaoxi Zhang 1, Zhiyi Huang 1, Chuan Wu 1, Zongpeng Li 2, Francis C.M.

(work appeared in SODA 10’) Yuk Hei Chan (Tom)

A General Approach to Online Network Optimization Problems Seffi Naor Computer Science Dept. Technion Haifa, Israel Joint work: Noga Alon, Yossi Azar,

CSCI 3160 Design and Analysis of Algorithms Tutorial 12

Improved results for a memory allocation problem Rob van Stee University of Karlsruhe Germany Leah Epstein University of Haifa Israel WADS 2007 WAOA 2007.

Load Balancing Tasks with Overlapping Requirements Milan Vojnovic Microsoft Research Joint work with Dan Alistarh, Christos Gkantsidis, Jennifer Iglesias,

Throughput Competitive Online Routing Baruch Awerbuch Yossi Azar Serge Plotkin.

Limits of Local Algorithms in Random Graphs

Applications of types of SATs Arash Ahadi What is SAT?

Yossi Azar Tel Aviv University Joint work with Ilan Cohen Serving in the Dark 1.

Equality Function Computation (How to make simple things complicated) Nitin Vaidya University of Illinois at Urbana-Champaign Joint work with Guanfeng.

Presented by Dajiang Zhu 09/20/2011.  Motivation  Introduction & Conclusion  Pre – Definition Approximation Algorithms  Two problems as examples SUBSET-SUM.

© 2009 IBM Corporation 1 Improving Consolidation of Virtual Machines with Risk-aware Bandwidth Oversubscription in Compute Clouds Amir Epstein Joint work.

Bounding Variance and Expectation of Longest Path Lengths in DAGs Jeff Edmonds, York University Supratik Chakraborty, IIT Bombay.

Dynamic Resource Monitoring and Allocation in a virtualized environment.

1 Tight Bounds for Delay-Sensitive Aggregation Yvonne Anne Oswald Stefan Schmid Roger Wattenhofer Distributed Computing Group LEA.

First Fit Coloring of Interval Graphs William T. Trotter Georgia Institute of Technology.

An Analysis of First-Fit N.S. Narayanaswamy (IITM) Work with R. Subhash Babu.

Jennifer Campbell November 30,  Problem Statement and Motivation  Analysis of previous work  Simple - competitive strategy  Near optimal deterministic.

Introduction Conclusion Process Evaluation Task Teacher Page.

Virtualization and Databases Ashraf Aboulnaga University of Waterloo.

Instructor Neelima Gupta Table of Contents Factor 2 algorithm for Bin Packing Factor 2 algorithm for Minimum Makespan Scheduling Reference:

Improving the Performance Competitive Ratios of Transactional Memory Contention Managers Gokarna Sharma Costas Busch Louisiana State University, USA WTTM.

Adversarial Coloring, Covering and Domination Chip Klostermeyer.

With Extra Bandwidth and Time for Adjustment TCP is Competitive J. Edmonds, S. Datta, and P. Dymond.

Computability NP complete problems. Space complexity. Homework: [Post proposal]. Find PSPACE- Complete problems. Work on presentations.

1 Windows Scheduling as a Restricted Version of Bin-packing. Amotz Bar-Noy Brooklyn College Richard Ladner Tami Tamir University of Washington.

The Online Track Assignment Problem Marc Demange, ESSEC Benjamin Leroy-Beaulieu, EPFL Gabriele di Stefano, L’Aquilla Marc Demange, ESSEC Benjamin Leroy-Beaulieu,

Given this 3-SAT problem: (x1 or x2 or x3) AND (¬x1 or ¬x2 or ¬x2) AND (¬x3 or ¬x1 or x2) 1. Draw the graph that you would use if you want to solve this.

Of 17 Limits of Local Algorithms in Random Graphs Madhu Sudan MSR Joint work with David Gamarnik (MIT) 7/11/2013Local Algorithms on Random Graphs1.

Scheduling Parallel DAG Jobs to Minimize the Average Flow Time K. Agrawal, J. Li, K. Lu, B. Moseley.

Online Bipartite Matching with Augmentations Presentation by Henry Lin Joint work with Kamalika Chaudhuri, Costis Daskalakis, and Robert Kleinberg.

Adversarial Coloring, Covering and Domination Chip Klostermeyer.

BAHIR DAR UNIVERSITY Institute of technology Faculty of Computing Department of information technology Msc program Distributed Database Article Review.

Bin Packing First fit decreasing algorithm

New Characterizations in Turnstile Streams with Applications

From Algorithm to System to Cloud Computing

Deadline Scheduling and Heavy tail distributionS

What is the next line of the proof?

Monomer-dimer model and a new deterministic approximation algorithm for computing a permanent of a 0,1 matrix David Gamarnik MIT Joint work with Dmitriy.

3.2 Virtualisation.

On Scheduling in Map-Reduce and Flow-Shops

Bin Packing First fit decreasing algorithm

Richard Anderson Lecture 28 Coping with NP-Completeness

Deadline Scheduling and Heavy tailED distributions

Bin Packing First fit decreasing algorithm

Bin Packing First fit decreasing algorithm

Selfish Load Balancing

LECTURE 2-7 Complete Problems in PH

Branch and Bound Example

Acyclic k-Coloring. Acyclic k-Coloring Acyclic Coloring with Division Vertices.

CSC 380: Design and Analysis of Algorithms

Online Ranking for Tournament Graphs

Presentation transcript:

Tight Bounds for Online Vector Bin Packing Ilan Cohen Joint work with : Yossi Azar,Bruce Shepherd, Seny Kamara

Jobs Scheduling Scheduler Server 1 Server N

Jobs Scheduling CPU Server MemoryGPU…

Cloud Computing

Vector Bin Packing

On Line Algorithms

Competitive Ratio

Related Results

Our Results

Vector Bin Packing

Our Results

VBP(B=1) Lower Bound Online- VBP (B=1) α bins. Online- Graph coloring α colors

On-line Graph Coloring aabbccdde e

VBP(B=1) Lower Bound Online- VBP(B=1) α bins Online- Graph coloring α colors

Reduction VBP to Graph Coloring

Ind: Vec:

Reduction VBP to Graph Coloring aabbccddee

Ind: Vec:

Reduction VBP to Graph Coloring aabbccdd

VBP(B=1) Lower Bound Online- VBP(B=1) α bins Online- Graph coloring α colors

VBP(B=2) Lower Bound Online VBP(B=2) α bins α classes of Triangle-free sub graphs Online- Graph coloring α·k colors k colors for each sub graph

Reduction VBP to Graph Coloring

Reduction VBP(B=2) to Graph Coloring

a b c d

VBP(B=2) Lower Bound Online VBP(B=2) α bins α classes of Triangle-free sub graphs Online- Graph coloring α·k colors

Reduction VBP(B=2) to Graph Coloring

On-line Graph Coloring

VBP(B=2) Lower Bound Online VBP(B=2) α bins α classes of Triangle-free sub graphs Online- Graph coloring α·k colors

abcd Coloring vertices of bin j

Correctness

Analysis

VBP Lower Bound Online VBP (B) α bins α classes of B+1 clique free graphs Online- Graph coloring α· colors α·k classes of B clique free graphs

B Clique Free to B-1 Clique Free

Reduction VBP to Graph Coloring

Scheme

Analysis

Upper Bound (B > 1)

Pack Into Virtual bins B cBlog(d) OPT virtual bins All Vector Stream:

B r bins B B B cBlog(d) Distribute bin vectors Virtual Bin i:

The virtual VBP algorithm.

Proof Sketch

B r bins B B B cBlog(d) Distribute bin vectors Virtual Bin i:

Distributing the vectors

De-randomize the algorithm

Conclusions

Open Questions

Thank you!

The {0,1}-VBP Upper Bound

cBlog(d) Distribute bin vectors B r bins Virtual Bin i: B B B

Our Results

Distribute bin vectors B r machines Bin i’s vectors cBlog(d)

Lower Bounds (B = 1)

cBlog(d) Distribute bin vectors B r machines Virtual Bin i: B B B

Unrelated Machine Model