Single machine models: Maximum Lateness 12 Approximation ratio for EDD for problem 1 r j,d j < 0 L max. structure of a schedule Q...


 Katrina Roberta Owen
 2 years ago
 Views:
Transcription
1 Lecture 4 Scheduling 1 Single machine models: Maximum Lateness 12 Approximation ratio for EDD for problem 1 r j,d j < 0 L max structure of a schedule 0 Q b c r(q) C c S b Q interference job b: last scheduled job from Q with q b < q c Lemma: For the objective value L max (EDD) of an EDD schedule we have: (Proofs were asked as exercise) 1. L max (EDD) L max < q c 2. L max (EDD) L max < p b Theorem: EDD is 2approximation algorithm for 1 r j,d j < 0 L max
2 Lecture 4 Scheduling 2 Single machine models: Maximum Lateness 13 Approximation ratio for EDD for problem 1 r j,d j < 0 L max Remarks: EDD is also a 2approximation for 1 prec,r j,d j < 0 L max (uses modified release and due dates) by an iteration technique the approximation factor can be reduced to 3/2
3 Lecture 4 Scheduling 3 Single machine models: Maximum Lateness 14 Enumerative methods for problem 1 r j L max we again will use headbodytail notation Simple branch and bound method: branch on level i of the search tree by selecting a job to be scheduled on position i if in a node of the search tree on level i the set of already scheduled jobs is denoted by S and the finishing time of the jobs from S by t, for position i we only have to consider jobs k with r k < min j / S (max{t,r j} + p j ) lower bound: solve for remaining jobs 1 r j,pmtn L max search strategy: depth first search + selecting next job via lower bound
4 Lecture 4 Scheduling 4 Single machine models: Maximum Lateness 15 Advanced b&bmethods for problem 1 r j L max node of search tree = restricted instance restrictions = set of precedence constraints branching = adding precedence constraints between certain pairs of jobs after adding precedence constraints, modify release and due dates apply EDD to instance given in a node critical sequence has no interference job: EDD solves instance optimal backtrack critical sequence has an interference job: branch
5 Lecture 4 Scheduling 5 Single machine models: Maximum Lateness 16 Advanced b&bmethods for problem 1 r j L max (cont.) branching, given set Q, critical job c, interference job b, and set Q of jobs from Q following b Q C c b c... r(q) S b Q L max = S b + p b + p(q ) + q(q ) < r(q ) + p b + p(q ) + q(q ) if b is scheduled between jobs of Q the value is at least r(q ) + p b + p(q ) + q(q ); i.e. worse than the current schedule
6 Lecture 4 Scheduling 6 Single machine models: Maximum Lateness 16 Advanced b&bmethods for problem 1 r j L max (cont.) branching, given set Q, critical job c, interference job b, and set Q of jobs from Q following b Q C c b c... r(q) S b Q L max = S b + p b + p(q ) + q(q ) < r(q ) + p b + p(q ) + q(q ) if b is scheduled between jobs of Q the value is at least r(q ) + p b + p(q ) + q(q ); i.e. worse than the current schedule branch by adding either b Q or Q b
7 Lecture 4 Scheduling 7 Single machine models: Maximum Lateness 17 Advanced b&bmethods for problem 1 r j L max (cont.) lower bounds in a node: maximum of lower bound of parent node r(q ) + p(q ) + q(q ) r(q {b}) + p(q {b}) + q(q {b}) using the modified release and due dates upper bound UB: best value of the EDD schedules discard a node if lower bound UB search strategy: select node with minimum lower bound
8 Lecture 4 Scheduling 8 Single machine models: Maximum Lateness 18 Advanced b&bmethods for problem 1 r j L max (cont.) speed up possibility: let k / Q {b} with r(q ) + p k + p(q ) + q(q ) UB if r(q ) + p(q ) + p k + q k UB then add k Q if r k + p k + p(q ) + q(q ) UB then add Q k
9 Lecture 4 Scheduling 9 Single machine models: Number of Tardy Jobs 1 Problem 1 U j : Structure of an optimal schedule: set S 1 of jobs meeting their due dates set S 2 of jobs being late jobs of S 1 are scheduled before jobs from S 2 jobs from S 1 are scheduled in EDD order jobs from S 2 are scheduled in an arbitrary order Result: a partition of the set of jobs into sets S 1 and S 2 is sufficient to describe a solution
10 Lecture 4 Scheduling 10 Single machine models: Number of Tardy Jobs 2 Algorithm for 1 U j (MooreHodgson) 1. enumerate jobs such that d 1... d n ; 2. S 1 := ; t := 0; 3. FOR j:=1 TO n DO 4. S 1 := S 1 {j}; t := t + p j ; 5. IF t > d j THEN 6. Find job k with largest p k value in S 1 ; 7. S 1 := S 1 \ {k}; t := t p k ; 8. END 9. END
11 Lecture 4 Scheduling 11 Single machine models: Number of Tardy Jobs 3 Remarks on MooreHodgson Principle: schedule jobs in order of increasing due dates and always when a job gets late, remove the job with largest processing time; all removed jobs are late complexity: O(n log(n)) Example: n = 5; p = (7, 8, 4, 6, 6); d = (9, 17, 18, 19, 21)
12 Lecture 4 Scheduling 12 Single machine models: Number of Tardy Jobs 3 Remarks on MooreHodgson Principle: schedule jobs in order of increasing due dates and always when a job gets late, remove the job with largest processing time; all removed jobs are late complexity: O(n log(n)) Example: n = 5; p = (7, 8, 4, 6, 6); d = (9, 17, 18, 19, 21) d 3
13 Lecture 4 Scheduling 13 Single machine models: Number of Tardy Jobs 3 Remarks on MooreHodgson Principle: schedule jobs in order of increasing due dates and always when a job gets late, remove the job with largest processing time; all removed jobs are late complexity: O(n log(n)) Example: n = 5; p = (7, 8, 4, 6, 6); d = (9, 17, 18, 19, 21) d 5
14 Lecture 4 Scheduling 14 Single machine models: Number of Tardy Jobs 3 Remarks on MooreHodgson Principle: schedule jobs in order of increasing due dates and always when a job gets late, remove the job with largest processing time; all removed jobs are late complexity: O(n log(n)) Example: n = 5; p = (7, 8, 4, 6, 6); d = (9, 17, 18, 19, 21) MooreHodgson computes an optimal solution Proof on the board
15 Lecture 4 Scheduling 15 Single machine models: Weighted Number of Tardy Jobs 1 Problem 1 w j U j problem 1 w j U j is NPhard even if all due dates are the same; i.e. 1 d j = d w j U j is NPhard Proof on the board (reduction from PARTITION) priority based heuristic (WSPTrule): schedule jobs in increasing p j /w j order
16 Lecture 4 Scheduling 16 Single machine models: Weighted Number of Tardy Jobs 1 Problem 1 w j U j problem 1 w j U j is NPhard even if all due dates are the same; i.e. 1 d j = d w j U j is NPhard Proof on the board (reduction from PARTITION) priority based heuristic (WSPTrule): schedule jobs in increasing p j /w j order WSPT may perform arbitrary bad for 1 w j U j :
17 Lecture 4 Scheduling 17 Single machine models: Weighted Number of Tardy Jobs 1 Problem 1 w j U j problem 1 w j U j is NPhard even if all due dates are the same; i.e. 1 d j = d w j U j is NPhard Proof on the board (reduction from PARTITION) priority based heuristic (WSPTrule): schedule jobs in increasing p j /w j order WSPT may perform arbitrary bad for 1 w j U j : n = 3;p = (1, 1,M); w = (1+ǫ, 1,M ǫ);d = (1+M, 1+M, 1+M) wj U j (WSPT)/ w j U j (opt) = (M ǫ)/(1 + ǫ)
18 Lecture 4 Scheduling 18 Single machine models: Weighted Number of Tardy Jobs 2 Dynamic Programming for 1 w j U j assume d 1... d n as for 1 U j a solution is given by a partition of the set of jobs into sets S 1 and S 2 and jobs in S 1 are in EDD order Definition: F j (t) := minimum criterion value for scheduling the first j jobs such that the processing time of the ontime jobs is at most t F n (T) with T = n j=1 p j is optimal value for problem 1 w j U j Initial conditions: F j (t) = { for t < 0; j = 1,...,n 0 for t 0; j = 0 (1)
19 Lecture 4 Scheduling 19 Single machine models: Weighted Number of Tardy Jobs 3 Dynamic Programming for 1 w j U j (cont.) if 0 t d j and j is late in the schedule corresponding to F j (t), we have F j (t) = F j 1 (t) + w j if 0 t d j and j is on time in the schedule corresponding to F j (t), we have F j (t) = F j 1 (t p j )
20 Lecture 4 Scheduling 20 Single machine models: Weighted Number of Tardy Jobs 3 Dynamic Programming for 1 w j U j (cont.) if 0 t d j and j is late in the schedule corresponding to F j (t), we have F j (t) = F j 1 (t) + w j if 0 t d j and j is on time in the schedule corresponding to F j (t), we have F j (t) = F j 1 (t p j ) summarizing, we get for j = 1,...,n: { min{f F j (t) = j 1 (t p j ),F j 1 (t) + w j } for 0 t d j F j (d j ) for d j < t T (2)
21 Lecture 4 Scheduling 21 Single machine models: Weighted Number of Tardy Jobs 4 DPalgorithm for 1 w j U j 1. initialize F j (t) according to (1) 2. FOR j := 1 TO n DO 3. FOR t := 0 TO T DO 4. update F j (t) according to (2) 5. w j U j (OPT) = F n (d n )
22 Lecture 4 Scheduling 22 Single machine models: Weighted Number of Tardy Jobs 4 DPalgorithm for 1 w j U j 1. initialize F j (t) according to (1) 2. FOR j := 1 TO n DO 3. FOR t := 0 TO T DO 4. update F j (t) according to (2) 5. w j U j (OPT) = F n (d n ) complexity is O(n n j=1 p j ) thus, algorithm is pseudopolynomial
Scheduling Single Machine Scheduling. Tim Nieberg
Scheduling Single Machine Scheduling Tim Nieberg Single machine models Observation: for nonpreemptive problems and regular objectives, a sequence in which the jobs are processed is sufficient to describe
More informationClassification  Examples
Lecture 2 Scheduling 1 Classification  Examples 1 r j C max given: n jobs with processing times p 1,...,p n and release dates r 1,...,r n jobs have to be scheduled without preemption on one machine taking
More informationClassification  Examples 1 1 r j C max given: n jobs with processing times p 1,..., p n and release dates
Lecture 2 Scheduling 1 Classification  Examples 11 r j C max given: n jobs with processing times p 1,..., p n and release dates r 1,..., r n jobs have to be scheduled without preemption on one machine
More informationScheduling Shop Scheduling. Tim Nieberg
Scheduling Shop Scheduling Tim Nieberg Shop models: General Introduction Remark: Consider non preemptive problems with regular objectives Notation Shop Problems: m machines, n jobs 1,..., n operations
More informationScheduling Parallel Machine Scheduling. Tim Nieberg
Scheduling Parallel Machine Scheduling Tim Nieberg Problem P C max : m machines n jobs with processing times p 1,..., p n Problem P C max : m machines n jobs with processing times p 1,..., p { n 1 if job
More informationMinimum Makespan Scheduling
Minimum Makespan Scheduling Minimum makespan scheduling: Definition and variants Factor 2 algorithm for identical machines PTAS for identical machines Factor 2 algorithm for unrelated machines Martin Zachariasen,
More informationAn improved online algorithm for scheduling on two unrestrictive parallel batch processing machines
This is the PrePublished Version. An improved online algorithm for scheduling on two unrestrictive parallel batch processing machines Q.Q. Nong, T.C.E. Cheng, C.T. Ng Department of Mathematics, Ocean
More informationA binary search algorithm for a special case of minimizing the lateness on a single machine
Issue 3, Volume 3, 2009 45 A binary search algorithm for a special case of minimizing the lateness on a single machine Nodari Vakhania Abstract We study the problem of scheduling jobs with release times
More information8.1 Min Degree Spanning Tree
CS880: Approximations Algorithms Scribe: Siddharth Barman Lecturer: Shuchi Chawla Topic: Min Degree Spanning Tree Date: 02/15/07 In this lecture we give a local search based algorithm for the Min Degree
More information2.3 Scheduling jobs on identical parallel machines
2.3 Scheduling jobs on identical parallel machines There are jobs to be processed, and there are identical machines (running in parallel) to which each job may be assigned Each job = 1,,, must be processed
More informationA Branch and Bound Algorithm for Solving the Binary Bilevel Linear Programming Problem
A Branch and Bound Algorithm for Solving the Binary Bilevel Linear Programming Problem John Karlof and Peter Hocking Mathematics and Statistics Department University of North Carolina Wilmington Wilmington,
More information! Solve problem to optimality. ! Solve problem in polytime. ! Solve arbitrary instances of the problem. #approximation algorithm.
Approximation Algorithms 11 Approximation Algorithms Q Suppose I need to solve an NPhard problem What should I do? A Theory says you're unlikely to find a polytime algorithm Must sacrifice one of three
More informationScheduling. Open shop, job shop, flow shop scheduling. Related problems. Open shop, job shop, flow shop scheduling
Scheduling Basic scheduling problems: open shop, job shop, flow job The disjunctive graph representation Algorithms for solving the job shop problem Computational complexity of the job shop problem Open
More informationMultiRobot Task Scheduling
MultiRobot Task Scheduling Yu ("Tony") Zhang Lynne E. Parker Distributed Intelligence Laboratory Electrical Engineering and Computer Science Department University of Tennessee, Knoxville TN, USA IEEE
More informationIntroduction to Scheduling Theory
Introduction to Scheduling Theory Arnaud Legrand Laboratoire Informatique et Distribution IMAG CNRS, France arnaud.legrand@imag.fr November 8, 2004 1/ 26 Outline 1 Task graphs from outer space 2 Scheduling
More informationScheduling Jobs and Preventive Maintenance Activities on Parallel Machines
Scheduling Jobs and Preventive Maintenance Activities on Parallel Machines Maher Rebai University of Technology of Troyes Department of Industrial Systems 12 rue Marie Curie, 10000 Troyes France maher.rebai@utt.fr
More informationThe Goldberg Rao Algorithm for the Maximum Flow Problem
The Goldberg Rao Algorithm for the Maximum Flow Problem COS 528 class notes October 18, 2006 Scribe: Dávid Papp Main idea: use of the blocking flow paradigm to achieve essentially O(min{m 2/3, n 1/2 }
More information5 Scheduling. Operations Planning and Control
5 Scheduling Operations Planning and Control Some Background Machines (resources) are Machines process jobs (molding machine, x ray machine, server in a restaurant, computer ) Machine Environment Single
More informationDynamic TCP Acknowledgement: Penalizing Long Delays
Dynamic TCP Acknowledgement: Penalizing Long Delays Karousatou Christina Network Algorithms June 8, 2010 Karousatou Christina (Network Algorithms) Dynamic TCP Acknowledgement June 8, 2010 1 / 63 Layout
More informationComplexity Theory. IE 661: Scheduling Theory Fall 2003 Satyaki Ghosh Dastidar
Complexity Theory IE 661: Scheduling Theory Fall 2003 Satyaki Ghosh Dastidar Outline Goals Computation of Problems Concepts and Definitions Complexity Classes and Problems Polynomial Time Reductions Examples
More informationDynamic programming. Doctoral course Optimization on graphs  Lecture 4.1. Giovanni Righini. January 17 th, 2013
Dynamic programming Doctoral course Optimization on graphs  Lecture.1 Giovanni Righini January 1 th, 201 Implicit enumeration Combinatorial optimization problems are in general NPhard and we usually
More informationFrom Last Time: Remove (Delete) Operation
CSE 32 Lecture : More on Search Trees Today s Topics: Lazy Operations Run Time Analysis of Binary Search Tree Operations Balanced Search Trees AVL Trees and Rotations Covered in Chapter of the text From
More informationScheduling a sequence of tasks with general completion costs
Scheduling a sequence of tasks with general completion costs Francis Sourd CNRSLIP6 4, place Jussieu 75252 Paris Cedex 05, France Francis.Sourd@lip6.fr Abstract Scheduling a sequence of tasks in the acceptation
More informationApproximation Algorithms. Scheduling. Approximation algorithms. Scheduling jobs on a single machine
Approximation algorithms Approximation Algorithms Fast. Cheap. Reliable. Choose two. NPhard problems: choose 2 of optimal polynomial time all instances Approximation algorithms. Tradeoff between time
More informationChapter 11. 11.1 Load Balancing. Approximation Algorithms. Load Balancing. Load Balancing on 2 Machines. Load Balancing: Greedy Scheduling
Approximation Algorithms Chapter Approximation Algorithms Q. Suppose I need to solve an NPhard problem. What should I do? A. Theory says you're unlikely to find a polytime algorithm. Must sacrifice one
More informationApproximability of TwoMachine NoWait Flowshop Scheduling with Availability Constraints
Approximability of TwoMachine NoWait Flowshop Scheduling with Availability Constraints T.C. Edwin Cheng 1, and Zhaohui Liu 1,2 1 Department of Management, The Hong Kong Polytechnic University Kowloon,
More informationDuplicating and its Applications in Batch Scheduling
Duplicating and its Applications in Batch Scheduling Yuzhong Zhang 1 Chunsong Bai 1 Shouyang Wang 2 1 College of Operations Research and Management Sciences Qufu Normal University, Shandong 276826, China
More informationLecture Notes 12: Scheduling  Cont.
Online Algorithms 18.1.2012 Professor: Yossi Azar Lecture Notes 12: Scheduling  Cont. Scribe:Inna Kalp 1 Introduction In this Lecture we discuss 2 scheduling models. We review the scheduling over time
More informationTutorial 8. NPComplete Problems
Tutorial 8 NPComplete Problems Decision Problem Statement of a decision problem Part 1: instance description defining the input Part 2: question stating the actual yesorno question A decision problem
More informationApproximation Algorithms
Approximation Algorithms or: How I Learned to Stop Worrying and Deal with NPCompleteness Ong Jit Sheng, Jonathan (A0073924B) March, 2012 Overview Key Results (I) General techniques: Greedy algorithms
More informationOffline sorting buffers on Line
Offline sorting buffers on Line Rohit Khandekar 1 and Vinayaka Pandit 2 1 University of Waterloo, ON, Canada. email: rkhandekar@gmail.com 2 IBM India Research Lab, New Delhi. email: pvinayak@in.ibm.com
More information24. The Branch and Bound Method
24. The Branch and Bound Method It has serious practical consequences if it is known that a combinatorial problem is NPcomplete. Then one can conclude according to the present state of science that no
More informationSingle machine parallel batch scheduling with unbounded capacity
Workshop on Combinatorics and Graph Theory 21th, April, 2006 Nankai University Single machine parallel batch scheduling with unbounded capacity Yuan Jinjiang Department of mathematics, Zhengzhou University
More information! Solve problem to optimality. ! Solve problem in polytime. ! Solve arbitrary instances of the problem. !approximation algorithm.
Approximation Algorithms Chapter Approximation Algorithms Q Suppose I need to solve an NPhard problem What should I do? A Theory says you're unlikely to find a polytime algorithm Must sacrifice one of
More informationCompletion Time Scheduling and the WSRPT Algorithm
Completion Time Scheduling and the WSRPT Algorithm Bo Xiong, Christine Chung Department of Computer Science, Connecticut College, New London, CT {bxiong,cchung}@conncoll.edu Abstract. We consider the online
More informationGuessing Game: NPComplete?
Guessing Game: NPComplete? 1. LONGESTPATH: Given a graph G = (V, E), does there exists a simple path of length at least k edges? YES 2. SHORTESTPATH: Given a graph G = (V, E), does there exists a simple
More informationFindTheNumber. 1 FindTheNumber With Comps
FindTheNumber 1 FindTheNumber With Comps Consider the following twoperson game, which we call FindTheNumber with Comps. Player A (for answerer) has a number x between 1 and 1000. Player Q (for questioner)
More informationJUSTINTIME SCHEDULING WITH PERIODIC TIME SLOTS. Received December May 12, 2003; revised February 5, 2004
Scientiae Mathematicae Japonicae Online, Vol. 10, (2004), 431 437 431 JUSTINTIME SCHEDULING WITH PERIODIC TIME SLOTS Ondřej Čepeka and Shao Chin Sung b Received December May 12, 2003; revised February
More informationONLINE DEGREEBOUNDED STEINER NETWORK DESIGN. Sina Dehghani Saeed Seddighin Ali Shafahi Fall 2015
ONLINE DEGREEBOUNDED STEINER NETWORK DESIGN Sina Dehghani Saeed Seddighin Ali Shafahi Fall 2015 ONLINE STEINER FOREST PROBLEM An initially given graph G. s 1 s 2 A sequence of demands (s i, t i ) arriving
More informationSimultaneous Job Scheduling and Resource Allocation on Parallel Machines
Simultaneous Job Scheduling and Resource Allocation on Parallel Machines ZhiLong Chen* Department of Systems Engineering University of Pennsylvania Philadelphia, PA 191046315 zlchen@seas.upenn.edu February
More informationApplied Algorithm Design Lecture 5
Applied Algorithm Design Lecture 5 Pietro Michiardi Eurecom Pietro Michiardi (Eurecom) Applied Algorithm Design Lecture 5 1 / 86 Approximation Algorithms Pietro Michiardi (Eurecom) Applied Algorithm Design
More informationTwo Algorithms for the StudentProject Allocation Problem
Two Algorithms for the StudentProject Allocation Problem David J. Abraham 1, Robert W. Irving 2, and David F. Manlove 2 1 Computer Science Department, CarnegieMellon University, 5000 Forbes Ave, Pittsburgh
More informationA Numerical Study on the Wiretap Network with a Simple Network Topology
A Numerical Study on the Wiretap Network with a Simple Network Topology Fan Cheng and Vincent Tan Department of Electrical and Computer Engineering National University of Singapore Mathematical Tools of
More informationMapReduce and Distributed Data Analysis. Sergei Vassilvitskii Google Research
MapReduce and Distributed Data Analysis Google Research 1 Dealing With Massive Data 2 2 Dealing With Massive Data Polynomial Memory Sublinear RAM Sketches External Memory Property Testing 3 3 Dealing With
More informationAperiodic Task Scheduling
Aperiodic Task Scheduling JianJia Chen (slides are based on Peter Marwedel) TU Dortmund, Informatik 12 Germany Springer, 2010 2014 年 11 月 19 日 These slides use Microsoft clip arts. Microsoft copyright
More informationProtein Threading. Bioinformatics 404 DIKU Spring 2006
Protein Threading Bioinformatics 404 DIKU Spring 2006 Agenda Protein Threading in general Branch and bound Refresh Protein Threading with B&B Evaluation and optimization Performance Engbo Jørgensen & Leon
More information8.1 Makespan Scheduling
600.469 / 600.669 Approximation Algorithms Lecturer: Michael Dinitz Topic: Dynamic Programing: MinMakespan and Bin Packing Date: 2/19/15 Scribe: Gabriel Kaptchuk 8.1 Makespan Scheduling Consider an instance
More informationList Scheduling in Order of αpoints on a Single Machine
List Scheduling in Order of αpoints on a Single Machine Martin Skutella Fachbereich Mathematik, Universität Dortmund, D 4422 Dortmund, Germany martin.skutella@unidortmund.de http://www.mathematik.unidortmund.de/
More informationPLANNING AND SCHEDULING
PLANNING AND SCHEDULING Andrew Kusiak 2139 Seamans Center Iowa City, Iowa 522421527 Tel: 319335 5934 Fax: 319335 5669 andrewkusiak@uiowa.edu http://www.icaen.uiowa.edu/~ankusiak Forecasting Balancing
More informationThe Conference Call Search Problem in Wireless Networks
The Conference Call Search Problem in Wireless Networks Leah Epstein 1, and Asaf Levin 2 1 Department of Mathematics, University of Haifa, 31905 Haifa, Israel. lea@math.haifa.ac.il 2 Department of Statistics,
More informationAlgorithm Design and Analysis
Algorithm Design and Analysis LECTURE 27 Approximation Algorithms Load Balancing Weighted Vertex Cover Reminder: Fill out SRTEs online Don t forget to click submit Sofya Raskhodnikova 12/6/2011 S. Raskhodnikova;
More informationClustering and scheduling maintenance tasks over time
Clustering and scheduling maintenance tasks over time Per Kreuger 20080429 SICS Technical Report T2008:09 Abstract We report results on a maintenance scheduling problem. The problem consists of allocating
More informationResource Allocation and Scheduling
Lesson 3: Resource Allocation and Scheduling DEIS, University of Bologna Outline Main Objective: joint resource allocation and scheduling problems In particular, an overview of: Part 1: Introduction and
More informationOnline Scheduling for Cloud Computing and Different Service Levels
2012 IEEE 201226th IEEE International 26th International Parallel Parallel and Distributed and Distributed Processing Processing Symposium Symposium Workshops Workshops & PhD Forum Online Scheduling for
More informationLoad balancing of temporary tasks in the l p norm
Load balancing of temporary tasks in the l p norm Yossi Azar a,1, Amir Epstein a,2, Leah Epstein b,3 a School of Computer Science, Tel Aviv University, Tel Aviv, Israel. b School of Computer Science, The
More informationIn Search of Influential Event Organizers in Online Social Networks
In Search of Influential Event Organizers in Online Social Networks ABSTRACT Kaiyu Feng 1,2 Gao Cong 2 Sourav S. Bhowmick 2 Shuai Ma 3 1 LILY, Interdisciplinary Graduate School. Nanyang Technological University,
More informationA class of online scheduling algorithms to minimize total completion time
A class of online scheduling algorithms to minimize total completion time X. Lu R.A. Sitters L. Stougie Abstract We consider the problem of scheduling jobs online on a single machine and on identical
More informationReal Time Scheduling Basic Concepts. Radek Pelánek
Real Time Scheduling Basic Concepts Radek Pelánek Basic Elements Model of RT System abstraction focus only on timing constraints idealization (e.g., zero switching time) Basic Elements Basic Notions task
More information1 Approximating Set Cover
CS 05: Algorithms (Grad) Feb 224, 2005 Approximating Set Cover. Definition An Instance (X, F ) of the setcovering problem consists of a finite set X and a family F of subset of X, such that every elemennt
More information6.852: Distributed Algorithms Fall, 2009. Class 2
.8: Distributed Algorithms Fall, 009 Class Today s plan Leader election in a synchronous ring: Lower bound for comparisonbased algorithms. Basic computation in general synchronous networks: Leader election
More informationGRAPH THEORY LECTURE 4: TREES
GRAPH THEORY LECTURE 4: TREES Abstract. 3.1 presents some standard characterizations and properties of trees. 3.2 presents several different types of trees. 3.7 develops a counting method based on a bijection
More informationAnswers to some of the exercises.
Answers to some of the exercises. Chapter 2. Ex.2.1 (a) There are several ways to do this. Here is one possibility. The idea is to apply the kcenter algorithm first to D and then for each center in D
More information5.1 Bipartite Matching
CS787: Advanced Algorithms Lecture 5: Applications of Network Flow In the last lecture, we looked at the problem of finding the maximum flow in a graph, and how it can be efficiently solved using the FordFulkerson
More informationReihe Informatik 11 / 1996 Constructing Optimal Bushy Processing Trees for Join Queries is NPhard Wolfgang Scheufele Guido Moerkotte 1 Constructing Optimal Bushy Processing Trees for Join Queries is NPhard
More informationR u t c o r Research R e p o r t. A Method to Schedule Both Transportation and Production at the Same Time in a Special FMS.
R u t c o r Research R e p o r t A Method to Schedule Both Transportation and Production at the Same Time in a Special FMS Navid Hashemian a Béla Vizvári b RRR 32011, February 21, 2011 RUTCOR Rutgers
More informationProject and Production Management Prof. Arun Kanda Department of Mechanical Engineering Indian Institute of Technology, Delhi
Project and Production Management Prof. Arun Kanda Department of Mechanical Engineering Indian Institute of Technology, Delhi Lecture  15 Limited Resource Allocation Today we are going to be talking about
More informationBest Monotone Degree Bounds for Various Graph Parameters
Best Monotone Degree Bounds for Various Graph Parameters D. Bauer Department of Mathematical Sciences Stevens Institute of Technology Hoboken, NJ 07030 S. L. Hakimi Department of Electrical and Computer
More informationTU e. Advanced Algorithms: experimentation project. The problem: load balancing with bounded lookahead. Input: integer m 2: number of machines
The problem: load balancing with bounded lookahead Input: integer m 2: number of machines integer k 0: the lookahead numbers t 1,..., t n : the job sizes Problem: assign jobs to machines machine to which
More informationFairness in Routing and Load Balancing
Fairness in Routing and Load Balancing Jon Kleinberg Yuval Rabani Éva Tardos Abstract We consider the issue of network routing subject to explicit fairness conditions. The optimization of fairness criteria
More informationLecture 7: Approximation via Randomized Rounding
Lecture 7: Approximation via Randomized Rounding Often LPs return a fractional solution where the solution x, which is supposed to be in {0, } n, is in [0, ] n instead. There is a generic way of obtaining
More informationThe StudentProject Allocation Problem
The StudentProject Allocation Problem David J. Abraham, Robert W. Irving, and David F. Manlove Department of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK Email: {dabraham,rwi,davidm}@dcs.gla.ac.uk.
More informationMeasuring Rationality with the Minimum Cost of Revealed Preference Violations. Mark Dean and Daniel Martin. Online Appendices  Not for Publication
Measuring Rationality with the Minimum Cost of Revealed Preference Violations Mark Dean and Daniel Martin Online Appendices  Not for Publication 1 1 Algorithm for Solving the MASP In this online appendix
More informationIntroduction to Algorithms Review information for Prelim 1 CS 4820, Spring 2010 Distributed Wednesday, February 24
Introduction to Algorithms Review information for Prelim 1 CS 4820, Spring 2010 Distributed Wednesday, February 24 The final exam will cover seven topics. 1. greedy algorithms 2. divideandconquer algorithms
More informationScheduling Realtime Tasks: Algorithms and Complexity
Scheduling Realtime Tasks: Algorithms and Complexity Sanjoy Baruah The University of North Carolina at Chapel Hill Email: baruah@cs.unc.edu Joël Goossens Université Libre de Bruxelles Email: joel.goossens@ulb.ac.be
More informationVirtual Machine Resource Allocation for Service Hosting on Heterogeneous Distributed Platforms
Virtual Machine Resource Allocation for Service Hosting on Heterogeneous Distributed Platforms Mark Stillwell, Frédéric Vivien INRIA, France Email: mark.stillwell@inrialpes.fr, Frederic.Vivien@inria.fr
More informationNear Optimal Solutions
Near Optimal Solutions Many important optimization problems are lacking efficient solutions. NPComplete problems unlikely to have polynomial time solutions. Good heuristics important for such problems.
More informationChapter 6: Episode discovery process
Chapter 6: Episode discovery process Algorithmic Methods of Data Mining, Fall 2005, Chapter 6: Episode discovery process 1 6. Episode discovery process The knowledge discovery process KDD process of analyzing
More informationA Linear Programming Based Method for Job Shop Scheduling
A Linear Programming Based Method for Job Shop Scheduling Kerem Bülbül Sabancı University, Manufacturing Systems and Industrial Engineering, OrhanlıTuzla, 34956 Istanbul, Turkey bulbul@sabanciuniv.edu
More informationOnline and Offline Selling in Limit Order Markets
Online and Offline Selling in Limit Order Markets Kevin L. Chang 1 and Aaron Johnson 2 1 Yahoo Inc. klchang@yahooinc.com 2 Yale University ajohnson@cs.yale.edu Abstract. Completely automated electronic
More informationConstraintBased Scheduling: A Tutorial
ConstraintBased Scheduling: A Tutorial Claude Le Pape ILOG S. A. 9, rue de Verdun F94253 Gentilly Cedex Tel: +33 1 49 08 29 67 Fax: +33 1 49 08 35 10 Email: clepape@ilog.fr Given a set of resources with
More informationSolving Systems of Linear Equations
LECTURE 5 Solving Systems of Linear Equations Recall that we introduced the notion of matrices as a way of standardizing the expression of systems of linear equations In today s lecture I shall show how
More informationCS711008Z Algorithm Design and Analysis
CS711008Z Algorithm Design and Analysis Lecture 7 Binary heap, binomial heap, and Fibonacci heap 1 Dongbo Bu Institute of Computing Technology Chinese Academy of Sciences, Beijing, China 1 The slides were
More informationDynamic programming formulation
1.24 Lecture 14 Dynamic programming: Job scheduling Dynamic programming formulation To formulate a problem as a dynamic program: Sort by a criterion that will allow infeasible combinations to be eli minated
More informationCompetitive Analysis of QoS Networks
Competitive Analysis of QoS Networks What is QoS? The art of performance analysis What is competitive analysis? Example: Scheduling with deadlines Example: Smoothing realtime streams Example: Overflow
More informationSteiner Tree Approximation via IRR. Randomized Rounding
Steiner Tree Approximation via Iterative Randomized Rounding Graduate Program in Logic, Algorithms and Computation μπλ Network Algorithms and Complexity June 18, 2013 Overview 1 Introduction Scope Related
More informationScheduling and (Integer) Linear Programming
Scheduling and (Integer) Linear Programming Christian Artigues LAAS  CNRS & Université de Toulouse, France artigues@laas.fr Master Class CPAIOR 2012  Nantes Christian Artigues Scheduling and (Integer)
More informationA Constraint Programming based Column Generation Approach to Nurse Rostering Problems
Abstract A Constraint Programming based Column Generation Approach to Nurse Rostering Problems Fang He and Rong Qu The Automated Scheduling, Optimisation and Planning (ASAP) Group School of Computer Science,
More information9th MaxPlanck Advanced Course on the Foundations of Computer Science (ADFOCS) PrimalDual Algorithms for Online Optimization: Lecture 1
9th MaxPlanck Advanced Course on the Foundations of Computer Science (ADFOCS) PrimalDual Algorithms for Online Optimization: Lecture 1 Seffi Naor Computer Science Dept. Technion Haifa, Israel Introduction
More informationVirtual Time and Timeout in ClientServer Networks
Virtual Time and Timeout in ClientServer Networks Jayadev Misra July 13, 2011 Contents 1 Introduction 2 1.1 Background.............................. 2 1.1.1 Causal Model of Virtual Time...............
More information1.1 Related work For nonpreemptive scheduling on uniformly related machines the rst algorithm with a constant competitive ratio was given by Aspnes e
A Lower Bound for OnLine Scheduling on Uniformly Related Machines Leah Epstein Jir Sgall September 23, 1999 lea@math.tau.ac.il, Department of Computer Science, TelAviv University, Israel; sgall@math.cas.cz,
More informationLecture 1: Course overview, circuits, and formulas
Lecture 1: Course overview, circuits, and formulas Topics in Complexity Theory and Pseudorandomness (Spring 2013) Rutgers University Swastik Kopparty Scribes: John Kim, Ben Lund 1 Course Information Swastik
More informationKCover of Binary sequence
KCover of Binary sequence Prof Amit Kumar Prof Smruti Sarangi Sahil Aggarwal Swapnil Jain Given a binary sequence, represent all the 1 s in it using at most k covers, minimizing the total length of all
More informationBranchandPrice Approach to the Vehicle Routing Problem with Time Windows
TECHNISCHE UNIVERSITEIT EINDHOVEN BranchandPrice Approach to the Vehicle Routing Problem with Time Windows Lloyd A. Fasting May 2014 Supervisors: dr. M. Firat dr.ir. M.A.A. Boon J. van Twist MSc. Contents
More informationA Beam Search Heuristic for MultiMode Single Resource Constrained Project Scheduling
A Beam Search Heuristic for MultiMode Single Resource Constrained Project Scheduling Chuda Basnet Department of Management Systems The University of Waikato Private Bag 3105 Hamilton chuda@waikato.ac.nz
More informationCounting Falsifying Assignments of a 2CF via Recurrence Equations
Counting Falsifying Assignments of a 2CF via Recurrence Equations Guillermo De Ita Luna, J. Raymundo Marcial Romero, Fernando Zacarias Flores, Meliza Contreras González and Pedro Bello López Abstract
More informationLecture 4 Online and streaming algorithms for clustering
CSE 291: Geometric algorithms Spring 2013 Lecture 4 Online and streaming algorithms for clustering 4.1 Online kclustering To the extent that clustering takes place in the brain, it happens in an online
More informationModern Optimization Methods for Big Data Problems MATH11146 The University of Edinburgh
Modern Optimization Methods for Big Data Problems MATH11146 The University of Edinburgh Peter Richtárik Week 3 Randomized Coordinate Descent With Arbitrary Sampling January 27, 2016 1 / 30 The Problem
More informationTopic: Greedy Approximations: Set Cover and Min Makespan Date: 1/30/06
CS880: Approximations Algorithms Scribe: Matt Elder Lecturer: Shuchi Chawla Topic: Greedy Approximations: Set Cover and Min Makespan Date: 1/30/06 3.1 Set Cover The Set Cover problem is: Given a set of
More informationNotes on Factoring. MA 206 Kurt Bryan
The General Approach Notes on Factoring MA 26 Kurt Bryan Suppose I hand you n, a 2 digit integer and tell you that n is composite, with smallest prime factor around 5 digits. Finding a nontrivial factor
More informationArithmetic Coding: Introduction
Data Compression Arithmetic coding Arithmetic Coding: Introduction Allows using fractional parts of bits!! Used in PPM, JPEG/MPEG (as option), Bzip More time costly than Huffman, but integer implementation
More information