Cross-Monotonic Multicast
|
|
- Easter Cameron
- 5 years ago
- Views:
Transcription
1 Cross-Monotonic Multicast Zongpeng Li Department of Computer Science University of Calgary April 17,
2 Multicast Multicast models one-to-many data dissemination in a computer network Example: live Video Streaming on the Internet 2
3 Network: G = (V, E) Min-Cost Multicast Link capacities: c : E Q + Unit flow cost on each link: w : E Q + Each receiver should receive data at rate d Flow rate on each link during routing: f : E Q + Total routing cost: e E w(e)f(e) Goal: compute min-cost multicast flow f that achieves multicast rate d 3
4 Using multicast trees: Min-Cost Multicast w(e) = 1, e (every tree link has a cost 1.0 for a unit flow on it) For throughput d = 1: minimum tree has cost 5 Q: how to share the cost among the receivers? 4
5 with network coding: Min-Cost Multicast 0.5 b b b a+b a+b a a a+b 0.5 a Every link flow has rate 0.5. Total cost e w(e)f(e) = = 4.5. Q: how to share the cost among the receivers? 5
6 Min-Cost Multicast A multicast rate d is feasible in a directed network if and only if it is feasible as a unicast rate to every multicast receiver independently. [Ahlswede et al., IT 2000] Optimal multicast can be modelled using LP [Lun et al., INFOCOM 2005][Li et al., INFOCOM 2005] Network flow LPs with extra constraints Tailored solution algorithms, efficient, distributed Now: cooperative environment selfish/strategic receivers 6
7 Game Theory Aspects of Computer Networks Classic network protocol design assume cooperative and altruistic user behavior e.g., TCP congestion control Not always safe Network game theory face the reality: strategic network users selfish network traffic market-driven network infrastructure Network operators, protocol designers : induce desired behaviors from selfish network agents, for the well-being of the entire network 7
8 The Multicast Game Selfish Traffic [Li, IEEE INFOCOM 2007] Shadow prices from dual LP Shadow price based costing sharing and link tolls Every min-cost multicast flow can be enforced Selfish Users [Li, IEEE INFOCOM 2008] You are here! Selfish Links Induce truthful cost reports from links Apply the Vickrey-Clarke-Groves Mechanism Efficient computation of Vickrey prices, ongoing work 8
9 The Background Story Potential set of users, T (think of Internet media streaming) Each with private valuation of the multicast service For each subset of potential users A T Compute multicast routing f A f A has cost f A Share the cost among users in A Which set A to serve? How to share the cost? We really want users to tell us their true valuations! 9
10 Strategyproof Multicast Strategyproof mechanisms Telling the truth is for the best interest of a user herself dominant strategy Group-strategyproof mechanisms Further being robust against collusion The key: Cross-Monotonic Cost Sharing [Moulin,Shenker, 2001] 10
11 Cross-Monotonicity A B AC AB ABC ABE Travel down any of these Criss-Crossing routes, a node s cost share should be monotonically decreasing. 11
12 From C-S to Group-stragetyproofness The simultaneous Cournot Tatonnement [Moulin, 1982]: 1. Start with full set T 2. Ask each user: how much do you wish to pay for the service? 3. Compute C-S cost share for each user 4. Exclude a user from the service set if her willingness to pay is under the computed cost share 5. Loop to 2., till convergence 6. Serve users in the converged set 12
13 Cross-Monotonic Optimal Cross-Monotonic Multicast min-cost multicast routing Budget Balanced Recover routing cost from user payments In-Core Users motivated to participate No-Positive Transfers Never pay someone to participate Efficient Maximize net social utility 13
14 The hardness of the problem OPT + C-S + B-B = hard Submodular costs always have C-S sharing schemes Multicast cost is not submodular Fundamental conflict between primal optimality and dual smoothness 14
15 The hardness of the problem OPT + C-S + B-B = hard OPT + C-S = easy Use optimal routing computed by LP Every user always pays 0 OPT + B-B = easy Use optimal routing computed by LP Split link flow cost evenly among receivers using it C-S + B-B = easy Restrict route selection to one base tree For each subset of users, use a corresponding subtree Split link flow cost evenly among receivers using it 15
16 The hardness of the problem OPT + C-S + B-B = hard Direct LP dual is not smooth Local sharing is not in-core S 4 4 S 4 T 1 T 3 2 T 1 T
17 Directed Networks, positive result A 1 k-budget-balanced, optimal, cross-monotonic multicast scheme For any A T : (1) Solve min-cost multicast LP, let f A be the optimal solution (2) for each receiver u in A: Solve min-cost S u unicast flow f u (3) Route multicast flows as specified in f A (4) Let each u A pay y A (u) = f u A 17
18 Directed Networks, negative result No optimal, cross-monotonic, ( 2 k + ɛ)-budget-balanced scheme, ɛ > 0 h nodes in each partite... T 11 T 21 T 12 T l-partite T l 2 T 1h T 2h T lh T (j 1,j 2,..j l ) [1..h] l : l1 T 1j 1 δ δ 1 T 2j 2 S δ... T ljl k: total number of potential multicast receivers k = hl 18
19 Probabilistic proof Directed Networks, negative result randomly pick service set A = A 1 A 2, show expected B-B factor is low A 1 : uniformly randomly pick a partite i A 2 : j i, uniformly randomly pick a user in partite j E A ( T ij A y A(T ij )) = 1 E A ( T ij A 1 y A (T ij )) + E A ( T ij A 2 y A (T ij )) 2 he A2,T ij A 1 (y A2 +T ij (T ij )) +E A2,T ij A 1 ( T ij A 2 y A2 +T ij (T ij )) = 3 h( 1 l + δ) + (l 1)( 1 l + δ) = 4 (h + l 1)( 1 l + δ) 2 k 19
20 Undirected Networks, Negative Result No optimal, cross-monotonic, ( ɛ)-budget-balanced scheme, ɛ > 0 (j 1,j 2,..j l ) [1..h] l : T 1j 1 1 S 1 1 T lj l 1... T 2j 2 20
21 Undirected Networks, Positive Result A k+1 (2k+1)ζ -budget-balanced, optimal, cross-monotonic multicast scheme ζ: the coding advantage proven: 2 [Li et al., CISS 2004] contrived networks: 8 7 random networks: always 1 believed: always close to 1 k+1 (2k+1)ζ should be close to 1 2, almost tight bound Idea: smooth dual growing, from primal-dual algorithm design 21
22 The Complexity for Maximum Budget-Balance Input: multicast network network topology link capacities and costs sender, potential receivers Output: maximum b-b ratio for optimal and crossmonotonic multicast schemes Brute-force solution: two-stage linear optimization (solve large # of LPs) NP-Hard? 22
23 Maximum B-B: two-stage linear optimization Stage 1: A T, compute f A: Minimize Subject to: uv w( uv)f( uv) v N (u) f i( uv) = v N (u) f i( vu) f i ( T i S) = d f i ( uv) f( uv) c( uv) T i A, u T i A T i A, uv f i ( uv), f( uv) 0 T i A, uv 23
24 Maximum B-B: two-stage linear optimization Stage 2: compute maximum b-b ratio x: Maximize x Subject to: { x f A u A y A(u) f A A T y A (u) y B (u) u B A T x, y A (u) 0 u A T 24
Cross-Monotonic Multicast
This full text paper was peer reviewed at the direction of IEEE Communications ociety subject matter experts for publication in the IEEE INFOCOM 008 proceedings. Cross-Monotonic Multicast Zongpeng Li Department
More informationA BGP-Based Mechanism for Lowest-Cost Routing
A BGP-Based Mechanism for Lowest-Cost Routing Joan Feigenbaum, Christos Papadimitriou, Rahul Sami, Scott Shenker Presented by: Tony Z.C Huang Theoretical Motivation Internet is comprised of separate administrative
More informationShadow Prices vs. Vickrey Prices in Multipath Routing
hadow Prices vs. Vickrey Prices in Multipath Routing Parthasarathy Ramanujam, Zongpeng Li, Lisa Higham Department of Computer cience, University of Calgary {pkramanu, zongpeng, higham}@ucalgary.ca Abstract
More informationProject: A survey and Critique on Algorithmic Mechanism Design
Project: A survey and Critique on Algorithmic Mechanism Design 1 Motivation One can think of many systems where agents act according to their self interest. Therefore, when we are in the process of designing
More informationThe Index Coding Problem: A Game-Theoretical Perspective
The Index Coding Problem: A Game-Theoretical Perspective Yu-Pin Hsu, I-Hong Hou, and Alex Sprintson Department of Electrical and Computer Engineering Texas A&M University {yupinhsu, ihou, spalex}@tamu.edu
More informationApproximation Techniques for Utilitarian Mechanism Design
Approximation Techniques for Utilitarian Mechanism Design Department of Computer Science RWTH Aachen Germany joint work with Patrick Briest and Piotr Krysta 05/16/2006 1 Introduction to Utilitarian Mechanism
More informationCombinatorial Auctions: A Survey by de Vries and Vohra
Combinatorial Auctions: A Survey by de Vries and Vohra Ashwin Ganesan EE228, Fall 2003 September 30, 2003 1 Combinatorial Auctions Problem N is the set of bidders, M is the set of objects b j (S) is the
More informationGroup Strategyproof Mechanisms via Primal-Dual Algorithms. Key Points to Discuss
Group Strategyproof Mechanisms via Primal-Dual Algorithms Martin Pál and Éva Tardos (2003) Key Points to Discuss The Cost-Sharing Problem Metric Facility Location Single Source Rent-or-Buy Definition of
More informationThe Multiple Unicast Network Coding Conjecture. and a geometric framework for studying it
The Multiple Unicast Network Coding Conjecture and a geometric framework for studying it Tang Xiahou, Chuan Wu, Jiaqing Huang, Zongpeng Li June 30 2012 1 Multiple Unicast: Network Coding = Routing? Undirected
More informationMechanism Design for Multicast Cost Sharing in Wireless Networks
Mechanism Design for Multicast Cost Sharing in Wireless Networks April 24, 2008 1 Introduction A large amount of Internet applications, involve multiple clients getting service from a single server. Unicast
More informationLecture Overview. 2 Shortest s t path. 2.1 The LP. 2.2 The Algorithm. COMPSCI 530: Design and Analysis of Algorithms 11/14/2013
COMPCI 530: Design and Analysis of Algorithms 11/14/2013 Lecturer: Debmalya Panigrahi Lecture 22 cribe: Abhinandan Nath 1 Overview In the last class, the primal-dual method was introduced through the metric
More informationOn Benefits of Network Coding in Bidirected Networks and Hyper-networks
On Benefits of Network Coding in Bidirected Networks and Hyper-networks Zongpeng Li University of Calgary / INC, CUHK December 1 2011, at UNSW Joint work with: Xunrui Yin, Xin Wang, Jin Zhao, Xiangyang
More informationCSE 417 Network Flows (pt 3) Modeling with Min Cuts
CSE 417 Network Flows (pt 3) Modeling with Min Cuts Reminders > HW6 is due on Friday start early bug fixed on line 33 of OptimalLineup.java: > change true to false Review of last two lectures > Defined
More informationWhy VCG auctions can hardly be applied to the pricing of inter-domain and ad hoc networks
Why VCG auctions can hardly be applied to the pricing of inter-domain and ad hoc networks Patrick Maillé GET/ENST Bretagne 2, rue de la Châtaigneraie - CS 17607 35576 Cesson Sévigné Cedex - FRANCE Email:
More informationMin-Cost Multicast Networks in Euclidean Space
Xunrui Yin, Yan Wang, Xin Wang, Xiangyang Xue 1 Zongpeng Li 23 1 Fudan University Shanghai, China 2 University of Calgary Alberta, Canada 3 Institute of Network Coding, Chinese University of Hong Kong,
More informationMin-Cost Multicast Networks in Euclidean Space
Min-Cost Multicast Networks in Euclidean Space Xunrui Yin, Yan Wang, Xin Wang, Xiangyang Xue School of Computer Science Fudan University {09110240030,11110240029,xinw,xyxue}@fudan.edu.cn Zongpeng Li Dept.
More informationApproximation Algorithms: The Primal-Dual Method. My T. Thai
Approximation Algorithms: The Primal-Dual Method My T. Thai 1 Overview of the Primal-Dual Method Consider the following primal program, called P: min st n c j x j j=1 n a ij x j b i j=1 x j 0 Then the
More informationIntroduction to algorithmic mechanism design
Introduction to algorithmic mechanism design Elias Koutsoupias Department of Computer Science University of Oxford EWSCS 2014 March 5-7, 2014 Part I Game Theory and Computer Science Why Game Theory and
More informationMechanisms for Internet Routing: A Study 1
Mechanisms for Internet Routing: A Study 1 Aditya Akella Shuchi Chawla 3 Srini Seshan 4 July, 00 CMU-CS-0-163 School of Computer Science Carnegie Mellon University Pittsburgh, PA 1513 Abstract In this
More informationDistributed Algorithmic Mechanism Design for Network Problems
Distributed Algorithmic Mechanism Design for Network Problems Rahul Sami Ph.D. Dissertation Defense Advisor: Joan Feigenbaum Committee: Ravindran Kannan Arvind Krishnamurthy Scott Shenker (ICSI & Berkeley)
More informationMechanism Design in Large Congestion Games
Mechanism Design in Large Congestion Games Ryan Rogers, Aaron Roth, Jonathan Ullman, and Steven Wu July 22, 2015 Routing Game l e (y) Routing Game Routing Game A routing game G is defined by Routing Game
More informationCS 473: Algorithms. Ruta Mehta. Spring University of Illinois, Urbana-Champaign. Ruta (UIUC) CS473 1 Spring / 36
CS 473: Algorithms Ruta Mehta University of Illinois, Urbana-Champaign Spring 2018 Ruta (UIUC) CS473 1 Spring 2018 1 / 36 CS 473: Algorithms, Spring 2018 LP Duality Lecture 20 April 3, 2018 Some of the
More informationAbsorbing Random walks Coverage
DATA MINING LECTURE 3 Absorbing Random walks Coverage Random Walks on Graphs Random walk: Start from a node chosen uniformly at random with probability. n Pick one of the outgoing edges uniformly at random
More informationAbsorbing Random walks Coverage
DATA MINING LECTURE 3 Absorbing Random walks Coverage Random Walks on Graphs Random walk: Start from a node chosen uniformly at random with probability. n Pick one of the outgoing edges uniformly at random
More informationMathematical Tools for Engineering and Management
Mathematical Tools for Engineering and Management Lecture 8 8 Dec 0 Overview Models, Data and Algorithms Linear Optimization Mathematical Background: Polyhedra, Simplex-Algorithm Sensitivity Analysis;
More informationDistributed Mechanism Design and Computer Security
Distributed Mechanism Design and Computer Security John Mitchell Vanessa Teague Stanford University Acknowledgements: J. Feigenbaum, R. Sami, A. Scedrov General problem Want to design distributed systems
More informationNetwork Improvement for Equilibrium Routing
Network Improvement for Equilibrium Routing UMANG BHASKAR University of Waterloo and KATRINA LIGETT California Institute of Technology Routing games are frequently used to model the behavior of traffic
More informationA List Heuristic for Vertex Cover
A List Heuristic for Vertex Cover Happy Birthday Vasek! David Avis McGill University Tomokazu Imamura Kyoto University Operations Research Letters (to appear) Online: http://cgm.cs.mcgill.ca/ avis revised:
More informationImproving network robustness
Improving network robustness using distance-based graph measures Sander Jurgens November 10, 2014 dr. K.A. Buchin Eindhoven University of Technology Department of Math and Computer Science dr. D.T.H. Worm
More informationBroadcast in Ad hoc Wireless Networks with Selfish Nodes: A Bayesian Incentive Compatibility Approach
Broadcast in Ad hoc Wireless Networks with Selfish Nodes: A Bayesian Incentive Compatibility Approach N. Rama Suri Research Student, Electronic Enterprises Laboratory, Dept. of Computer Science and Automation,
More informationApproximation Algorithms
Approximation Algorithms Prof. Tapio Elomaa tapio.elomaa@tut.fi Course Basics A 4 credit unit course Part of Theoretical Computer Science courses at the Laboratory of Mathematics There will be 4 hours
More informationAutonomous Nodes and Distributed Mechanisms
Autonomous Nodes and Distributed Mechanisms John C. Mitchell 1 and Vanessa Teague 2 1 Stanford University, Stanford CA 94305, USA, mitchell@cs.stanford.edu 2 Stanford University, Stanford CA 94305, USA,
More informationLecture 2. 1 Introduction. 2 The Set Cover Problem. COMPSCI 632: Approximation Algorithms August 30, 2017
COMPSCI 632: Approximation Algorithms August 30, 2017 Lecturer: Debmalya Panigrahi Lecture 2 Scribe: Nat Kell 1 Introduction In this lecture, we examine a variety of problems for which we give greedy approximation
More informationUsing VCG based Designing and Electing Secure Leader Model for Intrusion Detection System in Manet
International Journal of Wireless Networks and Communications. ISSN 0975-6507 Volume 4, Number 1 (2012), pp. 71-81 International Research Publication House http://www.irphouse.com Using VCG based Designing
More information1 Overview. 2 Applications of submodular maximization. AM 221: Advanced Optimization Spring 2016
AM : Advanced Optimization Spring 06 Prof. Yaron Singer Lecture 0 April th Overview Last time we saw the problem of Combinatorial Auctions and framed it as a submodular maximization problem under a partition
More informationWHILE traditional information transmission in a data network. Bounding the Coding Advantage of Combination Network Coding in Undirected Networks
570 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 58, NO. 2, FEBRUARY 2012 Bounding the Coding Advantage of Combination Network Coding in Undirected Networks Shreya Maheshwar, Zongpeng Li, Member, IEEE,
More informationCS Foundations of Communication Complexity
CS 2429 - Foundations of Communication Complexity Lecturer: Toniann Pitassi 1 Applications of Communication Complexity There are many applications of communication complexity. In our survey article, The
More informationCSE 417 Network Flows (pt 4) Min Cost Flows
CSE 417 Network Flows (pt 4) Min Cost Flows Reminders > HW6 is due Monday Review of last three lectures > Defined the maximum flow problem find the feasible flow of maximum value flow is feasible if it
More information6 Randomized rounding of semidefinite programs
6 Randomized rounding of semidefinite programs We now turn to a new tool which gives substantially improved performance guarantees for some problems We now show how nonlinear programming relaxations can
More informationReliable IPTV Transport Network. Dongmei Wang AT&T labs-research Florham Park, NJ
Reliable IPTV Transport Network Dongmei Wang AT&T labs-research Florham Park, NJ Page 2 Outline Background on IPTV Motivations for IPTV Technical challenges How to design a reliable IPTV backbone network
More informationCollege of Computer & Information Science Fall 2007 Northeastern University 14 September 2007
College of Computer & Information Science Fall 2007 Northeastern University 14 September 2007 CS G399: Algorithmic Power Tools I Scribe: Eric Robinson Lecture Outline: Linear Programming: Vertex Definitions
More informationAlgorithm Design and Analysis
Algorithm Design and Analysis LECTURE 29 Approximation Algorithms Load Balancing Weighted Vertex Cover Reminder: Fill out SRTEs online Don t forget to click submit Sofya Raskhodnikova 12/7/2016 Approximation
More informationVCG Auction-based Bandwidth Allocation with Network Coding in Wireless Networks
VCG Auction-based Bandwidth Allocation with Network Coding in Wireless Networks PIRIYA CHAIKIJWATANA TAKUJI TACHIBANA Nara Institute of Science and Technology Graduate School of Information Science 8916-5
More informationNash equilibria in Voronoi Games on Graphs
Nash equilibria in Voronoi Games on Graphs Christoph Dürr, Nguyễn Kim Thắng (Ecole Polytechnique) ESA, Eilat October 07 Plan Motivation : Study the interaction between selfish agents on Internet k players,
More informationCSc 545 Lecture topic: The Criss-Cross method of Linear Programming
CSc 545 Lecture topic: The Criss-Cross method of Linear Programming Wanda B. Boyer University of Victoria November 21, 2012 Presentation Outline 1 Outline 2 3 4 Please note: I would be extremely grateful
More informationSpectrum Auction Framework for Access Allocation in Cognitive Radio Networks
University of Pennsylvania ScholarlyCommons Departmental Papers (ESE) Department of Electrical & Systems Engineering 12-17-2010 Spectrum Auction Framework for Access Allocation in Cognitive Radio Networks
More informationNash Equilibrium Load Balancing
Nash Equilibrium Load Balancing Computer Science Department Collaborators: A. Kothari, C. Toth, Y. Zhou Load Balancing A set of m servers or machines. A set of n clients or jobs. Each job can be run only
More informationIntroduction to Algorithms / Algorithms I Lecturer: Michael Dinitz Topic: Algorithms and Game Theory Date: 12/3/15
600.363 Introduction to Algorithms / 600.463 Algorithms I Lecturer: Michael Dinitz Topic: Algorithms and Game Theory Date: 12/3/15 25.1 Introduction Today we re going to spend some time discussing game
More informationRandomized rounding of semidefinite programs and primal-dual method for integer linear programming. Reza Moosavi Dr. Saeedeh Parsaeefard Dec.
Randomized rounding of semidefinite programs and primal-dual method for integer linear programming Dr. Saeedeh Parsaeefard 1 2 3 4 Semidefinite Programming () 1 Integer Programming integer programming
More informationCommunication Complexity of Combinatorial Auctions with Submodular Valuations
Communication Complexity of Combinatorial Auctions with Submodular Valuations Shahar Dobzinski Weizmann Institute of Science Jan Vondrák IBM Almaden Research ACM-SIAM SODA 2013, New Orleans Dobzinski-Vondrák
More informationThe k-center problem Approximation Algorithms 2009 Petros Potikas
Approximation Algorithms 2009 Petros Potikas 1 Definition: Let G=(V,E) be a complete undirected graph with edge costs satisfying the triangle inequality and k be an integer, 0 < k V. For any S V and vertex
More informationApproximation Algorithms
Approximation Algorithms Prof. Tapio Elomaa tapio.elomaa@tut.fi Course Basics A new 4 credit unit course Part of Theoretical Computer Science courses at the Department of Mathematics There will be 4 hours
More information1. Lecture notes on bipartite matching February 4th,
1. Lecture notes on bipartite matching February 4th, 2015 6 1.1.1 Hall s Theorem Hall s theorem gives a necessary and sufficient condition for a bipartite graph to have a matching which saturates (or matches)
More informationApproximating Node-Weighted Multicast Trees in Wireless Ad-Hoc Networks
Approximating Node-Weighted Multicast Trees in Wireless Ad-Hoc Networks Thomas Erlebach Department of Computer Science University of Leicester, UK te17@mcs.le.ac.uk Ambreen Shahnaz Department of Computer
More informationAn Optimal Dynamic Pricing Framework for Autonomous Mobile Ad Hoc Networks
An Optimal Dynamic Pricing Framework for Autonomous Mobile Ad Hoc Networks Z. James Ji, Wei (Anthony) Yu, and K. J. Ray Liu Electrical and Computer Engineering Department and Institute for Systems Research
More informationAPPLIED MECHANISM DESIGN FOR SOCIAL GOOD
APPLIED MECHANISM DESIGN FOR SOCIAL GOOD JOHN P DICKERSON Lecture #10 09/29/2016 CMSC828M Tuesdays & Thursdays 12:30pm 1:45pm THIS CLASS: ORGAN EXCHANGE 2 KIDNEY TRANSPLANTATION US waitlist: over 100,000
More informationPrimal-Dual Methods for Approximation Algorithms
Primal-Dual Methods for Approximation Algorithms Nadia Hardy, April 2004 The following is based on: Approximation Algorithms for NP-Hard Problems. D.Hochbaum, ed. Chapter 4: The primal-dual method for
More informationAlgorithms, Games, and Networks February 21, Lecture 12
Algorithms, Games, and Networks February, 03 Lecturer: Ariel Procaccia Lecture Scribe: Sercan Yıldız Overview In this lecture, we introduce the axiomatic approach to social choice theory. In particular,
More informationINDIAN STATISTICAL INSTITUTE
INDIAN STATISTICAL INSTITUTE Mid Semestral Examination M. Tech (CS) - II Year, 202-203 (Semester - IV) Topics in Algorithms and Complexity Date : 28.02.203 Maximum Marks : 60 Duration : 2.5 Hours Note:
More informationCPSC 536N: Randomized Algorithms Term 2. Lecture 10
CPSC 536N: Randomized Algorithms 011-1 Term Prof. Nick Harvey Lecture 10 University of British Columbia In the first lecture we discussed the Max Cut problem, which is NP-complete, and we presented a very
More informationOn the Approximability of Modularity Clustering
On the Approximability of Modularity Clustering Newman s Community Finding Approach for Social Nets Bhaskar DasGupta Department of Computer Science University of Illinois at Chicago Chicago, IL 60607,
More informationRepetition: Primal Dual for Set Cover
Repetition: Primal Dual for Set Cover Primal Relaxation: k min i=1 w ix i s.t. u U i:u S i x i 1 i {1,..., k} x i 0 Dual Formulation: max u U y u s.t. i {1,..., k} u:u S i y u w i y u 0 Harald Räcke 428
More informationWE study in this paper information dissemination in an
IEEE TRANS. ON INFORMATION THEORY & IEEE/ACM TRANS. ON NETWORKING, SECIAL ISSUE ON NETWORKING & INFORMATION THEORY, JUNE 6 On Achieving Maximum Multicast Throughput in Undirected Networks Zongpeng Li,
More informationIntroduction Multirate Multicast Multirate multicast: non-uniform receiving rates. 100 M bps 10 M bps 100 M bps 500 K bps
Stochastic Optimal Multirate Multicast in Socially Selfish Wireless Networks Hongxing Li 1, Chuan Wu 1, Zongpeng Li 2, Wei Huang 1, and Francis C.M. Lau 1 1 The University of Hong Kong, Hong Kong 2 University
More informationStrategyproof Mechanisms towards Evolutionary Topology Formation in Autonomous Networks
1 Strategyproof Mechanisms towards Evolutionary Topology Formation in Autonomous Networks Selwyn Yuen, Baochun Li Department of Electrical and Computer Engineering University of Toronto {swsyuen,bli}@eecg.toronto.edu
More informationGENERAL ASSIGNMENT PROBLEM via Branch and Price JOHN AND LEI
GENERAL ASSIGNMENT PROBLEM via Branch and Price JOHN AND LEI Outline Review the column generation in Generalized Assignment Problem (GAP) GAP Examples in Branch and Price 2 Assignment Problem The assignment
More informationConvergence Issues in Competitive Games
Convergence Issues in Competitive Games Vahab S Mirrokni 1, Adrian Vetta 2 and A Sidoropoulous 3 1 Computer Science and Artificial Intelligence Laboratory (CSAIL), MIT mail: mirrokni@theorylcsmitedu 2
More informationUnderstanding the Internet Graph. Christos H. Papadimitriou
Understanding the Internet Graph Christos H. Papadimitriou www.cs.berkeley.edu/~christos Goals To understand the Internet topology using tools from graph and game theory To contribute to the rigorous foundations
More informationApproximation Algorithms
Approximation Algorithms Group Members: 1. Geng Xue (A0095628R) 2. Cai Jingli (A0095623B) 3. Xing Zhe (A0095644W) 4. Zhu Xiaolu (A0109657W) 5. Wang Zixiao (A0095670X) 6. Jiao Qing (A0095637R) 7. Zhang
More informationVertical Handover Decision Strategies A double-sided auction approach
Vertical Handover Decision Strategies A double-sided auction approach Working paper Hoang-Hai TRAN Ph.d student DIONYSOS Team INRIA Rennes - Bretagne Atlantique 1 Content Introduction Handover in heterogeneous
More informationIn this lecture, we ll look at applications of duality to three problems:
Lecture 7 Duality Applications (Part II) In this lecture, we ll look at applications of duality to three problems: 1. Finding maximum spanning trees (MST). We know that Kruskal s algorithm finds this,
More informationInteger Programming ISE 418. Lecture 7. Dr. Ted Ralphs
Integer Programming ISE 418 Lecture 7 Dr. Ted Ralphs ISE 418 Lecture 7 1 Reading for This Lecture Nemhauser and Wolsey Sections II.3.1, II.3.6, II.4.1, II.4.2, II.5.4 Wolsey Chapter 7 CCZ Chapter 1 Constraint
More informationUsing Hybrid Algorithm in Wireless Ad-Hoc Networks: Reducing the Number of Transmissions
Using Hybrid Algorithm in Wireless Ad-Hoc Networks: Reducing the Number of Transmissions R.Thamaraiselvan 1, S.Gopikrishnan 2, V.Pavithra Devi 3 PG Student, Computer Science & Engineering, Paavai College
More informationHidden Information and Actions in Multi-Hop Wireless Ad Hoc Networks
Hidden Information and Actions in Multi-Hop Wireless Ad Hoc Networks Xiang-Yang Li, YanWei Wu, Ping Xu, GuiHai Chen, Mo Li ABSTRACT For multi-hop ad hoc networks formed by individually owned nodes, the
More informationFemto-Matching: Efficient Traffic Offloading in Heterogeneous Cellular Networks
Femto-Matching: Efficient Traffic Offloading in Heterogeneous Cellular Networks Wei Wang, Xiaobing Wu, Lei Xie and Sanglu Lu Nanjing University April 28, 2015 1/1 Heterogeneous Cellular Networks femto-cell
More informationTopology Control in Wireless Networks 4/24/06
Topology Control in Wireless Networks 4/4/06 1 Topology control Choose the transmission power of the nodes so as to satisfy some properties Connectivity Minimize power consumption, etc. Last class Percolation:
More informationMutually Exclusive Data Dissemination in the Mobile Publish/Subscribe System
Mutually Exclusive Data Dissemination in the Mobile Publish/Subscribe System Ning Wang and Jie Wu Dept. of Computer and Info. Sciences Temple University Road Map Introduction Problem and challenge Centralized
More informationStorage Allocation Based on Client Preferences
The Interdisciplinary Center School of Computer Science Herzliya, Israel Storage Allocation Based on Client Preferences by Benny Vaksendiser Prepared under the supervision of Dr. Tami Tamir Abstract Video
More informationprinceton univ. F 15 cos 521: Advanced Algorithm Design Lecture 2: Karger s Min Cut Algorithm
princeton univ. F 5 cos 5: Advanced Algorithm Design Lecture : Karger s Min Cut Algorithm Lecturer: Pravesh Kothari Scribe:Pravesh (These notes are a slightly modified version of notes from previous offerings
More informationGraphs and Network Flows IE411. Lecture 21. Dr. Ted Ralphs
Graphs and Network Flows IE411 Lecture 21 Dr. Ted Ralphs IE411 Lecture 21 1 Combinatorial Optimization and Network Flows In general, most combinatorial optimization and integer programming problems are
More informationLecture 6: Multicast
Lecture 6: Multicast Challenge: how do we efficiently send messages to a group of machines? Need to revisit all aspects of networking Last time outing This time eliable delivery Ordered delivery Congestion
More informationImportant separators and parameterized algorithms
Important separators and parameterized algorithms Dániel Marx 1 1 Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI) Budapest, Hungary PCSS 2017 Vienna, Austria September
More informationCS270 Combinatorial Algorithms & Data Structures Spring Lecture 19:
CS270 Combinatorial Algorithms & Data Structures Spring 2003 Lecture 19: 4.1.03 Lecturer: Satish Rao Scribes: Kevin Lacker and Bill Kramer Disclaimer: These notes have not been subjected to the usual scrutiny
More informationMulti-Commodity Flow with In-Network Processing
Multi-Commodity Flow with In-Network Processing Moses Charikar Yonatan Naamad Jennifer Rexford X. Kelvin Zou Outline 1 Routing and Steering 2 In-Network Processing Computer Networks are now dual-purpose.
More informationApproximation Algorithms
Chapter 8 Approximation Algorithms Algorithm Theory WS 2016/17 Fabian Kuhn Approximation Algorithms Optimization appears everywhere in computer science We have seen many examples, e.g.: scheduling jobs
More informationBalancing Transport and Physical Layers in Wireless Ad Hoc Networks: Jointly Optimal Congestion Control and Power Control
Balancing Transport and Physical Layers in Wireless Ad Hoc Networks: Jointly Optimal Congestion Control and Power Control Mung Chiang Electrical Engineering Department, Princeton University NRL/NATO Workshop
More informationOn the Min-Max 2-Cluster Editing Problem
JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 29, 1109-1120 (2013) On the Min-Max 2-Cluster Editing Problem LI-HSUAN CHEN 1, MAW-SHANG CHANG 2, CHUN-CHIEH WANG 1 AND BANG YE WU 1,* 1 Department of Computer
More informationContents. Overview Multicast = Send to a group of hosts. Overview. Overview. Implementation Issues. Motivation: ISPs charge by bandwidth
EECS Contents Motivation Overview Implementation Issues Ethernet Multicast IGMP Routing Approaches Reliability Application Layer Multicast Summary Motivation: ISPs charge by bandwidth Broadcast Center
More informationGraph Algorithms. Many problems in networks can be modeled as graph problems.
Graph Algorithms Graph Algorithms Many problems in networks can be modeled as graph problems. - The topology of a distributed system is a graph. - Routing table computation uses the shortest path algorithm
More informationOutline. CS38 Introduction to Algorithms. Approximation Algorithms. Optimization Problems. Set Cover. Set cover 5/29/2014. coping with intractibility
Outline CS38 Introduction to Algorithms Lecture 18 May 29, 2014 coping with intractibility approximation algorithms set cover TSP center selection randomness in algorithms May 29, 2014 CS38 Lecture 18
More informationHomework 2: Multi-unit combinatorial auctions (due Nov. 7 before class)
CPS 590.1 - Linear and integer programming Homework 2: Multi-unit combinatorial auctions (due Nov. 7 before class) Please read the rules for assignments on the course web page. Contact Vince (conitzer@cs.duke.edu)
More information1 Unweighted Set Cover
Comp 60: Advanced Algorithms Tufts University, Spring 018 Prof. Lenore Cowen Scribe: Yuelin Liu Lecture 7: Approximation Algorithms: Set Cover and Max Cut 1 Unweighted Set Cover 1.1 Formulations There
More informationSubject: Adhoc Networks
ISSUES IN AD HOC WIRELESS NETWORKS The major issues that affect the design, deployment, & performance of an ad hoc wireless network system are: Medium Access Scheme. Transport Layer Protocol. Routing.
More informationLinear Programming Motivation: The Diet Problem
Agenda We ve done Greedy Method Divide and Conquer Dynamic Programming Network Flows & Applications NP-completeness Now Linear Programming and the Simplex Method Hung Q. Ngo (SUNY at Buffalo) CSE 531 1
More informationSpectrum Bidding in Wireless Networks and Related. Ping Xu. Advisor: Xiang-Yang Li 1. Feb. 11th, 2008
1 Advisor: Xiang-Yang Li 1 1 Illinois Institute of Technology Feb. 11th, 2008 Outline : : Spectrum Scarcity Problem Figure: Frequency Allocations of The Radio Spectrum in US. university-log White Space
More informationChapter II. Linear Programming
1 Chapter II Linear Programming 1. Introduction 2. Simplex Method 3. Duality Theory 4. Optimality Conditions 5. Applications (QP & SLP) 6. Sensitivity Analysis 7. Interior Point Methods 1 INTRODUCTION
More informationUrban dashboardistics Damon Wischik Dept. of Computer Science and Technology
Urban dashboardistics Damon Wischik Dept. of Computer Science and Technology UNIVERSITY OF CAMBRIDGE Wardrop modelled route choice by drivers in a traffic network. Braess discovered paradoxical outcomes
More informationCompetitive and Deterministic Embeddings of Virtual Networks
Competitive and Deterministic Embeddings of Virtual Networks Guy Even (Tel Aviv Uni) Moti Medina (Tel Aviv Uni) Gregor Schaffrath (T-Labs Berlin) Stefan Schmid (T-Labs Berlin) The Virtual Network Embedding
More informationCOMP260 Spring 2014 Notes: February 4th
COMP260 Spring 2014 Notes: February 4th Andrew Winslow In these notes, all graphs are undirected. We consider matching, covering, and packing in bipartite graphs, general graphs, and hypergraphs. We also
More informationCombinatorial Optimization
Combinatorial Optimization Frank de Zeeuw EPFL 2012 Today Introduction Graph problems - What combinatorial things will we be optimizing? Algorithms - What kind of solution are we looking for? Linear Programming
More information