16:198:673:01: Network Design and Game Theory, Spring 2008 (Course Index: 67432)


Instructor: Mohammad T. HajiAghayi


Latest Announcements (Last updated 05/04/08)


        Please note that each student has 25 min for his/her presentation on May 5, 2008. Also please have your slides on a USB memory key to avoid delays in presentations. Also e-mail me your slides at mthajiaghayiATgmailDOTcom for grading by May 5.

        The due date for final projects is May 12, 2008. Please e-mail your final project by this time, or you may get incomplete for the grade.

Pease e-mail me your slides for presentation by 4/14/08 such that I can put them in this website. Use email address mthajiaghayiATgmailDOTcom only for this purpose.

        Notice the mid-term exam on 3/31/08 in the class (it starts at 4pm). Mid-term exam is open-book (but not open-laptop). 

        The second assignment is due March 3 in the class; in this assignment you are supposed to find two real-world network applications for probabilistic embedding of graph metrics into trees. I expect a write-up of 1.5 to 2 pages.

        Please send me scribe notes within 5 days of the class when you have still fresh mind about the topic. We will finalize them within a week then.

        Please e-mail me the topic of your project by 2/25/08.

        Please note to the change of the classroom to Hill Center 120.

        Select papers for presentations from the list below by Feb 17 and send me an e-mail regarding them before the class. We are deciding about the matching in the class.

        The first assignment is due Feb 11 in the class; in this assignment you are supposed to find two real-world network applications for two of set cover, unique coverage, and budgeted maximum coverage. I expect a write-up of 1 to 1.5 pages in total including both applications.

        Please see me or send me an e-mail regarding the topic of your project by Feb 25 to hopefully finalize it by March 1.

        First lecture on January 28, 2008.

        Templates .tex .sty to scribe.


Course Description

Network Design or more generally networking with its many variants is one of the most active research areas in computer science involving researchers from System, Networks, Algorithm Design, Graph Theory, Discrete Optimization, Game Theory and Information Theory. Especially mathematical modeling of networks plays a vital role in the understanding of computer and communication networks and provides insights into questions such as allocation of network resources, analysis and effects of competitive and/or cooperative agents, Internet protocols, wireless network protocols, network dynamics, queuing systems, performance optimization, and network traffic and topology. These models shed light onto fundamental performance limits and trade-offs in practical scenarios. In addition, new problems in this area are constantly propounded by practitioners working in various aspects of network design such as construction, routing and staged deployment. Furthermore, many new design paradigms such as ATM, Ad hoc and Wireless networking add rich new flavors to existing problems. On the other hand, many of the key algorithmic challenges in the context of the internet, the largest network in the world, require considering the objectives and interests of the different participants involved. These include problems ranging from pricing goods and resources, to improving search, to routing, and more generally to understanding how incentives of participants can be harnessed to improve the behavior of the overall system. As a result, Mechanism Design and Algorithmic Game Theory, which can be viewed as ``incentive-aware algorithm design'', have become an increasingly important part of network design in recent years.


Recent results show a strong relation between network design and game theory, and techniques from each seem well-poised to help with key problems of the other. My first goal in this course is to study these connections which produce powerful mechanisms for adaptive and networked environments, and improve the experience of users of the Web and internet. However we also focus on active area of applications of algorithms in networking to understand current trends, identify understudied areas, and potentially formulate new directions for further investigation. Below I highlight some of the main selection of topics and their corresponding references that we will cover in this course (we may add more references later to this list).

Reference Books:


Algorithmic Game Theory, edited by Nisan, Roughgarden, Tardos, and Vazirani, Cambridge University Press, 2007.
Approximation Algorithms, by Vazirani, Springer, 2001
Randomized Algorithms, by Motwani and Raghavan, Cambridge University Press, 2000.
Algorithm Design, by Kleinberg and Tardos, Addison-Wesley, 2006.

Detailed Schedule (see the references below):


1/28/08: Review of course description, review of different approximation algorithms for set cover.

My scanned handwritten notes: pages a b c

Scribe notes by students


2/04/08: Review of maximum coverage with budget and unique coverage.

My scanned handwritten notes: pages a b c d (see the slides of 2/11 for more details on unique coverage)

Scribe notes by students


2/11/08: An overview of algorithms for wireless networks and cell breathing.

My slides


2/18/08: Review of probabilistic embedding into trees: definitions and applications.

My scanned handwritten notes: pages a b c d

Scribe notes by students


2/25/08: Review of Bartal-FRT proof for probabilistic embedding into trees, also another application of this technique for network design

My scanned handwritten notes: pages a b c d e

Scribe notes by students


3/03/08: Guest lecturer: Aaron Archer, Review of algorithms for Steiner tree, Prize-collecting version, k-MST

Scanned handwritten notes: pages a b c d e f g h i j k

Scribe notes by students


3/10/08: Review of algorithms for facility location and connected facility location (single-sink rent-or-buy network design)

Scanned handwritten notes: pages a b c d e

Scribe notes by students


3/17/08: Spring break


3/24/08: Review of algorithms for single-sink and multi-commodity non-uniform buy-at-bulk network design

Scanned handwritten notes: pages a b c (for single-sink), My slides (for multi-commodity)

Scribe notes by students


3/31/08: Mid-term exam.


4/07/08: Review of Price of Anarchy results for networks

Scanned handwritten notes: pages a b c d e

Scribe notes by students


4/14/08: Paper presentations by students. Please choose your paper to present from the following list (the preferable list) OR papers in the references:


Mohit Singh and Lap Chi Lau, Approximating Minimum Bounded Degree Spanning Tress to within One of Optimal , STOC 2007.

Slides by students


E. Anshelevich, A. Dasgupta, J. Kleinberg, E. Tardos, T. Wexler, and T. Roughgarden, The Price of Stability for Network Design with Fair Cost Allocation, FOCS '04.

Slides by students


Katrina Ligett, Avrim Blum, MohammadTaghi Hajiaghayi, and Aaron Roth, Regret, Minimization and the Price of Total Anarchy. STOC 2008

Slides by students


R. Johari and J.N. Tsitsiklis. Efficiency loss in a network resource allocation game, Mathematics of Operation Research, 29(3): 407-435

Slides by students


Chandra Chekuri, Julia Chuzoy, Liane Lewin-Eytan, Seffi Naor and Ariel Orda, Non-Cooperative Multicast and Facility Location Games , ACM EC 2006.

Slides by students


Naveen Garg, Goran Konjevod and R. Ravi, A Polylogarithmic Approximation Algorithm for the Group Steiner Tree Problem, SODA 1998 OR Chandra Chekuri, Guy Even, and Guy Kortsarz, A greedy approximation algorithm for the group Steiner problem, Discrete Applied Mathematics, 154(1):15--34, 2006.

Slides by students

E.D. Demaine; M.T. Hajiaghayi; H. Mahini; S. Oveisgharan; A. Sayedi; M. Zadimoghadam; Minimizing movement, SODA 2007.

Slides by students


4/21/08: Guest lecturer: MohammadHossein Bateni, Review of network creation games

Scanned handwritten notes: pages a b c

Scribe notes by students


4/28/08: Review of oblivious routing algorithms

Scanned handwritten notes: pages a b c d e

Scribe notes by students


5/05/08: Last day of the class: project presentations by students.


Tentative Course Topics and References:


Set cover, maximum coverage and unique coverage:

Above book Approximation Algorithms, by Vazirani, 2001.

The Budgeted Maximum Coverage Problem, Samir Khuller, Anna Moss, Joseph (Seffi) Naor, Information Processing Letters, 1997.

E.D. Demaine, U. Feige, M.T. Hajiaghayi; M.R. Salavatipour; Combination can be hard: approximability of the unique coverage problem, SIAM Journal on Computing. A preliminary version appeared in the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Vancouver, Miami, Florida, January 22-24, 2006, pp. 162-171.


Technique of probabilistic embedding into trees:

Yair Bartal: Probabilistic Approximations of Metric Spaces and Its AlgorithmicApplications . FOCS 1996: 184-193

Jittat Fakcheroenphol, Kunal Talwar and Satish Rao, A tight bound on approximating arbitrary metrics by tree metrics

STOC 2003, J. Comput. Syst. Sci. 69(3): 485-497 (2004).

Michael Elkin, Yuval Emek, Daniel Spielman and Shang-Hua Teng, Lower-Stretch Spanning Trees, 37th ACM Symposium on Theory of Computing, 2005.


Planar Networks:

Brenda S. Baker, Approximation Algorithms for NP-Complete Problems on Planar Graphs. J. ACM 41(1): 153-180. (1994)

E.D. Demaine; M.T. Hajiaghayi; K Kawarabayashi; Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring, In Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS), Pittsburgh, PA, October 23-25, 2005, pp. 637-646.

Philip N. Klein, A linear-time approximation scheme for TSP for planar weighted graphs, Proceedings, 46th IEEE Symposium on Foundations of Computer Science (2005), pp. 647--656.

E.D. Demaine; M.T. Hajiaghayi; The Bidimensionality Theory and Its Algorithmic Applications,

A servey in Computer Journal, To appear.


Oblivious routing:

Harald Rcke. Minimizing Congestion in General Networks. In Proc. of the 43rd FOCS, pp. 43-52, 2002.

Harrelson, Hildrum, and Rao, A polynomial-time tree decomposition to minimize congestion. SPAA 2003.

Yossi Azar, Edith Cohen, Amos Fiat, Haim Kaplan, and Harald Rcke. Optimal Oblivious Routing in Polynomial Time. In Proc. of the 35th STOC, pp. 383-388, 2003.

A. Gupta; M.T. Hajiaghayi; H. Raecke; Oblivious Network Design, In Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Vancouver, Miami, Florida, January 22-24, 2006, pp. 970-979.


Cost sharing:

Anupam Gupta, Amit Kumar, Tim Roughgarden, Simpler and better approximation algorithms for network design. STOC 2003: 365-372

Anupam Gupta, Amit Kumar, Martin Pl and Tim Roughgarden Approximation Via Cost-Sharing: A Simple Approximation Algorithm for the Multicommodity Rent-or-Buy Problem. J. ACM, 54(3), March 2007

Jain and Mahdian, Cost Sharing, in Algorithmic Game Theory book above.


Buy-at-bulk network design:

Adam Meyerson, Kamesh Munagala, and Serge Plotkin: Cost-Distance: Two-Metric Network Design. IEEE Symposium on Foundations of Computer Science (FOCS) 2000.

Adam Meyerson. Online Facility Location. FOCS 2001.

Sudipto Guha, Adam Meyerson, and Kamesh Munagala: Hierarchical Placement and Network Design Problems. IEEE Symposium on Foundations of Computer Science (FOCS) 2000.

David B. Shmoys, va Tardos, Karen Aardal: Approximation Algorithms for Facility Location Problems. STOC 1997: 265-274

C. Chekuri; S. Khanna; S. Naor: A deterministic algorithm for the cost-distance problem. SODA 2001: 232-233.

C. Chekuri; M.T. Hajiaghayi; G. Kortsarz; M. R. Salavatipour: Approximation algorithms for node–weighted buy-at-bulk networks, In Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), New Orleans, LA, January 7-9, 2007, pp. 1265--1274.

C. Chekuri; M.T. Hajiaghayi; G. Kortsarz; M. R. Salavatipour: Approximation algorithms for non-uniform buy-at-bulk network design problems In Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS), Berkeley, PA, October 22-24, 2006, pp. 677—686.


Price of anarchy and selfish routing:

T. Roughgarden, The Price of Anarchy Is Independent of the Network Topology, Journal of Computer and System Sciences, 67(2):341--364, 2003. (Conference version in STOC 2002.)

E. Tardos, lecture notes from Cornell CS684.

J. R. Correa, N. E. Stier Moses, and A. S. Schulz, Selfish Routing in Capacitated Networks, Mathematics of Operations Research, 2004 (to appear).

J. R. Correa, N. E. Stier Moses, and A. S. Schulz, A geometric approach to the price of anarchy in nonatomic congestion games, Games and Economic of Behavior, to appear, 2008.

T. Roughgarden and E. Tardos, How Bad Is Selfish Routing?, Journal of the ACM, 49(2):236--259, 2002.


Network creation and formation games:

E. Tardos and T. Wexler, Network Formation Games, in Algorithmic Game Theory book above.

Alex Fabrikant, Ankur Luthra, Elitza N. Maneva, Christos H. Papadimitriou, Scott Shenker: On a network creation game. PODC 2003: 347-351.

E.D. Demaine; M.T. Hajiaghayi; H. Mahini; M. Zadimoghadam; The price of anarchy in network creation games, In Proceedings of the 26th Annual ACM Symposium on Principles of Distributed Computing (PODC), Portland, Oregon, August 2007, pages 292—298.


Online mechanism design:

D. Parkes, On-line Mechanisms, in Algorithmic Game Theory book above.

M.T. Hajiaghayi; R.D. Kleinberg; M. Mahdian; D.C. Parkes; Online Auctions with Re-usable Goods, In Proceedings of the 6th ACM Conference on Electronic Commerce (EC), pp. 165-174, Vancouver, Canada, June 5-8, 2005.

Hajiaghayi, M.T.; Kleinberg, R.; Parkes, D.C.; Adaptive Limited-Supply Online Auctions, Proc. ACM Conference on Electronic Commerce (EC), pp. 71-80, May 17-20, 2004. New York.


Profit maximization auctions:

Jason Hartline, Anna Karlin, Profit Maximization in Mechanism Design, in Algorithmic Game Theory book above.

Andrew Goldberg, Jason Hartline, Anna Karlin, Mike Saks, and Andrew Wright, Competitive Auctions, Games and Economic Behavior, 2006.

Venkatesan Guruswami, Jason D. Hartline, Anna R. Karlin, David Kempe, Claire Kenyon, Frank McSherry: On profit-maximizing envy-free pricing, SODA 2005: 1164-1173.


Wireless network design:

M.T. Hajiaghayi; N. Immorlica; V.S. Mirrokni; Power Optimization in Fault-Tolerant Topology Control Algorithms for Wireless Multi-hop Networks, IEEE/ACM Transactions on Networking. To appear. A preliminary version appeared in the Ninth Annual International Conference on Mobile Computing and Networking (MOBICOM), San Diego, CA, September 15-18 2003, pp. 300-312.

M.T. Hajiahgayi; G. Kortsarz; V. S. Mirrokni; Z. Nutov; Power Optimization for Connectivity Problems, A Mathematical Programming, Series B for selected papers from IPCO 2005. Vol 110, No 1, pp. 195--208, 2007.

Goemans, Li, Mirrokni and Thottan, Market Sharing games applied to Content Distribution in Ad-Hoc Networks , MobiHoc 2004.

J.L. Bredin; E.D. Demaine; M.T. Hajiaghayi; D. Rus; Deploying Sensor Nets with Guaranteed Capacity and Fault Tolerance, In Proceedings of the 6th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc), Urbana-Champaign, IL, May 2005, pp. 309--319.




A basic course in algorithms is required. Already passing an advanced course in algorithms or networking can be quite helpful. If you are unsure of whether you have sufficient background for this course or not, please contact the instructor in the first week of the class or before.


Tentative Grading & Evaluation


Each student will be expected to scribe 1-2 lectures and participate in class discussions (10%). There will be two homeworks (7.5% each), one mid-term exam (20%), a paper presentation in the class (15%) and a (possibly collaborative) project and its brief presentation in the class (40%). A very strong project can potentially compensate the low grades in other parts. Details about the project and ideas will be given in the second week of the class, though the general ideas can be seen from the course topics.


Other Resources (from here)


Tips for good technical writing

The elements of style by William Strunk Jr. and E. B. White (follow the "External links" at the bottom of this page for online copies of this book).

Writing a technical paper, by Professor Michael Ernst.

Tips for writing technical papers, by Professor Jennifer Widom.

Writing suggestions, by Professor Barton Miller.

How to write a dissertation, by Professor Douglas Comer (most of the content on this page applies to all forms of technical writing).


Tips for effective presentation

Giving a technical talk, by Professor Michael Ernst.

Tips for a good conference talk, by Professor Jennifer Widom.

Oral presentation advice, by Professor Mark Hill.


General Information


Mohammad T. HajiAghayi


Mondays from 4pm-6:45pm


482 Hill Center

Office hours:      

By appointment via e-mail OR the hour immediately following class.


120 Hill Center




The first 8 letters of instructor’s last name (AT) research (DOT) att (DOT) com