How To Explore a Fast Changing World (On the Cover Time of Dynamic Graphs) Chen Avin Ben Gurion University Joint work with Michal Koucky & Zvi Lotker (ICALP-08)

Slides:

Advertisements

Similar presentations

1 A Graph-Theoretic Network Security Game M. Mavronicolas , V. Papadopoulou , A. Philippou  and P. Spirakis § University of Cyprus, Cyprus  University.

Advertisements

Ion Stoica, Robert Morris, David Karger, M. Frans Kaashoek, Hari Balakrishnan MIT and Berkeley presented by Daniel Figueiredo Chord: A Scalable Peer-to-peer.

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

Routing in a Parallel Computer. A network of processors is represented by graph G=(V,E), where |V| = N. Each processor has unique ID between 1 and N.

Backtrack Algorithm for Listing Spanning Trees R. C. Read and R. E. Tarjan (1975) Presented by Levit Vadim.

1 K-clustering in Wireless Ad Hoc Networks using local search Rachel Ben-Eliyahu-Zohary JCE and BGU Joint work with Ran Giladi (BGU) and Stuart Sheiber.

Structuring Unstructured Peer-to-Peer Networks Stefan Schmid Roger Wattenhofer Distributed Computing Group HiPC 2007 Goa, India.

A Distributed and Oblivious Heap Christian Scheideler and Stefan Schmid Dept. of Computer Science University of Paderborn.

Approximation Algorithms for Unique Games Luca Trevisan Slides by Avi Eyal.

Parallel random walks Brian Moffat. Outline What are random walks What are Markov chains What are cover/hitting/mixing times Speed ups for different graphs.

On the Topologies Formed by Selfish Peers Thomas Moscibroda Stefan Schmid Roger Wattenhofer IPTPS 2006 Santa Barbara, California, USA.

Volcano Routing Scheme Routing in a Highly Dynamic Environment Yashar Ganjali Stanford University Joint work with: Nick McKeown SECON 2005, Santa Clara,

Taming Dynamic and Selfish Peers “Peer-to-Peer Systems and Applications” Dagstuhl Seminar March 26th-29th, 2006 Stefan Schmid Distributed Computing Group.

1 University of Freiburg Computer Networks and Telematics Prof. Christian Schindelhauer Distributed Coloring in Õ(  log n) Bit Rounds COST 293 GRAAL and.

Institute of Computer Science University of Wroclaw Page Migration in Dynamic Networks Marcin Bieńkowski Joint work with: Jarek Byrka (Centrum voor Wiskunde.

Geometric Spanners for Routing in Mobile Networks Jie Gao, Leonidas Guibas, John Hershberger, Li Zhang, An Zhu.

Dynamic Hypercube Topology Stefan Schmid URAW 2005 Upper Rhine Algorithms Workshop University of Tübingen, Germany.

Robust Network Design with Exponential Scenarios By: Rohit Khandekar Guy Kortsarz Vahab Mirrokni Mohammad Salavatipour.

Building Low-Diameter P2P Networks Eli Upfal Department of Computer Science Brown University Joint work with Gopal Pandurangan and Prabhakar Raghavan.

CSE 326: Data Structures NP Completeness Ben Lerner Summer 2007.

CSE 421 Algorithms Richard Anderson Lecture 4. What does it mean for an algorithm to be efficient?

1 Brief Announcement: Distributed Broadcasting and Mapping Protocols in Directed Anonymous Networks Michael Langberg: Open University of Israel Moshe Schwartz:

1 University of Freiburg Computer Networks and Telematics Prof. Christian Schindelhauer Wireless Sensor Networks 22nd Lecture Christian Schindelhauer.

1 Random Walks in WSN 1.Efficient and Robust Query Processing in Dynamic Environments using Random Walk Techniques, Chen Avin, Carlos Brito, IPSN 2004.

W. D. Grover TRLabs & University of Alberta © Wayne D. Grover 2002, 2003 Graph theory and routing (initial background) E E Lecture 4.

Lecture 20: April 12 Introduction to Randomized Algorithms and the Probabilistic Method.

An introduction to Approximation Algorithms Presented By Iman Sadeghi.

Decomposing Networks and Polya Urns with the Power of Choice Joint work with Christos Amanatidis, Richard Karp, Christos Papadimitriou, Martha Sideri Presented.

Efficient and Robust Query Processing in Dynamic Environments Using Random Walk Techniques Chen Avin Carlos Brito.

1 Introduction to Approximation Algorithms. 2 NP-completeness Do your best then.

MCS312: NP-completeness and Approximation Algorithms

Computing and Communicating Functions over Sensor Networks A.Giridhar and P. R. Kumar Presented by Srikanth Hariharan.

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

Theory of Computing Lecture 15 MAS 714 Hartmut Klauck.

1 Introduction to Approximation Algorithms. 2 NP-completeness Do your best then.

Network Characterization via Random Walks B. Ribeiro, D. Towsley UMass-Amherst.

Advanced Algorithm Design and Analysis (Lecture 13) SW5 fall 2004 Simonas Šaltenis E1-215b

CCAN: Cache-based CAN Using the Small World Model Shanghai Jiaotong University Internet Computing R&D Center.

Expanders via Random Spanning Trees R 許榮財 R 黃佳婷 R 黃怡嘉.

ＲａｎｄｏｍＷａｌｋｓｏｎＤｉｓｔｒｉｂｕｔｅｄＮｅｔｗｏｒｋｓＭａｓａｆｕｍｉＹａｍａｓｈｉｔａ (Kyushu Univ., Japan)

1 “Erdos and the Internet” Milena Mihail Georgia Tech. The Internet is a remarkable phenomenon that involves graph theory in a natural way and gives rise.

CSE 326: Data Structures NP Completeness Ben Lerner Summer 2007.

On Survivable Routing of Mesh Topologies in IP-over-WDM Networks Maciej Kurant, Patrick Thiran EPFL, Switzerland Infocom 2005, March 13-17, Miami.

Project funded by the Future and Emerging Technologies arm of the IST Programme Analytical Insights into Immune Search Niloy Ganguly Center for High Performance.

Challenges and Opportunities Posed by Power Laws in Network Analysis Bruno Ribeiro UMass Amherst MURI REVIEW MEETING Berkeley, 26 th Oct 2011.

Many random walks are faster than one Noga AlonTel Aviv University Chen AvinBen Gurion University Michal KouckyCzech Academy of Sciences Gady KozmaWeizmann.

Markov Chains and Random Walks. Def: A stochastic process X={X(t),t ∈ T} is a collection of random variables. If T is a countable set, say T={0,1,2, …

A correction The definition of knot in page 147 is not correct. The correct definition is: A knot in a directed graph is a subgraph with the property that.

CSE 421 Algorithms Richard Anderson Lecture 27 NP-Completeness and course wrap up.

Topics Paths and Circuits (11.2) A B C D E F G.

Approximation, Chance and Networks Lecture Notes BISS 2005, Bertinoro March Alessandro Panconesi University La Sapienza of Rome.

Joint Power and Channel Minimization in Topology Control: A Cognitive Network Approach J ORGE M ORI A LEXANDER Y AKOBOVICH M ICHAEL S AHAI L EV F AYNSHTEYN.

Graph theory and networks. Basic definitions  A graph consists of points called vertices (or nodes) and lines called edges (or arcs). Each edge joins.

Routing Topology Algorithms Mustafa Ozdal 1. Introduction How to connect nets with multiple terminals? Net topologies needed before point-to-point routing.

Network RS Codes for Efﬁcient Network Adversary Localization Sidharth Jaggi Minghua Chen Hongyi Yao.

Anonymous communication over social networks Shishir Nagaraja and Ross Anderson Security Group Computer Laboratory.

Mobility Increases the Connectivity of K-hop Clustered Wireless Networks Qingsi Wang, Xinbing Wang and Xiaojun Lin.

Network Coding Tomography for Network Failures

Fast Parallel Algorithms for Edge-Switching to Achieve a Target Visit Rate in Heterogeneous Graphs Maleq Khan September 9, 2014 Joint work with: Hasanuzzaman.

Graphs David Kauchak cs302 Spring Admin HW 12 and 13 (and likely 14) You can submit revised solutions to any problem you missed Also submit your.

1 “Hybrid Search Schemes for Unstructured Peer- to-Peer Networks” “Random Walks in Peer-to-Peer Networks” Christos Gkantsidis, Milena Mihail, Amin Saberi.

SYNERGY: A Game-Theoretical Approach for Cooperative Key Generation in Wireless Networks Jingchao Sun, Xu Chen, Jinxue Zhang, Yanchao Zhang, and Junshan.

The walkers problem J.D., X.Perez, M.Serna, N.Wormald Partially supported by the EC 6th FP : DELIS.

Introduction to Randomized Algorithms and the Probabilistic Method

A Study of Group-Tree Matching in Large Scale Group Communications

An introduction to Approximation Algorithms Presented By Iman Sadeghi

Michael Langberg: Open University of Israel

Grade 11 AP Mathematics Graph Theory

Intro to NP Completeness

Richard Anderson Lecture 30 NP-Completeness

Presentation transcript:

How To Explore a Fast Changing World (On the Cover Time of Dynamic Graphs) Chen Avin Ben Gurion University Joint work with Michal Koucky & Zvi Lotker (ICALP-08)

Israeli Networking Seminar 29-May Motivation Today’s communication networks are dynamic: mobility, communication fluctuations, duty cycles, clients joining and leaving, etc. Structure-base schemes (e.g., spanning tress, routing tables) are thus problematic. Turning attention to structure-free solutions. Random-walk-based protocols are simple, local, distributed and robust to topology changes. Robust to topology changes ??!!

Israeli Networking Seminar 29-May RW on Static Graphs The Simple Random Walk on Graph. Cover Time, hitting time are bounded by n 3. Random walk can be efficient for some applications/networks, i.e., the time to visit a subset of N nodes, can be linear in N. Partial cover time. Tempting to use on dynamic networks

Israeli Networking Seminar 29-May Main Results Question: What Question: What will be the expected number of steps for a random walk on dynamic network to visit every node in the network (i.e., Cover Time). Answers in short: Bad, very bad (compare to static network). Can be fixed by the “Lazy Random Walk”.

Israeli Networking Seminar 29-May Dynamic Model Evolving Graphs: Random walk on dynamic graph Worst case analysis: a game between the walker and an oblivious adversary that controls the network dynamics. G 1 G 2 G 3 G 4 G 5...

Israeli Networking Seminar 29-May The adversary has a simple (deterministic) strategy to increase h(1,n): The Cover Time of this dynamic graph is exponential! “Sisyphus Wheel” n-3 n-2 n... n-1

Israeli Networking Seminar 29-May The Lazy Random Walk Lazy random walk: At each step of the walk pick a vertex v from V(G) uniformly at random and if there is an edge from the current vertex to the vertex v then move to v otherwise stay at the current vertex. Theorem: For any connected evolving graph G the cover time of the lazy random walk on G is O(n 5 ln 2 n). ?? Slower is faster ?? :-)

Israeli Networking Seminar 29-May Summary Demonstrate that the cover time of the simple random walk on dynamic graphs is significantly different from the case of static graphs: exponential vs. polynomial. The cover time is bounded to be polynomial by the use of lazy random walk. Gives some theoretical justification for the use of random-walks-techniques in dynamic networks, but careful attention is required.

Thank You!