# How To Explore a Fast Changing World - PowerPoint PPT Presentation

1 / 9

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). Motivation.

## Related searches for How To Explore a Fast Changing World

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

How To Explore a Fast Changing World

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

### 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)

### 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 ??!!

### RW on Static Graphs

• The Simple Random Walk on Graph.

• Cover Time, hitting time arebounded by n3.

• 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

### Main Results

• 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).

• Can be fixed by the “Lazy Random Walk”.

G1 G2 G3 G4 G5 ...

### 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.

### “Sisyphus Wheel”

• The adversary has a simple (deterministic) strategy to increase h(1,n):

• The Cover Time of this dynamic graph is exponential!

...

3

n-1

2

n-3

1

n-2

n

### 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 graphG the cover time of the lazy random walk onG is O(n5ln2n).

• ?? Slower is faster ?? :-)

### 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!