cse 501 research overview atri rudra [email protected]
Post on 19-Dec-2015
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TRANSCRIPT
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Research Interests
Theoretical Computer Science Coding Theory Algorithmic Game Theory Sublinear algorithms Approximation and online algorithms
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Coding Theory
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The setupC(x)
x
y = C(x)+error
x Give up
Mapping C Error-correcting code or just code Encoding: x C(x) Decoding: y X C(x) is a codeword
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Different Channels and Codes Internet
Checksum used in multiple layers of TCP/IP stack
Cell phones Satellite broadcast
TV Deep space
telecommunications Mars Rover
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“Unusual” Channels
Data Storage CDs and DVDs RAID ECC memory
Paper bar codes UPS (MaxiCode)
Codes are all around us
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Redundancy vs. Error-correction Repetition code: Repeat every bit say 100
times Good error correcting properties Too much redundancy
Parity code: Add a parity bit Minimum amount of redundancy Bad error correcting properties
Two errors go completely undetected
Neither of these codes are satisfactory
1 1 1 0 0 1
1 0 0 0 0 1
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Two main challenges in coding theory Problem with parity example
Messages mapped to codewords which do not differ in many places
Need to pick a lot of codewords that differ a lot from each other
Efficient decoding Naive algorithm: check received word with all
codewords
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The fundamental tradeoff
Correct as many errors as possible with as little redundancy as possible
Can one achieve the “optimal” tradeoff with efficient encoding and decoding ?
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A “low level” view
Think of each symbol in being a packet The setup
Sender wants to send k packets After encoding sends n packets Some packets get corrupted Receiver needs to recover the original k packets
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The Optimal Tradeoff
C(x) sent, y received
How much of y must be correct to recover x ? At least k packets must be correct
[Guruswami, R. STOC 2006] An explicit code along with efficient decoding
algorithm Works as long as (almost) k packets are correct
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So what is left to do?
I cheated a bit in the last slide
The result only holds for large packets
We do not know an “optimal” code over smaller symbols (for example bits)
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Algorithmic Game Theory
Online auction of digital goods [Blum, Kumar, R., Wu SODA 2003]
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Online Auctions of Digital goods Say you want to sell mp3s of a song
Can make copies with no extra cost Buyers arrive one by one
Specify how much they are willing to pay You need to decide to sell or not
At what price ? You want to make lots of money $5
OK, $4
$1
No
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However…
Why not just sell at the value specified by a buyer ? Buyers are selfish
They will lie to get a better deal Why not charge a single fixed price ?
Do not know best price in advance The challenge
Build a online pricing scheme that gives buyers no incentive to cheat
Our work gives pricing scheme as good as best fixed price [Blum, Kumar, R., Wu SODA 2003]
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Problems I am interested in
Problems motivated by game theory Sometimes, “old” problem with a twist
What is the best way to pair up potential couples in a dating site? Twist on the classical graph matching problem
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Sublinear Algorithms
Data Streams [Beame, Jayram, R. STOC 2007]
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Data Streams (one application) Databases are huge
Fully reside in disk memory Main memory
Fast, not much of it Disk memory
Slow, lots of it Random access is
expensive Sequential scan is
reasonably cheap
Main memory
Disk Memory
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Data Streams (one application) Given a restriction on
number of random accesses to disk memory
How much main memory is required ?
For computations such as join of tables
Answer: a lot [Beame, Jayram, R. STOC
2007] Open question: computing
other functions?
Main memory
Disk memory
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Approximation Algorithms
Ranking in Tournaments [Coppersmith, Fleischer, R. SODA 2006]
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US Open 2005
Everyone plays everyone
Rank the players Min #upsets Rank by number
of wins Break ties
Venus Williams Maria Sharapova
Kim Clijsters Nadia Petrova
#1 #2
#3#4
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Ranking in Tournament results [Coppersmith, Fleischer, R. SODA 2006] Ordering by number of wins is 5-approx
Ties broken arbitrarily Problem shown to be NP-hard in 2005
Application in Rank Aggregation Gives provable guarantee for Borda’s method
(1781!) Future Directions
Try and analyze (variants) of heuristics that work well in practice
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Research Interests
Theoretical Computer Science Coding Theory Algorithmic Game Theory Sublinear algorithms Approximation and online algorithms
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For more information…
My Office is Bell 123: drop by! [email protected]
CSE 510C this fall Course on error correcting codes