On the Multicommodity Flow Problem
OD version
K origindestination pairs of nodes
(s1, t1), (s2, t2), , (sK, tK)
Network G = (N, A)
dk = amount of flow that must be sent from sk to tk.
uij = capacity on (i,j) shared by all commodities
k
cij = cost of sen
Optimal Routing
View routing as a global optimization problem
Assumptions:
Eytan Modiano
Slide 2
The required traffic rate between each sourcedestination pair is
known in advance
The cost of using a link is a function of the flow on that link
The total n
FLOW CONTROL
QuickTime and a
Photo  JPEG decompressor
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QuickTime and a
GIF decompressor
are needed to see this picture.
LIDS
Flow control: endtoend mechanism for regulating traffic between source
and destination
Congestio
Higher Layers
Application
Application
Virtual network service
Presentation
Presentation
Virtual session
Session
Session
Virtual link for end to end messag
es
Transport
Transport
TCP, UDP
Virtual link for end to end packets
Network
Network
Network
Network
On the Multicommodity Flow Problem
OD version
K origindestination pairs of nodes
(s1, t1), (s2, t2), , (sK, tK)
Network G = (N, A)
dk = amount of flow that must be sent from sk to tk.
uij = capacity on (i,j) shared by all commodities
k
cij = cost of sen
6.857 Computer and network Security
Lecture 15
Today:
Digital signatures
Security definition for digital signatures
Hash and sign
RSAPKCS
RSAPSS
El Gamal digital signatures
DSA(NIST standard)
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6.857 Computer and Network Security
Lecture 14
Admin:
Problem Set #4 out
Today:
Malleability of El Gamal
INDCCA2 security (CramerShoup claim)
RSA
Making RSA INDCCA2 secure (OAEP)
Other aspects of RSA security
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PRACTICE QUESTIONS FOR 15.561 FINAL EXAMINATION
Spring 2005
CLARIFICATION: This is not a practice final but a collection of questions similar to those likely to
be on the final.
COMPUTER FUNDAMENTALS PRACTICE QUESTIONS
Multiplechoice questions: SELECT TH
6.189 Multicore Programming Primer
#1) FOR I = 1 to n
FOR J = 1 to n
A[I, J] = A[I+1, J1] + 1
MiniQuiz #6 (1/24/2007)
#3) FOR I = 1 to n
FOR J = 1 to n
A[I, J] = A[J, I]
J
I
J
I
#2) FOR I = 1 to n
FOR J = 1 to n
B[J] = B[J1]
J
I
green arrows indicate a