CS4335 Design and Analysis of Algorithms
One term paper
Fin
d an open problem from
the
internet
that you are interested in.
Give a short
description (background, application, etc.) of the
problem
.
And then give
the
problem
definition
in
mathematical
language
.
Search the
rel
ated
work on this
problem and s
ummarize the current status
.
No more than 1 page
.
Tips
:
You can use
http://www.nada.kth.se/~viggo/problemlist/compendium.html
to find a problem you like. Usually
Wikipedia
contains more details about a problem. You can also use google (scholar.google.c
om) to research the
recent results on a problem. However, plagiarism should be avoided;
that is, you need to write in your own
language.
Attached is a sample just for your reference.
Sample Term Paper
Name:
Student ID
Longest Simple Path Problem
Introduction
We know
that
the shortest path problem of a graph can be solved easily.
A related
problem
is to find the longest path
between two vertices. If we allow duplicated
vertices on the path
, the longest path length can be infinity.
T
o avoid
this, we
disallow duplicated vertices
on a path. Such a path is a
simple path
; that is,
a path o
f
a graph is
simple
if
it contains
no
duplicated
vertices.
The longest simple path
problem is
then to fi
nd a
longest simple path
between two vertices of a graph. It is
useful
in information retrieval, VLSI design,
robot
patrolling
, etc.
Problem Definition
Let
G
be
undirected weighted graph
and G=
(V, E)
.
A
real value
is assigned to each
edge
as the respective
weight
. Given two vertices u and v (u, v
E),
the
goal
is to find
the
longest simple path from u to v.
Here, t
he length of a path is defined as total
weights of the edges belonging to the path.
State of the Art
Longest simple path problem
is NP

complete
[1]. Genetic algorithm, dynamic
programming
, mixed integer linear programming [
2, 3,
4] have been proposed
to
address the special instances of the problem
.
Karger et al.
propose
d
a
n approximate
algorithm
[5]
.
Reference
1.
Garey, M.R., Johnson, D.S
.: Computers and Intractability: A guide to the Theory of
NPCompleteness. W. H. Freeman, 1st ed. (1979)
2.
Wong, W.Y., Lau, T.P., King, I.: Information retrieval in p2p networks using genetic algorithm.
In: Proceedings of the 14th Int. World Wide Web Conferen
ce, Special interest tracks
and
posters. pp. 922
–
923 (2005)
3.
Schmidt, K., Schmidt, E.G.: A longest

path problem for evaluating the worst

case packetdelay
of switched ethernet. In: Proceedings of SIES’2010. pp. 205
–
208 (2010)
4.
Tseng, I.L., Chen, H.W., Lee, C.
I.: Obstacle

aware longest

path routing with parallel milp
solvers. In: Proceedings of WCECS

ICCS, Vol. 2. pp. 827
–
831 (2010)
5.
Karger, D., Motwani, R., Ramkumar, G.: On approximating the longest path in a
graph.Algorithmica 18, 421
–
432 (1993)
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