CS4335 Design and Analysis of Algorithms

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Oct 24, 2013 (4 years and 20 days ago)

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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)