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Author, Editor(s)

Author(s):

Boros, Endre
Elbassioni, Khaled M.
Khachiyan, Leonid
Gurvich, Vladimir
Makino, Kazuhisa

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Not MPG Author(s):

Boros, Endre
Gurvich, Vladimir
Khachiyan, Leonid
Makino, Kazuhisa

BibTeX cite key*:

Elbassioni2002a

Title

Title*:

Dual-Bounded Generating Problems: All Minimal Integer Solutions for a Monotone System of Linear Inequalities

Journal

Journal Title*:

SIAM Journal on Computing

Journal's URL:


Download URL
for the article:

http://epubs.siam.org/sam-bin/dbq/article/38876

Language:

English

Publisher

Publisher's
Name:

SIAM

Publisher's URL:


Publisher's
Address:


ISSN:


Vol, No, pp, Date

Volume*:

31

Number:


Publishing Date:

2002

Pages*:

20

Number of
VG Pages:


Page Start:

1624

Page End:

1643

Sequence Number:

5

DOI:


Note, Abstract, ©

Note:


(LaTeX) Abstract:

We consider the problem of enumerating all minimal integer
solutions of a monotone system of linear inequalities. We first show that for any monotone system of $r$ linear inequalities in $n$ variables, the number of maximal infeasible integer vectors is at most $rn$ times the number of minimal integer solutions to the system. This bound is accurate up to a $polylog(r)$ factor and leads to a polynomial-time reduction of the enumeration problem to a natural generalization of the well-known dualization problem for hypergraphs, in which dual pairs of hypergraphs are replaced by dual collections of integer vectors in a box. We provide a quasi-polynomial algorithm for the latter dualization problem. These results imply, in particular, that the problem of
incrementally generating all minimal integer solutions to a monotone system of linear inequalities can be done in quasi-polynomial time.

URL for the Abstract:


Categories,
Keywords:

Integer programming, complexity of incremental algorithms, dualization, quasi-polynomial time, monotone discrete binary functions, monotone inequalities, regular discrete functions

HyperLinks / References / URLs:


Copyright Message:


Personal Comments:


Download
Access Level:

Intranet

Correlation

MPG Unit:

Max-Planck-Institut für Informatik



MPG Subunit:

Algorithms and Complexity Group

Appearance:

MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort


BibTeX Entry:

@ARTICLE{Elbassioni2002a,
AUTHOR = {Boros, Endre and Elbassioni, Khaled M. and Khachiyan, Leonid and Gurvich, Vladimir and Makino, Kazuhisa},
TITLE = {Dual-Bounded Generating Problems: All Minimal Integer Solutions for a Monotone System of Linear Inequalities},
JOURNAL = {SIAM Journal on Computing},
PUBLISHER = {SIAM},
YEAR = {2002},
VOLUME = {31},
PAGES = {20},
}


Entry last modified by Christine Kiesel, 07/15/2014
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Editor(s)
[Library]
Created
02/22/2005 06:27:25 PM
Revisions
3.
2.
1.
0.
Editor(s)
Christine Kiesel
Khaled Elbassioni
Khaled Elbassioni
Khaled Elbassioni
Edit Dates
02.05.2007 16:47:37
04/20/2006 06:44:19 PM
02/23/2005 02:49:34 PM
02/22/2005 06:27:26 PM