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Author, Editor

Author(s):

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

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Not MPG Author(s):

Boros, Endre
Gurvich, Vladimir
Khachiyan, Leonid

Editor(s):



Not MPII Editor(s):

Krzysztof Diks,
Wojciech Rytter

BibTeX cite key*:

Elbassioni2002b

Title, Booktitle

Title*:

Matroid Intersections, Polymatroid Inequalities, and Related Problems


MFCS02.pdf (186.23 KB)

Booktitle*:

Mathematical Foundations of Computer Science 2002, 27th International Symposium, MFCS 2002

Event, URLs

URL of the conference:


URL for downloading the paper:


Event Address*:

Warsaw, Poland

Language:

English

Event Date*
(no longer used):


Organization:


Event Start Date:

26 August 2002

Event End Date:

30 August 2002

Publisher

Name*:

Springer

URL:


Address*:

Berlin, Germany

Type:


Vol, No, Year, pp.

Series:

Lecture Notes in Computer Science

Volume:

2420

Number:


Month:

August

Pages:

143-154

Year*:

2002

VG Wort Pages:


ISBN/ISSN:


Sequence Number:


DOI:




Note, Abstract, ©


(LaTeX) Abstract:

Given $m$ matroids $M_1,\ldots, M_m$ on the common ground set $V$, it is shown that all maximal subsets of $V$, independent in the $m$ matroids, can be generated in quasi-polynomial time. More generally, given a system of polymatroid inequalities $f_1(X) \ge t_1,\ldots,f_m(X) \ge t_m$ with quasi-polynomially bounded right hand sides $t_1,\ldots,t_m$, all minimal feasible solutions $X \subseteq V$ to the system can be generated in incremental quasi-polynomial time. Our proof of these results is based on a combinatorial inequality for polymatroid functions which may be of independent interest. Precisely, for a polymatroid function $f$ and an integer threshold $t\geq 1$, let $\alpha=\alpha(f,t)$ denote the number of maximal sets $X \subseteq V$ satisfying $f(X)< t$, let $\beta=\beta(f,t)$ be the number of minimal sets $X \subseteq V $ for which $f(X) \ge t$, and let $n=|V|$. We show that $\alpha \le\max\{n,\beta^{(\log t)/c}\}$, where $c=c(n,\beta)$ is the unique positive root of the equation $2^c(n^{c/\log\beta}-1)=1$. In particular, our bound implies that $\alpha \le (n\beta)^{\log t}$. We also give examples of polymatroid functions with arbitrarily large $t, n, \alpha$ and $\beta$ for which $\alpha \ge \beta^{(.551 \log t)/c}$.



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Access Level:

Public

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:

@INPROCEEDINGS{Elbassioni2002b,
AUTHOR = {Boros, Endre and Elbassioni, Khaled M. and Khachiyan, Leonid and Gurvich, Vladimir},
TITLE = {Matroid Intersections, Polymatroid Inequalities, and Related Problems},
BOOKTITLE = {Mathematical Foundations of Computer Science 2002, 27th International Symposium, MFCS 2002},
PUBLISHER = {Springer},
YEAR = {2002},
VOLUME = {2420},
PAGES = {143--154},
SERIES = {Lecture Notes in Computer Science},
ADDRESS = {Warsaw, Poland},
MONTH = {August},
}


Entry last modified by Christine Kiesel, 07/15/2014
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Editor(s)
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Created
02/22/2005 07:35:26 PM
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Editor(s)
Christine Kiesel
Christine Kiesel
Khaled Elbassioni
Khaled Elbassioni
Khaled Elbassioni
Edit Dates
02.05.2007 15:41:01
02.06.2006 15:17:59
04/20/2006 06:42:31 PM
02/22/2005 07:56:38 PM
02/22/2005 07:35:26 PM
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