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Author, Editor

Author(s):

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

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Not MPG Author(s):

Boros, Endre
Gurvich, Vladimir
Khachiyan, Leonid

Editor(s):

Farach-Colton, Martin

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Not MPII Editor(s):

Farach-Colton, Martin

BibTeX cite key*:

Elbassioni2004d

Title, Booktitle

Title*:

Generating Maximal Independent Sets for Hypergraphs with Bounded Edge-Intersections


LATIN04.pdf (182.6 KB)

Booktitle*:

LATIN 2004: Theoretical Informatics, 6th Latin American Symposium

Event, URLs

URL of the conference:


URL for downloading the paper:


Event Address*:

Buenos Aires, Argentina

Language:

English

Event Date*
(no longer used):


Organization:


Event Start Date:

5 April 2004

Event End Date:

8 April 2004

Publisher

Name*:

Springer

URL:


Address*:

Berlin, Germany

Type:


Vol, No, Year, pp.

Series:

Lecture Notes in Computer Science

Volume:

2976

Number:


Month:

April

Pages:

488-498

Year*:

2004

VG Wort Pages:


ISBN/ISSN:

3-540-21258-2

Sequence Number:


DOI:




Note, Abstract, ©


(LaTeX) Abstract:

Given a finite set $V$, and integers $k \geq 1$ and $r \geq 0$,
denote by $\AA(k,r)$ the class of hypergraphs $\cA \subseteq 2^V$
with $(k,r)$-bounded intersections, i.e. in which
the intersection of any $k$ distinct hyperedges has size at most $r$. We consider the problem $MIS(\cA,\cI)$:
given a hypergraph $\cA$ and a subfamily $\cI \subseteq \In$,
of its maximal independent sets (MIS) $\In$, either extend this subfamily by constructing a new MIS $I \in \In \setminus \cI$
or prove that there are no more MIS, that is $\cI = \In$.
We show that for hypergraphs $\cA\in\AA(k,r)$ with $k+r\le const$, problem MIS$(\cA,\cI)$ is NC-reducible to problem MIS$(\cA',\emptyset)$ of generating a single MIS for
a partial subhypergraph $\cA'$ of $\cA$. In particular, for this class of hypergraphs, we get an incremental polynomial algorithm for generating all MIS. Furthermore, combining this result with the currently known algorithms for finding a single maximal independent set of a hypergraph, we obtain efficient parallel algorithms for incrementally generating all MIS for hypergraphs in the classes $\AA(1,c)$, $\AA(c,0)$, and $\AA(2,1)$, where $c$ is a constant. We also show that,
for $\cA \in \AA(k,r)$, where $k+r\le const$, the problem of
generating all MIS of $\cA$ can be solved in incremental polynomial-time with space polynomial only in the size of $\cA$.



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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{Elbassioni2004d,
AUTHOR = {Boros, Endre and Elbassioni, Khaled M. and Gurvich, Vladimir and Khachiyan, Leonid},
EDITOR = {Farach-Colton, Martin},
TITLE = {Generating Maximal Independent Sets for Hypergraphs with Bounded Edge-Intersections},
BOOKTITLE = {LATIN 2004: Theoretical Informatics, 6th Latin American Symposium},
PUBLISHER = {Springer},
YEAR = {2004},
VOLUME = {2976},
PAGES = {488--498},
SERIES = {Lecture Notes in Computer Science},
ADDRESS = {Buenos Aires, Argentina},
MONTH = {April},
ISBN = {3-540-21258-2},
}


Entry last modified by Christine Kiesel, 05/02/2007
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Editor(s)
Khaled Elbassioni
Created
02/23/2005 02:33:12 PM
Revisions
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2.
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Editor(s)
Christine Kiesel
Christine Kiesel
Christine Kiesel
Khaled Elbassioni
Edit Dates
02.05.2007 15:39:34
23.05.2005 14:29:21
21.04.2005 16:22:57
02/23/2005 02:33:12 PM
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