Constrained Multilinear Detection and Generalized Graph Motifs
(2016) In Algorithmica 74(2). p.947-967- Abstract
- We introduce a new algebraic sieving technique to detect constrained multilinear monomials in multivariate polynomial generating functions given by an evaluation oracle. The polynomials are assumed to have coefficients from a field of characteristic two. As applications of the technique, we show an O^∗(2^k)-time polynomial space algorithm for the k-sized Graph Motif problem. We also introduce a new optimization variant of the problem, called Closest Graph Motif and solve it within the same time bound. The Closest Graph Motif problem encompasses several previously studied optimization variants, like Maximum Graph Motif, Min-Substitute Graph Motif, and Min-Add Graph Motif. Finally, we provide a piece of evidence that our result might be... (More)
- We introduce a new algebraic sieving technique to detect constrained multilinear monomials in multivariate polynomial generating functions given by an evaluation oracle. The polynomials are assumed to have coefficients from a field of characteristic two. As applications of the technique, we show an O^∗(2^k)-time polynomial space algorithm for the k-sized Graph Motif problem. We also introduce a new optimization variant of the problem, called Closest Graph Motif and solve it within the same time bound. The Closest Graph Motif problem encompasses several previously studied optimization variants, like Maximum Graph Motif, Min-Substitute Graph Motif, and Min-Add Graph Motif. Finally, we provide a piece of evidence that our result might be essentially tight: the existence of an O^∗((2−ϵ)^k)-time algorithm for the Graph Motif problem implies an O((2−ϵ′)^n)-time algorithm for Set Cover. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/5152001
- author
- Björklund, Andreas LU ; Kaski, Petteri and Kowalik, Lukasz
- organization
- publishing date
- 2016
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Algorithmica
- volume
- 74
- issue
- 2
- pages
- 947 - 967
- publisher
- Springer
- external identifiers
-
- wos:000369011300015
- scopus:84955628212
- ISSN
- 0178-4617
- DOI
- 10.1007/s00453-015-9981-1
- project
- Exact algorithms
- language
- English
- LU publication?
- yes
- id
- c0c7cc4e-a1f5-40f4-b7e4-53686f802f47 (old id 5152001)
- date added to LUP
- 2016-04-01 10:51:12
- date last changed
- 2022-04-28 02:02:15
@article{c0c7cc4e-a1f5-40f4-b7e4-53686f802f47,
abstract = {{We introduce a new algebraic sieving technique to detect constrained multilinear monomials in multivariate polynomial generating functions given by an evaluation oracle. The polynomials are assumed to have coefficients from a field of characteristic two. As applications of the technique, we show an O^∗(2^k)-time polynomial space algorithm for the k-sized Graph Motif problem. We also introduce a new optimization variant of the problem, called Closest Graph Motif and solve it within the same time bound. The Closest Graph Motif problem encompasses several previously studied optimization variants, like Maximum Graph Motif, Min-Substitute Graph Motif, and Min-Add Graph Motif. Finally, we provide a piece of evidence that our result might be essentially tight: the existence of an O^∗((2−ϵ)^k)-time algorithm for the Graph Motif problem implies an O((2−ϵ′)^n)-time algorithm for Set Cover.}},
author = {{Björklund, Andreas and Kaski, Petteri and Kowalik, Lukasz}},
issn = {{0178-4617}},
language = {{eng}},
number = {{2}},
pages = {{947--967}},
publisher = {{Springer}},
series = {{Algorithmica}},
title = {{Constrained Multilinear Detection and Generalized Graph Motifs}},
url = {{http://dx.doi.org/10.1007/s00453-015-9981-1}},
doi = {{10.1007/s00453-015-9981-1}},
volume = {{74}},
year = {{2016}},
}