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Constrained Multilinear Detection and Generalized Graph Motifs

Björklund, Andreas LU ; Kaski, Petteri and Kowalik, Lukasz (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)
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author
organization
publishing date
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
2015-03-09 14:04:29
date last changed
2017-10-22 03:24:09
@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},
  volume       = {74},
  year         = {2016},
}