Constrained Multilinear Detection and Generalized Graph Motifs

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...

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Vydáno v:Algorithmica Ročník 74; číslo 2; s. 947 - 967
Hlavní autoři: Björklund, Andreas, Kaski, Petteri, Kowalik, Łukasz
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.02.2016
Témata:
Algorithm Analysis and Problem Complexity
Algorithms
Computer and Information Sciences
Computer Science
Computer Sciences
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Data- och informationsvetenskap (Datateknik)
Datavetenskap (Datalogi)
Mathematics of Computing
Natural Sciences
Naturvetenskap
Theory of Computation
FPT algorithm
Constrained multilinear detection
Graph motif
ISSN:0178-4617, 1432-0541, 1432-0541
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Popis
Shrnutí: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 .
ISSN:0178-4617
1432-0541
1432-0541
DOI:10.1007/s00453-015-9981-1