Deterministic parameterized algorithms for the Graph Motif problem

Ron Y. Pinter, Hadas Shachnai, Meirav Zehavi

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We study the classic GRAPH MOTIF problem. Given a graph G=(V,E) with a set of colors for each node, and a multiset M of colors, we seek a subtree T⊆G, and a coloring assigning to each node in T a color from its set, such that T carries exactly (also with respect to multiplicity) the colors in M. GRAPH MOTIF plays a central role in the study of pattern matching problems, primarily motivated from the analysis of complex biological networks. Previous algorithms for GRAPH MOTIF and its variants either rely on techniques for developing randomized algorithms that − if derandomized − render them inefficient, or the algebraic narrow sieves technique for which there is no known derandomization. In this paper, we present fast deterministic parameterized algorithms for GRAPH MOTIF and its variants. Specifically, we give such an algorithm for the more general GRAPH MOTIF WITH DELETIONS problem, followed by faster algorithms for GRAPH MOTIF and other well-studied special cases. Our algorithms make non-trivial use of representative families, and a novel tool that we call guiding trees, together enabling the efficient construction of the output tree.

Original languageEnglish
Pages (from-to)162-178
Number of pages17
JournalDiscrete Applied Mathematics
StatePublished - 20 Nov 2016
Externally publishedYes


  • Graph motif
  • Guiding tree
  • Parameterized algorithm
  • Representative family

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


Dive into the research topics of 'Deterministic parameterized algorithms for the Graph Motif problem'. Together they form a unique fingerprint.

Cite this