Quasipolynomial representation of transversal matroids with applications in parameterized complexity

Daniel Lokshtanov, Pranabendu Misra, Fahad Panolan, Saket Saurabh, Meirav Zehavi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Deterministic polynomial-time computation of a representation of a transversal matroid is a longstanding open problem. We present a deterministic computation of a so-called union representation of a transversal matroid in time quasipolynomial in the rank of the matroid. More precisely, we output a collection of linear matroids such that a set is independent in the transversal matroid if and only if it is independent in at least one of them. Our proof directly implies that if one is interested in preserving independent sets of size at most r, for a given r ∈ N, but does not care whether larger independent sets are preserved, then a union representation can be computed deterministically in time quasipolynomial in r. This consequence is of independent interest, and sheds light on the power of union representation. Our main result also has applications in Parameterized Complexity. First, it yields a fast computation of representative sets, and due to our relaxation in the context of r, this computation also extends to (standard) truncations. In turn, this computation enables to efficiently solve various problems, such as subcases of subgraph isomorphism, motif search and packing problems, in the presence of color lists. Such problems have been studied to model scenarios where pairs of elements to be matched may not be identical but only similar, and color lists aim to describe the set of compatible elements associated with each element.

Original languageAmerican English
Title of host publication9th Innovations in Theoretical Computer Science, ITCS 2018
EditorsAnna R. Karlin
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770606
StatePublished - 1 Jan 2018
Event9th Innovations in Theoretical Computer Science, ITCS 2018 - Cambridge, United States
Duration: 11 Jan 201814 Jan 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs


Conference9th Innovations in Theoretical Computer Science, ITCS 2018
Country/TerritoryUnited States


  • Matroid representation
  • Representative set
  • Travserval matroid
  • Union representation

All Science Journal Classification (ASJC) codes

  • Software


Dive into the research topics of 'Quasipolynomial representation of transversal matroids with applications in parameterized complexity'. Together they form a unique fingerprint.

Cite this