---
res:
  bibo_abstract:
  - We consider two systems (α1, …, αm) and (β1, …,βn) of simple curves drawn on a
    compact two-dimensional surface M with boundary. Each αi and each βj is either
    an arc meeting the boundary of M at its two endpoints, or a closed curve. The
    αi are pairwise disjoint except for possibly sharing endpoints, and similarly
    for the βj. We want to “untangle” the βj from the ai by a self-homeomorphism of
    M; more precisely, we seek a homeomorphism φ:M→M fixing the boundary of M pointwise
    such that the total number of crossings of the ai with the φ(βj) is as small as
    possible. This problem is motivated by an application in the algorithmic theory
    of embeddings and 3-manifolds. We prove that if M is planar, i.e., a sphere with
    h ≥ 0 boundary components (“holes”), then O(mn) crossings can be achieved (independently
    of h), which is asymptotically tight, as an easy lower bound shows. In general,
    for an arbitrary (orientable or nonorientable) surface M with h holes and of (orientable
    or nonorientable) genus g ≥ 0, we obtain an O((m + n)4) upper bound, again independent
    of h and g. The proofs rely, among other things, on a result concerning simultaneous
    planar drawings of graphs by Erten and Kobourov.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Jiří
      foaf_name: Matoušek, Jiří
      foaf_surname: Matoušek
  - foaf_Person:
      foaf_givenName: Eric
      foaf_name: Sedgwick, Eric
      foaf_surname: Sedgwick
  - foaf_Person:
      foaf_givenName: Martin
      foaf_name: Tancer, Martin
      foaf_surname: Tancer
      foaf_workInfoHomepage: http://www.librecat.org/personId=38AC689C-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-1191-6714
  - foaf_Person:
      foaf_givenName: Uli
      foaf_name: Wagner, Uli
      foaf_surname: Wagner
      foaf_workInfoHomepage: http://www.librecat.org/personId=36690CA2-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-1494-0568
  bibo_doi: 10.1007/s11856-016-1294-9
  bibo_issue: '1'
  bibo_volume: 212
  dct_date: 2016^xs_gYear
  dct_identifier:
  - UT:000377265600002
  dct_language: eng
  dct_publisher: Springer@
  dct_title: Untangling two systems of noncrossing curves@
...