2,853 research outputs found
A Planarity Test via Construction Sequences
Optimal linear-time algorithms for testing the planarity of a graph are
well-known for over 35 years. However, these algorithms are quite involved and
recent publications still try to give simpler linear-time tests. We give a
simple reduction from planarity testing to the problem of computing a certain
construction of a 3-connected graph. The approach is different from previous
planarity tests; as key concept, we maintain a planar embedding that is
3-connected at each point in time. The algorithm runs in linear time and
computes a planar embedding if the input graph is planar and a
Kuratowski-subdivision otherwise
Planarity of Streamed Graphs
In this paper we introduce a notion of planarity for graphs that are
presented in a streaming fashion. A is a stream of
edges on a vertex set . A streamed graph is
- with respect to a positive integer window
size if there exists a sequence of planar topological drawings
of the graphs such that
the common graph is drawn the same in
and in , for . The Problem with window size asks whether a given streamed
graph is -stream planar. We also consider a generalization, where there
is an additional whose edges have to be present
during each time step. These problems are related to several well-studied
planarity problems.
We show that the Problem is NP-complete even when
the window size is a constant and that the variant with a backbone graph is
NP-complete for all . On the positive side, we provide
-time algorithms for (i) the case and (ii) all
values of provided the backbone graph consists of one -connected
component plus isolated vertices and no stream edge connects two isolated
vertices. Our results improve on the Hanani-Tutte-style -time
algorithm proposed by Schaefer [GD'14] for .Comment: 21 pages, 9 figures, extended version of "Planarity of Streamed
Graphs" (9th International Conference on Algorithms and Complexity, 2015
Homologous Pairing between Long DNA Double Helices
Molecular recognition between two double stranded (ds) DNA with homologous
sequences may not seem compatible with the B-DNA structure because the sequence
information is hidden when it is used for joining the two strands.
Nevertheless, it has to be invoked to account for various biological data.
Using quantum chemistry, molecular mechanics, and hints from recent genetics
experiments I show here that direct recognition between homologous dsDNA is
possible through formation of short quadruplexes due to direct complementary
hydrogen bonding of major groove surfaces in parallel alignment. The
constraints imposed by the predicted structures of the recognition units
determine the mechanism of complexation between long dsDNA. This mechanism and
concomitant predictions agree with available experimental data and shed light
upon the sequence effects and the possible involvement of topoisomerase II in
the recognition.Comment: 10 pages, 7 figures, Includes Supplemental Material. To appear in
Phys. Rev. Let
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