6,590 research outputs found
An Even Faster and More Unifying Algorithm for Comparing Trees via Unbalanced Bipartite Matchings
A widely used method for determining the similarity of two labeled trees is
to compute a maximum agreement subtree of the two trees. Previous work on this
similarity measure is only concerned with the comparison of labeled trees of
two special kinds, namely, uniformly labeled trees (i.e., trees with all their
nodes labeled by the same symbol) and evolutionary trees (i.e., leaf-labeled
trees with distinct symbols for distinct leaves). This paper presents an
algorithm for comparing trees that are labeled in an arbitrary manner. In
addition to this generality, this algorithm is faster than the previous
algorithms.
Another contribution of this paper is on maximum weight bipartite matchings.
We show how to speed up the best known matching algorithms when the input
graphs are node-unbalanced or weight-unbalanced. Based on these enhancements,
we obtain an efficient algorithm for a new matching problem called the
hierarchical bipartite matching problem, which is at the core of our maximum
agreement subtree algorithm.Comment: To appear in Journal of Algorithm
The history of degenerate (bipartite) extremal graph problems
This paper is a survey on Extremal Graph Theory, primarily focusing on the
case when one of the excluded graphs is bipartite. On one hand we give an
introduction to this field and also describe many important results, methods,
problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version
of our survey presented in Erdos 100. In this version 2 only a citation was
complete
Partition function of periodic isoradial dimer models
Isoradial dimer models were introduced in \cite{Kenyon3} - they consist of
dimer models whose underlying graph satisfies a simple geometric condition, and
whose weight function is chosen accordingly. In this paper, we prove a
conjecture of \cite{Kenyon3}, namely that for periodic isoradial dimer models,
the growth rate of the toroidal partition function has a simple explicit
formula involving the local geometry of the graph only. This is a surprising
feature of periodic isoradial dimer models, which does not hold in the general
periodic dimer case \cite{KOS}.Comment: 12 pages, 2 figure
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