16,122 research outputs found
Bounded Search Tree Algorithms for Parameterized Cograph Deletion: Efficient Branching Rules by Exploiting Structures of Special Graph Classes
Many fixed-parameter tractable algorithms using a bounded search tree have
been repeatedly improved, often by describing a larger number of branching
rules involving an increasingly complex case analysis. We introduce a novel and
general search strategy that branches on the forbidden subgraphs of a graph
class relaxation. By using the class of -sparse graphs as the relaxed
graph class, we obtain efficient bounded search tree algorithms for several
parameterized deletion problems. We give the first non-trivial bounded search
tree algorithms for the cograph edge-deletion problem and the trivially perfect
edge-deletion problems. For the cograph vertex deletion problem, a refined
analysis of the runtime of our simple bounded search algorithm gives a faster
exponential factor than those algorithms designed with the help of complicated
case distinctions and non-trivial running time analysis [21] and computer-aided
branching rules [11].Comment: 23 pages. Accepted in Discrete Mathematics, Algorithms and
Applications (DMAA
FLEET: Butterfly Estimation from a Bipartite Graph Stream
We consider space-efficient single-pass estimation of the number of
butterflies, a fundamental bipartite graph motif, from a massive bipartite
graph stream where each edge represents a connection between entities in two
different partitions. We present a space lower bound for any streaming
algorithm that can estimate the number of butterflies accurately, as well as
FLEET, a suite of algorithms for accurately estimating the number of
butterflies in the graph stream. Estimates returned by the algorithms come with
provable guarantees on the approximation error, and experiments show good
tradeoffs between the space used and the accuracy of approximation. We also
present space-efficient algorithms for estimating the number of butterflies
within a sliding window of the most recent elements in the stream. While there
is a significant body of work on counting subgraphs such as triangles in a
unipartite graph stream, our work seems to be one of the few to tackle the case
of bipartite graph streams.Comment: This is the author's version of the work. It is posted here by
permission of ACM for your personal use. Not for redistribution. The
definitive version was published in Seyed-Vahid Sanei-Mehri, Yu Zhang, Ahmet
Erdem Sariyuce and Srikanta Tirthapura. "FLEET: Butterfly Estimation from a
Bipartite Graph Stream". The 28th ACM International Conference on Information
and Knowledge Managemen
A survey on algorithmic aspects of modular decomposition
The modular decomposition is a technique that applies but is not restricted
to graphs. The notion of module naturally appears in the proofs of many graph
theoretical theorems. Computing the modular decomposition tree is an important
preprocessing step to solve a large number of combinatorial optimization
problems. Since the first polynomial time algorithm in the early 70's, the
algorithmic of the modular decomposition has known an important development.
This paper survey the ideas and techniques that arose from this line of
research
FPT algorithms to recognize well covered graphs
Given a graph , let and be the sizes of a minimum and a
maximum minimal vertex covers of , respectively. We say that is well
covered if (that is, all minimal vertex covers have the same
size). Determining if a graph is well covered is a coNP-complete problem. In
this paper, we obtain -time and -time
algorithms to decide well coveredness, improving results of Boria et. al.
(2015). Moreover, using crown decomposition, we show that such problems admit
kernels having linear number of vertices. In 2018, Alves et. al. (2018) proved
that recognizing well covered graphs is coW[2]-hard when the independence
number is the parameter. Contrasting with such
coW[2]-hardness, we present an FPT algorithm to decide well coveredness when
and the degeneracy of the input graph are aggregate parameters.
Finally, we use the primeval decomposition technique to obtain a linear time
algorithm for extended -laden graphs and -graphs, which is FPT
parameterized by , improving results of Klein et al (2013).Comment: 15 pages, 2 figure
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