274 research outputs found
A practical approximation algorithm for solving massive instances of hybridization number for binary and nonbinary trees
Reticulate events play an important role in determining evolutionary
relationships. The problem of computing the minimum number of such events to
explain discordance between two phylogenetic trees is a hard computational
problem. Even for binary trees, exact solvers struggle to solve instances with
reticulation number larger than 40-50. Here we present CycleKiller and
NonbinaryCycleKiller, the first methods to produce solutions verifiably close
to optimality for instances with hundreds or even thousands of reticulations.
Using simulations, we demonstrate that these algorithms run quickly for large
and difficult instances, producing solutions that are very close to optimality.
As a spin-off from our simulations we also present TerminusEst, which is the
fastest exact method currently available that can handle nonbinary trees: this
is used to measure the accuracy of the NonbinaryCycleKiller algorithm. All
three methods are based on extensions of previous theoretical work and are
publicly available. We also apply our methods to real data
07281 Abstracts Collection -- Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs
From 8th to 13th July 2007, the Dagstuhl Seminar ``Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
The Graph Motif problem parameterized by the structure of the input graph
The Graph Motif problem was introduced in 2006 in the context of biological
networks. It consists of deciding whether or not a multiset of colors occurs in
a connected subgraph of a vertex-colored graph. Graph Motif has been mostly
analyzed from the standpoint of parameterized complexity. The main parameters
which came into consideration were the size of the multiset and the number of
colors. Though, in the many applications of Graph Motif, the input graph
originates from real-life and has structure. Motivated by this prosaic
observation, we systematically study its complexity relatively to graph
structural parameters. For a wide range of parameters, we give new or improved
FPT algorithms, or show that the problem remains intractable. For the FPT
cases, we also give some kernelization lower bounds as well as some ETH-based
lower bounds on the worst case running time. Interestingly, we establish that
Graph Motif is W[1]-hard (while in W[P]) for parameter max leaf number, which
is, to the best of our knowledge, the first problem to behave this way.Comment: 24 pages, accepted in DAM, conference version in IPEC 201
09511 Abstracts Collection -- Parameterized complexity and approximation algorithms
From 14. 12. 2009 to 17. 12. 2009., the Dagstuhl Seminar 09511
``Parameterized complexity and approximation algorithms \u27\u27 was held
in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Parameterized complexity of the MINCCA problem on graphs of bounded decomposability
In an edge-colored graph, the cost incurred at a vertex on a path when two
incident edges with different colors are traversed is called reload or
changeover cost. The "Minimum Changeover Cost Arborescence" (MINCCA) problem
consists in finding an arborescence with a given root vertex such that the
total changeover cost of the internal vertices is minimized. It has been
recently proved by G\"oz\"upek et al. [TCS 2016] that the problem is FPT when
parameterized by the treewidth and the maximum degree of the input graph. In
this article we present the following results for the MINCCA problem:
- the problem is W[1]-hard parameterized by the treedepth of the input graph,
even on graphs of average degree at most 8. In particular, it is W[1]-hard
parameterized by the treewidth of the input graph, which answers the main open
problem of G\"oz\"upek et al. [TCS 2016];
- it is W[1]-hard on multigraphs parameterized by the tree-cutwidth of the
input multigraph;
- it is FPT parameterized by the star tree-cutwidth of the input graph, which
is a slightly restricted version of tree-cutwidth. This result strictly
generalizes the FPT result given in G\"oz\"upek et al. [TCS 2016];
- it remains NP-hard on planar graphs even when restricted to instances with
at most 6 colors and 0/1 symmetric costs, or when restricted to instances with
at most 8 colors, maximum degree bounded by 4, and 0/1 symmetric costs.Comment: 25 pages, 11 figure
Single-Exponential FPT Algorithms for Enumerating Secluded -Free Subgraphs and Deleting to Scattered Graph Classes
The celebrated notion of important separators bounds the number of small
-separators in a graph which are 'farthest from ' in a technical
sense. In this paper, we introduce a generalization of this powerful
algorithmic primitive that is phrased in terms of -secluded vertex sets:
sets with an open neighborhood of size at most .
In this terminology, the bound on important separators says that there are at
most maximal -secluded connected vertex sets containing but
disjoint from . We generalize this statement significantly: even when we
demand that avoids a finite set of forbidden induced
subgraphs, the number of such maximal subgraphs is and they can be
enumerated efficiently. This allows us to make significant improvements for two
problems from the literature.
Our first application concerns the 'Connected -Secluded -free
subgraph' problem, where is a finite set of forbidden induced
subgraphs. Given a graph in which each vertex has a positive integer weight,
the problem asks to find a maximum-weight connected -secluded vertex set such that does not contain an induced subgraph
isomorphic to any . The parameterization by is known to
be solvable in triple-exponential time via the technique of recursive
understanding, which we improve to single-exponential.
Our second application concerns the deletion problem to scattered graph
classes. Here, the task is to find a vertex set of size at most whose
removal yields a graph whose each connected component belongs to one of the
prescribed graph classes . We obtain a single-exponential
algorithm whenever each class is characterized by a finite number of
forbidden induced subgraphs. This generalizes and improves upon earlier results
in the literature.Comment: To appear at ISAAC'2
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