83 research outputs found
Model Counting for Formulas of Bounded Clique-Width
We show that #SAT is polynomial-time tractable for classes of CNF formulas
whose incidence graphs have bounded symmetric clique-width (or bounded
clique-width, or bounded rank-width). This result strictly generalizes
polynomial-time tractability results for classes of formulas with signed
incidence graphs of bounded clique-width and classes of formulas with incidence
graphs of bounded modular treewidth, which were the most general results of
this kind known so far.Comment: Extended version of a paper published at ISAAC 201
Between Treewidth and Clique-width
Many hard graph problems can be solved efficiently when restricted to graphs
of bounded treewidth, and more generally to graphs of bounded clique-width. But
there is a price to be paid for this generality, exemplified by the four
problems MaxCut, Graph Coloring, Hamiltonian Cycle and Edge Dominating Set that
are all FPT parameterized by treewidth but none of which can be FPT
parameterized by clique-width unless FPT = W[1], as shown by Fomin et al [7,
8]. We therefore seek a structural graph parameter that shares some of the
generality of clique-width without paying this price. Based on splits, branch
decompositions and the work of Vatshelle [18] on Maximum Matching-width, we
consider the graph parameter sm-width which lies between treewidth and
clique-width. Some graph classes of unbounded treewidth, like
distance-hereditary graphs, have bounded sm-width. We show that MaxCut, Graph
Coloring, Hamiltonian Cycle and Edge Dominating Set are all FPT parameterized
by sm-width
Parameterized Algorithms for Modular-Width
It is known that a number of natural graph problems which are FPT
parameterized by treewidth become W-hard when parameterized by clique-width. It
is therefore desirable to find a different structural graph parameter which is
as general as possible, covers dense graphs but does not incur such a heavy
algorithmic penalty.
The main contribution of this paper is to consider a parameter called
modular-width, defined using the well-known notion of modular decompositions.
Using a combination of ILPs and dynamic programming we manage to design FPT
algorithms for Coloring and Partitioning into paths (and hence Hamiltonian path
and Hamiltonian cycle), which are W-hard for both clique-width and its recently
introduced restriction, shrub-depth. We thus argue that modular-width occupies
a sweet spot as a graph parameter, generalizing several simpler notions on
dense graphs but still evading the "price of generality" paid by clique-width.Comment: to appear in IPEC 2013. arXiv admin note: text overlap with
arXiv:1304.5479 by other author
Linear MIM-Width of Trees
We provide an algorithm computing the linear maximum induced
matching width of a tree and an optimal layout.Comment: 19 pages, 7 figures, full version of WG19 paper of same nam
On the Treewidth of Dynamic Graphs
Dynamic graph theory is a novel, growing area that deals with graphs that
change over time and is of great utility in modelling modern wireless, mobile
and dynamic environments. As a graph evolves, possibly arbitrarily, it is
challenging to identify the graph properties that can be preserved over time
and understand their respective computability.
In this paper we are concerned with the treewidth of dynamic graphs. We focus
on metatheorems, which allow the generation of a series of results based on
general properties of classes of structures. In graph theory two major
metatheorems on treewidth provide complexity classifications by employing
structural graph measures and finite model theory. Courcelle's Theorem gives a
general tractability result for problems expressible in monadic second order
logic on graphs of bounded treewidth, and Frick & Grohe demonstrate a similar
result for first order logic and graphs of bounded local treewidth.
We extend these theorems by showing that dynamic graphs of bounded (local)
treewidth where the length of time over which the graph evolves and is observed
is finite and bounded can be modelled in such a way that the (local) treewidth
of the underlying graph is maintained. We show the application of these results
to problems in dynamic graph theory and dynamic extensions to static problems.
In addition we demonstrate that certain widely used dynamic graph classes
naturally have bounded local treewidth
A SAT Approach to Clique-Width
Clique-width is a graph invariant that has been widely studied in
combinatorics and computer science. However, computing the clique-width of a
graph is an intricate problem, the exact clique-width is not known even for
very small graphs. We present a new method for computing the clique-width of
graphs based on an encoding to propositional satisfiability (SAT) which is then
evaluated by a SAT solver. Our encoding is based on a reformulation of
clique-width in terms of partitions that utilizes an efficient encoding of
cardinality constraints. Our SAT-based method is the first to discover the
exact clique-width of various small graphs, including famous graphs from the
literature as well as random graphs of various density. With our method we
determined the smallest graphs that require a small pre-described clique-width.Comment: proofs in section 3 updated, results remain unchange
Clique-width : harnessing the power of atoms.
Many NP-complete graph problems are polynomial-time solvable on graph classes of bounded clique-width. Several of these problems are polynomial-time solvable on a hereditary graph class G if they are so on the atoms (graphs with no clique cut-set) of G . Hence, we initiate a systematic study into boundedness of clique-width of atoms of hereditary graph classes. A graph G is H-free if H is not an induced subgraph of G, and it is (H1,H2) -free if it is both H1 -free and H2 -free. A class of H-free graphs has bounded clique-width if and only if its atoms have this property. This is no longer true for (H1,H2) -free graphs, as evidenced by one known example. We prove the existence of another such pair (H1,H2) and classify the boundedness of clique-width on (H1,H2) -free atoms for all but 18 cases
E2F1 drives chemotherapeutic drug resistance via ABCG2
Multidrug resistance is a major barrier against successful chemotherapy, and this has been shown in vitro to be often caused by ATP-binding cassette (ABC) transporters. These transporters are frequently overexpressed in human cancers and confer an adverse prognosis in many common malignancies. The genetic factors, however, that initiate their expression in cancer are largely unknown. Here we report that the major multidrug transporter ABCG2 (BCRP/MXR) is directly and specifically activated by the transcription factor E2F1—a factor perturbed in the majority of human cancers. E2F1 regulates ABCG2 expression in multiple cell systems, and, importantly, we have identified a significant correlation between elevated E2F1 and ABCG2 expression in human lung cancers. We show that E2F1 causes chemotherapeutic drug efflux both in vitro and in vivo via ABCG2. Furthermore, the E2F1–ABCG2 axis suppresses chemotherapy-induced cell death that can be restored by the inhibition of ABCG2. These findings therefore identify a new axis in multidrug resistance and highlight a radical new function of E2F1 that is relevant to tumor therapy
- …