133 research outputs found
On the Minimum Degree up to Local Complementation: Bounds and Complexity
The local minimum degree of a graph is the minimum degree reached by means of
a series of local complementations. In this paper, we investigate on this
quantity which plays an important role in quantum computation and quantum error
correcting codes. First, we show that the local minimum degree of the Paley
graph of order p is greater than sqrt{p} - 3/2, which is, up to our knowledge,
the highest known bound on an explicit family of graphs. Probabilistic methods
allows us to derive the existence of an infinite number of graphs whose local
minimum degree is linear in their order with constant 0.189 for graphs in
general and 0.110 for bipartite graphs. As regards the computational complexity
of the decision problem associated with the local minimum degree, we show that
it is NP-complete and that there exists no k-approximation algorithm for this
problem for any constant k unless P = NP.Comment: 11 page
Fast Evaluation of Interlace Polynomials on Graphs of Bounded Treewidth
We consider the multivariate interlace polynomial introduced by Courcelle
(2008), which generalizes several interlace polynomials defined by Arratia,
Bollobas, and Sorkin (2004) and by Aigner and van der Holst (2004). We present
an algorithm to evaluate the multivariate interlace polynomial of a graph with
n vertices given a tree decomposition of the graph of width k. The best
previously known result (Courcelle 2008) employs a general logical framework
and leads to an algorithm with running time f(k)*n, where f(k) is doubly
exponential in k. Analyzing the GF(2)-rank of adjacency matrices in the context
of tree decompositions, we give a faster and more direct algorithm. Our
algorithm uses 2^{3k^2+O(k)}*n arithmetic operations and can be efficiently
implemented in parallel.Comment: v4: Minor error in Lemma 5.5 fixed, Section 6.6 added, minor
improvements. 44 pages, 14 figure
Parameterized Edge Hamiltonicity
We study the parameterized complexity of the classical Edge Hamiltonian Path
problem and give several fixed-parameter tractability results. First, we settle
an open question of Demaine et al. by showing that Edge Hamiltonian Path is FPT
parameterized by vertex cover, and that it also admits a cubic kernel. We then
show fixed-parameter tractability even for a generalization of the problem to
arbitrary hypergraphs, parameterized by the size of a (supplied) hitting set.
We also consider the problem parameterized by treewidth or clique-width.
Surprisingly, we show that the problem is FPT for both of these standard
parameters, in contrast to its vertex version, which is W-hard for
clique-width. Our technique, which may be of independent interest, relies on a
structural characterization of clique-width in terms of treewidth and complete
bipartite subgraphs due to Gurski and Wanke
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 Monadic Second-Order Transduction Hierarchy
We compare classes of finite relational structures via monadic second-order
transductions. More precisely, we study the preorder where we set C \subseteq K
if, and only if, there exists a transduction {\tau} such that
C\subseteq{\tau}(K). If we only consider classes of incidence structures we can
completely describe the resulting hierarchy. It is linear of order type
{\omega}+3. Each level can be characterised in terms of a suitable variant of
tree-width. Canonical representatives of the various levels are: the class of
all trees of height n, for each n \in N, of all paths, of all trees, and of all
grids
Well-quasi-ordering versus clique-width : new results on bigenic classes.
Daligault, Rao and Thomassé conjectured that if a hereditary class of graphs is well-quasi-ordered by the induced subgraph relation then it has bounded clique-width. Lozin, Razgon and Zamaraev recently showed that this conjecture is not true for infinitely defined classes. For finitely defined classes the conjecture is still open. It is known to hold for classes of graphs defined by a single forbidden induced subgraph H, as such graphs are well-quasi-ordered and are of bounded clique-width if and only if H is an induced subgraph of P4P4. For bigenic classes of graphs i.e. ones defined by two forbidden induced subgraphs there are several open cases in both classifications. We reduce the number of open cases for well-quasi-orderability of such classes from 12 to 9. Our results agree with the conjecture and imply that there are only two remaining cases to verify for bigenic classes
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
Open problems on graph coloring for special graph classes.
For a given graph G and integer k, the Coloring problem is that of testing whether G has a k-coloring, that is, whether there exists a vertex mapping c:V→{1,2,…}c:V→{1,2,…} such that c(u)≠c(v)c(u)≠c(v) for every edge uv∈Euv∈E. We survey known results on the computational complexity of Coloring for graph classes that are hereditary or for which some graph parameter is bounded. We also consider coloring variants, such as precoloring extensions and list colorings and give some open problems in the area of on-line coloring
Prevalence and risk factors of malaria among children in southern highland Rwanda
<p>Abstract</p> <p>Background</p> <p>Increased control has produced remarkable reductions of malaria in some parts of sub-Saharan Africa, including Rwanda. In the southern highlands, near the district capital of Butare (altitude, 1,768 m), a combined community-and facility-based survey on <it>Plasmodium </it>infection was conducted early in 2010.</p> <p>Methods</p> <p>A total of 749 children below five years of age were examined including 545 randomly selected from 24 villages, 103 attending the health centre in charge, and 101 at the referral district hospital. Clinical, parasitological, haematological, and socio-economic data were collected.</p> <p>Results</p> <p><it>Plasmodium falciparum </it>infection (mean multiplicity, 2.08) was identified by microscopy and PCR in 11.7% and 16.7%, respectively; 5.5% of the children had malaria. PCR-based <it>P. falciparum </it>prevalence ranged between 0 and 38.5% in the villages, and was 21.4% in the health centre, and 14.9% in the hospital. Independent predictors of infection included increasing age, low mid-upper arm circumference, absence of several household assets, reported recent intake of artemether-lumefantrine, and chloroquine in plasma, measured by ELISA. Self-reported bed net use (58%) reduced infection only in univariate analysis. In the communities, most infections were seemingly asymptomatic but anaemia was observed in 82% and 28% of children with and without parasitaemia, respectively, the effect increasing with parasite density, and significant also for submicroscopic infections.</p> <p>Conclusions</p> <p><it>Plasmodium falciparum </it>infection in the highlands surrounding Butare, Rwanda, is seen in one out of six children under five years of age. The abundance of seemingly asymptomatic infections in the community forms a reservoir for transmission in this epidemic-prone area. Risk factors suggestive of low socio-economic status and insufficient effectiveness of self-reported bed net use refer to areas of improvable intervention.</p
Incentives for retaining and motivating health workers in Pacific and Asian countries
This paper was initiated by the Australian Agency for International Development (AusAID) after identifying the need for an in-depth synthesis and analysis of available literature and information on incentives for retaining health workers in the Asia-Pacific region. The objectives of this paper are to
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