32,326 research outputs found
Reconfiguration of Dominating Sets
We explore a reconfiguration version of the dominating set problem, where a
dominating set in a graph is a set of vertices such that each vertex is
either in or has a neighbour in . In a reconfiguration problem, the goal
is to determine whether there exists a sequence of feasible solutions
connecting given feasible solutions and such that each pair of
consecutive solutions is adjacent according to a specified adjacency relation.
Two dominating sets are adjacent if one can be formed from the other by the
addition or deletion of a single vertex.
For various values of , we consider properties of , the graph
consisting of a vertex for each dominating set of size at most and edges
specified by the adjacency relation. Addressing an open question posed by Haas
and Seyffarth, we demonstrate that is not necessarily
connected, for the maximum cardinality of a minimal dominating set
in . The result holds even when graphs are constrained to be planar, of
bounded tree-width, or -partite for . Moreover, we construct an
infinite family of graphs such that has exponential
diameter, for the minimum size of a dominating set. On the positive
side, we show that is connected and of linear diameter for any
graph on vertices having at least independent edges.Comment: 12 pages, 4 figure
A reconfigurations analogue of Brooks’ theorem.
Let G be a simple undirected graph on n vertices with maximum degree Δ. Brooks’ Theorem states that G has a Δ-colouring unless G is a complete graph, or a cycle with an odd number of vertices. To recolour G is to obtain a new proper colouring by changing the colour of one vertex. We show that from a k-colouring, k > Δ, a Δ-colouring of G can be obtained by a sequence of O(n 2) recolourings using only the original k colours unless
G is a complete graph or a cycle with an odd number of vertices, or
k = Δ + 1, G is Δ-regular and, for each vertex v in G, no two neighbours of v are coloured alike.
We use this result to study the reconfiguration graph R k (G) of the k-colourings of G. The vertex set of R k (G) is the set of all possible k-colourings of G and two colourings are adjacent if they differ on exactly one vertex. It is known that
if k ≤ Δ(G), then R k (G) might not be connected and it is possible that its connected components have superpolynomial diameter,
if k ≥ Δ(G) + 2, then R k (G) is connected and has diameter O(n 2).
We complete this structural classification by settling the missing case:
if k = Δ(G) + 1, then R k (G) consists of isolated vertices and at most one further component which has diameter O(n 2).
We also describe completely the computational complexity classification of the problem of deciding whether two k-colourings of a graph G of maximum degree Δ belong to the same component of R k (G) by settling the case k = Δ(G) + 1. The problem is
O(n 2) time solvable for k = 3,
PSPACE-complete for 4 ≤ k ≤ Δ(G),
O(n) time solvable for k = Δ(G) + 1,
O(1) time solvable for k ≥ Δ(G) + 2 (the answer is always yes)
Extended Superconformal Algebras from Classical and Quantum Hamiltonian Reduction
We consider the extended superconformal algebras of the Knizhnik-Bershadsky
type with -algebra like composite operators occurring in the commutation
relations, but with generators of conformal dimension 1, and 2,
only. These have recently been neatly classified by several groups, and we
emphasize the classification based on hamiltonian reduction of affine Lie
superalgebras with even subalgebras . We reveiw the situation
and improve on previous formulations by presenting generic and very compact
expressions valid for all algebras, classical and quantum. Similarly generic
and compact free field realizations are presented as are corresponding
screening charges. Based on these a discussion of singular vectors is
presented. (Based on talk by J.L. Petersen at the Int. Workshop on "String
Theory, Quantum Gravity and the Unification of the Fundamental Interactions",
Rome Sep. 21-26, 1992)Comment: 30 pages, NBI-HE-92-8
Degree-constrained Subgraph Reconfiguration is in P
The degree-constrained subgraph problem asks for a subgraph of a given graph
such that the degree of each vertex is within some specified bounds. We study
the following reconfiguration variant of this problem: Given two solutions to a
degree-constrained subgraph instance, can we transform one solution into the
other by adding and removing individual edges, such that each intermediate
subgraph satisfies the degree constraints and contains at least a certain
minimum number of edges? This problem is a generalization of the matching
reconfiguration problem, which is known to be in P. We show that even in the
more general setting the reconfiguration problem is in P.Comment: Full version of the paper published at Mathematical Foundations of
Computer Science (MFCS) 201
Optimization of the Ballistic Guide Design for the SNS FNPB 8.9 A Neutron Line
The optimization of the ballistic guide design for the SNS Fundamental
Neutron Physics Beamline 8.9 A line is described. With a careful tuning of the
shape of the curve for the tapered section and the width of the straight
section, this optimization resulted in more than 75% increase in the neutron
flux exiting the 33 m long guide over a straight m=3.5 guide with the same
length.Comment: 21 pages, 13 figures; added a paragraph on existing ballistic guides
to respond to referee comments; accepted for publication in Nuclear Inst. and
Methods in Physics Research,
Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model and Biological Neurons
Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a comprehensive investigation across diverse simulated and experimental systems, encompassing star and complex networks of Rössler systems, coupled hysteresis-based electronic oscillators, microcircuits of leaky integrate-and-fire model neurons, and finally recordings from in-vitro cultures of spontaneously-growing neuronal networks. We systematically consider a range of dynamical measures, including the correlation dimension, nonlinear prediction error, permutation entropy, and other information-theoretical indices. The empirical evidence gathered reveals that under situations of weak synchronization, wherein rather than a collective behavior one observes significantly differentiated dynamics, denser connectivity tends to locally promote the emergence of stronger signatures of nonlinear dynamics. In deterministic systems, transition to chaos and generation of higher-dimensional signals were observed; however, when the coupling is stronger, this relationship may be lost or even inverted. In systems with a strong stochastic component, the generation of more temporally-organized activity could be induced. These observations have many potential implications across diverse fields of basic and applied science, for example, in the design of distributed sensing systems based on wireless coupled oscillators, in network identification and control, as well as in the interpretation of neuroscientific and other dynamical data
Exact Parametrization of Majorana Neutrino Mass Matrix with Large Mixing
Under the assumption that the neutrinos are Majorana particles we study how
the lepton mass matrices can be transformed into the simple form which has the
same physical quantities by removing redundant parameters. We propose the exact
parametrization of the lepton mass matrices which reflects the small nu_e-nu_mu
mixing and the large nu_mu-nu_tau mixing. The relations between the twelve
parameters and the physical quantities are shown. Furthermore we calculate the
MNS matrix by applying the assumptions used in the quark sector. Finally we
also check the validity of these assumptions from the experimental values.Comment: 11 pages, LaTeX, no figure
Reconfiguration on sparse graphs
A vertex-subset graph problem Q defines which subsets of the vertices of an
input graph are feasible solutions. A reconfiguration variant of a
vertex-subset problem asks, given two feasible solutions S and T of size k,
whether it is possible to transform S into T by a sequence of vertex additions
and deletions such that each intermediate set is also a feasible solution of
size bounded by k. We study reconfiguration variants of two classical
vertex-subset problems, namely Independent Set and Dominating Set. We denote
the former by ISR and the latter by DSR. Both ISR and DSR are PSPACE-complete
on graphs of bounded bandwidth and W[1]-hard parameterized by k on general
graphs. We show that ISR is fixed-parameter tractable parameterized by k when
the input graph is of bounded degeneracy or nowhere-dense. As a corollary, we
answer positively an open question concerning the parameterized complexity of
the problem on graphs of bounded treewidth. Moreover, our techniques generalize
recent results showing that ISR is fixed-parameter tractable on planar graphs
and graphs of bounded degree. For DSR, we show the problem fixed-parameter
tractable parameterized by k when the input graph does not contain large
bicliques, a class of graphs which includes graphs of bounded degeneracy and
nowhere-dense graphs
Reconfiguring Independent Sets in Claw-Free Graphs
We present a polynomial-time algorithm that, given two independent sets in a
claw-free graph , decides whether one can be transformed into the other by a
sequence of elementary steps. Each elementary step is to remove a vertex
from the current independent set and to add a new vertex (not in )
such that the result is again an independent set. We also consider the more
restricted model where and have to be adjacent
Preparation of linear hydroxy substituted polyphosphazenes
The synthesis of partially hydroxy-substituted phosphazene prepolymers amenable to processing into cellular, flexible polyurethane foams was investigated. Factors determined include (1) the environment of the hydroxyl group; (2) the ease of the hexachlorocyclotriphosphazene polymerization; (3) the nature of the nonreactive substituents; and (4) the mode of introduction of the hydroxyl entity. The specific approaches taken, the rationale of the selections made, and the results are discussed
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