3,390 research outputs found
Some Results On Convex Greedy Embedding Conjecture for 3-Connected Planar Graphs
A greedy embedding of a graph into a metric space is a
function such that in the embedding for every pair of
non-adjacent vertices there exists another vertex adjacent
to which is closer to than . This notion of greedy
embedding was defined by Papadimitriou and Ratajczak (Theor. Comput. Sci.
2005), where authors conjectured that every 3-connected planar graph has a
greedy embedding (possibly planar and convex) in the Euclidean plane. Recently,
greedy embedding conjecture has been proved by Leighton and Moitra (FOCS 2008).
However, their algorithm do not result in a drawing that is planar and convex
for all 3-connected planar graph in the Euclidean plane. In this work we
consider the planar convex greedy embedding conjecture and make some progress.
We derive a new characterization of planar convex greedy embedding that given a
3-connected planar graph , an embedding x: V \to \bbbr^2 of is
a planar convex greedy embedding if and only if, in the embedding , weight
of the maximum weight spanning tree () and weight of the minimum weight
spanning tree (\func{MST}) satisfies \WT(T)/\WT(\func{MST}) \leq
(\card{V}-1)^{1 - \delta}, for some .Comment: 19 pages, A short version of this paper has been accepted for
presentation in FCT 2009 - 17th International Symposium on Fundamentals of
Computation Theor
Efficient Algorithms for Distributed Detection of Holes and Boundaries in Wireless Networks
We propose two novel algorithms for distributed and location-free boundary
recognition in wireless sensor networks. Both approaches enable a node to
decide autonomously whether it is a boundary node, based solely on connectivity
information of a small neighborhood. This makes our algorithms highly
applicable for dynamic networks where nodes can move or become inoperative.
We compare our algorithms qualitatively and quantitatively with several
previous approaches. In extensive simulations, we consider various models and
scenarios. Although our algorithms use less information than most other
approaches, they produce significantly better results. They are very robust
against variations in node degree and do not rely on simplified assumptions of
the communication model. Moreover, they are much easier to implement on real
sensor nodes than most existing approaches.Comment: extended version of accepted submission to SEA 201
Equation of State Based Slip Spring Model for Entangled Polymer Dynamics
A mesoscopic, mixed particle- and field-based Brownian dynamics methodology
for the simulation of entangled polymer melts has been developed. Polymeric
beads consist of several Kuhn segments, and their motion is dictated by the
Helmholtz energy of the sample, which is a sum of the entropic elasticity of
chain strands between beads, slip springs, and nonbonded interactions. The
entanglement effect is introduced by the slip springs, which are springs
connecting either nonsuccessive beads on the same chain or beads on different
polymer chains. The terminal positions of slip springs are altered during the
simulation through a kinetic Monte Carlo hopping scheme, with rate-controlled
creation/destruction processes for the slip springs at chain ends. The rate
constants are consistent with the free energy function employed and satisfy
microscopic reversibility at equilibrium. The free energy of nonbonded
interactions is derived from an appropriate equation of state, and it is
computed as a functional of the local density by passing an orthogonal grid
through the simulation box; accounting for it is necessary for reproducing the
correct compressibility of the polymeric material. Parameters invoked by the
mesoscopic model are derived from experimental volumetric and viscosity data or
from atomistic molecular dynamics simulations, establishing a "bottom-up"
predictive framework for conducting slip spring simulations of polymeric
systems of specific chemistry. The mesoscopic simulation methodology is
implemented for the case of cis-1,4-polyisoprene, whose structure, dynamics,
thermodynamics, and linear rheology in the melt state are quantitatively
predicted and validated without a posteriori fitting the results to
experimental measurements.Comment: 80 pages, 17 figure
Dominators in Directed Graphs: A Survey of Recent Results, Applications, and Open Problems
The computation of dominators is a central tool in program optimization and code generation, and it has applications in other diverse areas includingconstraint programming, circuit testing, and biology. In this paper we survey recent results, applications, and open problems related to the notion of dominators in directed graphs,including dominator verification and certification, computing independent spanning trees, and connectivity and path-determination problems in directed graphs
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