42,434 research outputs found
Conflict-free connection numbers of line graphs
A path in an edge-colored graph is called \emph{conflict-free} if it contains
at least one color used on exactly one of its edges. An edge-colored graph
is \emph{conflict-free connected} if for any two distinct vertices of ,
there is a conflict-free path connecting them. For a connected graph , the
\emph{conflict-free connection number} of , denoted by , is defined
as the minimum number of colors that are required to make conflict-free
connected. In this paper, we investigate the conflict-free connection numbers
of connected claw-free graphs, especially line graphs. We first show that for
an arbitrary connected graph , there exists a positive integer such that
. Secondly, we get the exact value of the conflict-free
connection number of a connected claw-free graph, especially a connected line
graph. Thirdly, we prove that for an arbitrary connected graph and an
arbitrary positive integer , we always have , with only the exception that is isomorphic to a star of order
at least~ and . Finally, we obtain the exact values of ,
and use them as an efficient tool to get the smallest nonnegative integer
such that .Comment: 11 page
Conflict-free connection number of random graphs
An edge-colored graph is conflict-free connected if any two of its
vertices are connected by a path which contains a color used on exactly one of
its edges. The conflict-free connection number of a connected graph ,
denoted by , is the smallest number of colors needed in order to make
conflict-free connected. In this paper, we show that almost all graphs have
the conflict-free connection number 2. More precisely, let denote the
Erd\H{o}s-R\'{e}nyi random graph model, in which each of the
pairs of vertices appears as an edge with probability independent from
other pairs. We prove that for sufficiently large , if
, where . This
means that as soon as becomes connected with high probability,
.Comment: 13 page
A fast and practical grid based algorithm for point-feature label placement problem
Point-feature label placement (PFLP) is a major area of interest within the
filed of automated cartography, geographic information systems (GIS), and
computer graphics. The objective of a label placement problem is to assign a
label to each point feature so as to avoid conflicts, considering the
cartographic conventions. According to computational complexity analysis, the
labeling problem has been shown to be NP-Hard. It is also very challenging to
find a computationally efficient algorithm that is intended to be used for both
static and dynamic map labeling. In this paper, we propose a heuristic method
that first fills the free space of the map with rectangular shape labels like a
grid and then matches the corresponding point feature with the nearest label.
The performance of the proposed algorithm was evaluated through empirical tests
with different data set sizes. The results show that our algorithm based on
grid placement of labels is a useful, fast and practical solution for automated
map labeling
Leveraging Physical Layer Capabilites: Distributed Scheduling in Interference Networks with Local Views
In most wireless networks, nodes have only limited local information about
the state of the network, which includes connectivity and channel state
information. With limited local information about the network, each node's
knowledge is mismatched; therefore, they must make distributed decisions. In
this paper, we pose the following question - if every node has network state
information only about a small neighborhood, how and when should nodes choose
to transmit? While link scheduling answers the above question for
point-to-point physical layers which are designed for an interference-avoidance
paradigm, we look for answers in cases when interference can be embraced by
advanced PHY layer design, as suggested by results in network information
theory.
To make progress on this challenging problem, we propose a constructive
distributed algorithm that achieves rates higher than link scheduling based on
interference avoidance, especially if each node knows more than one hop of
network state information. We compare our new aggressive algorithm to a
conservative algorithm we have presented in [1]. Both algorithms schedule
sub-networks such that each sub-network can employ advanced
interference-embracing coding schemes to achieve higher rates. Our innovation
is in the identification, selection and scheduling of sub-networks, especially
when sub-networks are larger than a single link.Comment: 14 pages, Submitted to IEEE/ACM Transactions on Networking, October
201
New mathematical structures in renormalizable quantum field theories
Computations in renormalizable perturbative quantum field theories reveal
mathematical structures which go way beyond the formal structure which is
usually taken as underlying quantum field theory. We review these new
structures and the role they can play in future developments.Comment: 26p,4figs., Invited Contribution to Annals of Physics, minor typos
correcte
Queued cross-bar network models for replication and coded storage systems
Coding techniques may be useful for data center data survivability as well as
for reducing traffic congestion. We present a queued cross-bar network (QCN)
method that can be used for traffic analysis of both replication/uncoded and
coded storage systems. We develop a framework for generating QCN rate regions
(RRs) by analyzing their conflict graph stable set polytopes (SSPs). In doing
so, we apply recent results from graph theory on the characterization of
particular graph SSPs. We characterize the SSP of QCN conflict graphs under a
variety of traffic patterns, allowing for their efficient RR computation. For
uncoded systems, we show how to compute RRs and find rate optimal scheduling
algorithms. For coded storage, we develop a RR upper bound, for which we
provide an intuitive interpretation. We show that the coded storage RR upper
bound is achievable in certain coded systems in which drives store sufficient
coded information, as well in certain dynamic coding systems. Numerical
illustrations show that coded storage can result in gains in RR volume of
approximately 50%, averaged across traffic patterns
Conflict-Free Coloring and its Applications
Let be a hypergraph. A {\em conflict-free} coloring of is an
assignment of colors to such that in each hyperedge there is at
least one uniquely-colored vertex. This notion is an extension of the classical
graph coloring. Such colorings arise in the context of frequency assignment to
cellular antennae, in battery consumption aspects of sensor networks, in RFID
protocols and several other fields, and has been the focus of many recent
research papers. In this paper, we survey this notion and its combinatorial and
algorithmic aspects.Comment: 35 page
Introduction to a system for implementing neural net connections on SIMD architectures
Neural networks have attracted much interest recently, and using parallel architectures to simulate neural networks is a natural and necessary application. The SIMD model of parallel computation is chosen, because systems of this type can be built with large numbers of processing elements. However, such systems are not naturally suited to generalized communication. A method is proposed that allows an implementation of neural network connections on massively parallel SIMD architectures. The key to this system is an algorithm permitting the formation of arbitrary connections between the neurons. A feature is the ability to add new connections quickly. It also has error recovery ability and is robust over a variety of network topologies. Simulations of the general connection system, and its implementation on the Connection Machine, indicate that the time and space requirements are proportional to the product of the average number of connections per neuron and the diameter of the interconnection network
A system for routing arbitrary directed graphs on SIMD architectures
There are many problems which can be described in terms of directed graphs that contain a large number of vertices where simple computations occur using data from connecting vertices. A method is given for parallelizing such problems on an SIMD machine model that is bit-serial and uses only nearest neighbor connections for communication. Each vertex of the graph will be assigned to a processor in the machine. Algorithms are given that will be used to implement movement of data along the arcs of the graph. This architecture and algorithms define a system that is relatively simple to build and can do graph processing. All arcs can be transversed in parallel in time O(T), where T is empirically proportional to the diameter of the interconnection network times the average degree of the graph. Modifying or adding a new arc takes the same time as parallel traversal
Well-Stratified Linked Data for Well-Behaved Data Citation
In this paper we analyse the functional requirements of linked data citation
and identify a minimal set of operations and primitives needed to realize such
task. Citing linked data implies solving a series of data provenance issues and
finding a way to identify data subsets. Those two tasks can be handled defining
a simple type system inside data and verifying it with a type checker, which is
significantly less complex than interpreting reified RDF statements and can be
implemented in a non data invasive way. Finally we suggest that data citation
should be handled outside of the data, possibly with an ad-hoc language.Comment: in Bulletin of IEEE Technical Committee on Digital Libraries, Volume
12 Issue 1, May 201
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