4,806 research outputs found
"Graph Entropy, Network Coding and Guessing games"
We introduce the (private) entropy of a directed graph (in a new network coding sense) as well as a number of related concepts. We show that the entropy of a directed graph is identical to its guessing number and can be bounded from below with the number of vertices minus the size of the graphâs shortest index code. We show that the Network Coding solvability of each speciïŹc multiple unicast network is completely determined by the entropy (as well as by the shortest index code) of the directed graph that occur by identifying each source node with each corresponding target node. Shannonâs information inequalities can be used to calculate up- per bounds on a graphâs entropy as well as calculating the size of the minimal index code. Recently, a number of new families of so-called non-shannon-type information inequalities have been discovered. It has been shown that there exist communication networks with a ca- pacity strictly ess than required for solvability, but where this fact cannot be derived using Shannonâs classical information inequalities. Based on this result we show that there exist graphs with an entropy that cannot be calculated using only Shannonâs classical information inequalities, and show that better estimate can be obtained by use of certain non-shannon-type information inequalities
The Initial-Value Problem of Spherically Symmetric Wyman Sector Nonsymmetric Gravitational Theory
We cast the four-dimensional field equations of the Nonsymmetric
Gravitational Theory (NGT) into a form appropriate for numerical study. In
doing so, we have restricted ourselves to spherically symmetric spacetimes, and
we have kept only the Wyman sector of the theory. We investigate the
well-posedness of the initial-value problem of NGT for a particular data set
consisting of a pulse in the antisymmetric field on an asymptotically flat
space background. We include some analytic results on the solvability of the
initial-value problem which allow us to place limits on the regions of the
parameter space where the initial-value problem is solvable. These results are
confirmed by numerically solving the constraints.Comment: REVTeX 3.0 with epsf macros and AMS symbols, 18 pages, 9 figure
Consistency of a system of equations: What does that mean?
The concept of (structural) consistency also called structural solvability is an important basic tool for analyzing the structure of systems of equations. Our aim is to provide a sound and practically relevant meaning to this concept. The implications of consistency are expressed in terms of explicit density and stability results. We also illustrate, by typical examples, the limitations of the concept
The complexity of finite-valued CSPs
We study the computational complexity of exact minimisation of
rational-valued discrete functions. Let be a set of rational-valued
functions on a fixed finite domain; such a set is called a finite-valued
constraint language. The valued constraint satisfaction problem,
, is the problem of minimising a function given as
a sum of functions from . We establish a dichotomy theorem with respect
to exact solvability for all finite-valued constraint languages defined on
domains of arbitrary finite size.
We show that every constraint language either admits a binary
symmetric fractional polymorphism in which case the basic linear programming
relaxation solves any instance of exactly, or
satisfies a simple hardness condition that allows for a
polynomial-time reduction from Max-Cut to
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