17 research outputs found
On the Capacity Bounds of Undirected Networks
In this work we improve on the bounds presented by Li&Li for network coding
gain in the undirected case. A tightened bound for the undirected multicast
problem with three terminals is derived. An interesting result shows that with
fractional routing, routing throughput can achieve at least 75% of the coding
throughput. A tighter bound for the general multicast problem with any number
of terminals shows that coding gain is strictly less than 2. Our derived bound
depends on the number of terminals in the multicast network and approaches 2
for arbitrarily large number of terminals.Comment: 5 pages, 5 figures, ISIT 2007 conferenc
Normal Factor Graphs and Holographic Transformations
This paper stands at the intersection of two distinct lines of research. One
line is "holographic algorithms," a powerful approach introduced by Valiant for
solving various counting problems in computer science; the other is "normal
factor graphs," an elegant framework proposed by Forney for representing codes
defined on graphs. We introduce the notion of holographic transformations for
normal factor graphs, and establish a very general theorem, called the
generalized Holant theorem, which relates a normal factor graph to its
holographic transformation. We show that the generalized Holant theorem on the
one hand underlies the principle of holographic algorithms, and on the other
hand reduces to a general duality theorem for normal factor graphs, a special
case of which was first proved by Forney. In the course of our development, we
formalize a new semantics for normal factor graphs, which highlights various
linear algebraic properties that potentially enable the use of normal factor
graphs as a linear algebraic tool.Comment: To appear IEEE Trans. Inform. Theor
Duality between Feature Selection and Data Clustering
The feature-selection problem is formulated from an information-theoretic
perspective. We show that the problem can be efficiently solved by an extension
of the recently proposed info-clustering paradigm. This reveals the fundamental
duality between feature selection and data clustering,which is a consequence of
the more general duality between the principal partition and the principal
lattice of partitions in combinatorial optimization