1,250,081 research outputs found
Network Coding for Computing: Cut-Set Bounds
The following \textit{network computing} problem is considered. Source nodes
in a directed acyclic network generate independent messages and a single
receiver node computes a target function of the messages. The objective is
to maximize the average number of times can be computed per network usage,
i.e., the ``computing capacity''. The \textit{network coding} problem for a
single-receiver network is a special case of the network computing problem in
which all of the source messages must be reproduced at the receiver. For
network coding with a single receiver, routing is known to achieve the capacity
by achieving the network \textit{min-cut} upper bound. We extend the definition
of min-cut to the network computing problem and show that the min-cut is still
an upper bound on the maximum achievable rate and is tight for computing (using
coding) any target function in multi-edge tree networks and for computing
linear target functions in any network. We also study the bound's tightness for
different classes of target functions. In particular, we give a lower bound on
the computing capacity in terms of the Steiner tree packing number and a
different bound for symmetric functions. We also show that for certain networks
and target functions, the computing capacity can be less than an arbitrarily
small fraction of the min-cut bound.Comment: Submitted to the IEEE Transactions on Information Theory (Special
Issue on Facets of Coding Theory: from Algorithms to Networks); Revised on
Aug 9, 201
Development and Evaluation of the Nebraska Assessment of Computing Knowledge
One way to increase the quality of computing education research is to increase the quality of the measurement tools that are available to researchers, especially measures of students’ knowledge and skills. This paper represents a step toward increasing the number of available thoroughly-evaluated tests that can be used in computing education research by evaluating the psychometric properties of a multiple-choice test designed to differentiate undergraduate students in terms of their mastery of foundational computing concepts. Classical test theory and item response theory analyses are reported and indicate that the test is a reliable, psychometrically-sound instrument suitable for research with undergraduate students. Limitations and the importance of using standardized measures of learning in education research are discussed
Computing Multi-Homogeneous Bezout Numbers is Hard
The multi-homogeneous Bezout number is a bound for the number of solutions of
a system of multi-homogeneous polynomial equations, in a suitable product of
projective spaces.
Given an arbitrary, not necessarily multi-homogeneous system, one can ask for
the optimal multi-homogenization that would minimize the Bezout number.
In this paper, it is proved that the problem of computing, or even estimating
the optimal multi-homogeneous Bezout number is actually NP-hard.
In terms of approximation theory for combinatorial optimization, the problem
of computing the best multi-homogeneous structure does not belong to APX,
unless P = NP.
Moreover, polynomial time algorithms for estimating the minimal
multi-homogeneous Bezout number up to a fixed factor cannot exist even in a
randomized setting, unless BPP contains NP
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