1,012 research outputs found
On highly regular strongly regular graphs
In this paper we unify several existing regularity conditions for graphs,
including strong regularity, -isoregularity, and the -vertex condition.
We develop an algebraic composition/decomposition theory of regularity
conditions. Using our theoretical results we show that a family of non rank 3
graphs known to satisfy the -vertex condition fulfills an even stronger
condition, -regularity (the notion is defined in the text). Derived from
this family we obtain a new infinite family of non rank strongly regular
graphs satisfying the -vertex condition. This strengthens and generalizes
previous results by Reichard.Comment: 29 page
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Constructing and embedding mutually orthogonal Latin squares: reviewing both new and existing results
We review results for the embedding of orthogonal partial Latin squares in orthogonal Latin squares, comparing and contrasting these with results for embedding partial Latin squares in Latin squares. We also present a new construction that uses the existence of a set of mutually orthogonal Latin squares of order to construct a set of mutually orthogonal Latin squares of order
On the Saddle-point Solution and the Large-Coalition Asymptotics of Fingerprinting Games
We study a fingerprinting game in which the number of colluders and the
collusion channel are unknown. The encoder embeds fingerprints into a host
sequence and provides the decoder with the capability to trace back pirated
copies to the colluders.
Fingerprinting capacity has recently been derived as the limit value of a
sequence of maximin games with mutual information as their payoff functions.
However, these games generally do not admit saddle-point solutions and are very
hard to solve numerically. Here under the so-called Boneh-Shaw marking
assumption, we reformulate the capacity as the value of a single two-person
zero-sum game, and show that it is achieved by a saddle-point solution.
If the maximal coalition size is k and the fingerprinting alphabet is binary,
we show that capacity decays quadratically with k. Furthermore, we prove
rigorously that the asymptotic capacity is 1/(k^2 2ln2) and we confirm our
earlier conjecture that Tardos' choice of the arcsine distribution
asymptotically maximizes the mutual information payoff function while the
interleaving attack minimizes it. Along with the asymptotic behavior, numerical
solutions to the game for small k are also presented.Comment: submitted to IEEE Trans. on Information Forensics and Securit
A Minimaxmax Problem for Improving the Torsional Stability of Rectangular Plates
We use a gap function in order to compare the torsional performances of
different reinforced plates under the action of external forces. Then, we
address a shape optimization problem, whose target is to minimize the torsional
displacements of the plate: this leads us to set up a minimaxmax problem, which
includes a new kind of worst-case optimization. Two kinds of reinforcements are
considered: one aims at strengthening the plate, the other aims at weakening
the action of the external forces. For both of them, we study the existence of
optima within suitable classes of external forces and reinforcements. Our
results are complemented with numerical experiments and with a number of open
problems and conjectures
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