226 research outputs found
Reconstruction of complete interval tournaments
Let and be nonnegative integers ,
be a multigraph on vertices in which any pair of
vertices is connected with at least and at most edges and \textbf{v =}
be a vector containing nonnegative integers. We give
a necessary and sufficient condition for the existence of such orientation of
the edges of , that the resulted out-degree vector equals
to \textbf{v}. We describe a reconstruction algorithm. In worst case checking
of \textbf{v} requires time and the reconstruction algorithm works
in time. Theorems of H. G. Landau (1953) and J. W. Moon (1963) on the
score sequences of tournaments are special cases resp. of our result
Testing of random matrices
Let be a positive integer and be an
\linebreak \noindent sized matrix of independent random variables
having joint uniform distribution \hbox{Pr} {x_{ij} = k \hbox{for} 1 \leq k
\leq n} = \frac{1}{n} \quad (1 \leq i, j \leq n) \koz. A realization
of is called \textit{good}, if its each row and
each column contains a permutation of the numbers . We present and
analyse four typical algorithms which decide whether a given realization is
good
Leader election in synchronous networks
Worst, best and average number of messages and running time of leader election algorithms of different distributed systems are analyzed. Among others the known characterizations of the expected number of messages for LCR algorithm and of the worst number of messages of Hirschberg-Sinclair algorithm are improve
Construction of infinite de Bruijn arrays
AbstractWe construct a periodic array containing every k-ary m × n array as a subarray exactly once. Using the algorithm SUPER (which for k⩾3 generates an infinite k-ary sequence whose beginning parts of length km, m = 1,2,..., are de Bruijn sequences) we also construct infinite km × ∞ k-ary arrays in which each beginning part of size km × kmn − m, n = 1,2,..., as a periodic array, contains every k-ary m × n array exactly once
Reconstruction of score sets
The score set of a tournament is defined as the set of its different outdegrees. In 1978 Reid [15] published the conjecture that for any set of nonnegative integers D there exists a tournament T whose degree set is D. Reid proved the conjecture for tournaments containing n = 1, 2, and 3 vertices. In 1986 Hager [4] published a constructive proof of the conjecture for n = 4 and 5 vertices. In 1989 Yao [18] presented an arithmetical proof of the conjecture, but general polynomial construction algorithm is not known. In [6] we described polynomial time algorithms which reconstruct the score sets containing only elements less than 7. In [5] we improved this bound to 9
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