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In the Shapley-Scarf economy each agent is endowed with one unit of an indivisible good (house) and wants to exchange it for another, possibly the most preferred one among the houses in the market. In this economy, core is always nonempty and a core allocation can be found by the famous Top Trading Cycles algorithm. Recently, a modification of this economy, containing Q >= 2 types of goods (say, houses and cars for Q=2) has been introduced. We show that if the number of agents is 2, a complete...
It is shown that the problem of finding a minimum -basis, the -center problem, and the -median problem are -complete even in the case of such communication networks as planar graphs with maximum degree 3. Moreover, a near optimal -center problem is also -complete.
Using counterexample it has been shown that an algorithm which is minimax optimal and over all minimax optimal algorithms is minimean optimal and has a uniform behaviour need not to be minimean optimal.
In Hoare's (1961) original version of the algorithm
the partitioning element in the central divide-and-conquer
step is chosen uniformly at random from the set S in question.
Here we consider a variant where this element is the median
of a sample of size 2k+1 from S. We investigate convergence
in distribution of the number of comparisons required and obtain
a simple explicit result for the limiting
average performance of the median-of-three version.
We investigate the number of iterations needed by an addition algorithm due to Burks et al. if the input is random. Several authors have obtained results on the average case behaviour, mainly using analytic techniques based on generating functions. Here we take a more probabilistic view which leads to a limit theorem for the distribution of the random number of steps required by the algorithm and also helps to explain the limiting logarithmic periodicity as a simple discretization phenomenon.
We investigate the number of iterations needed by an addition algorithm due to
Burks et al. if the input is random. Several authors have obtained results on
the average case behaviour, mainly using analytic techniques based on generating functions. Here we
take a more probabilistic view which leads to a limit theorem for the distribution of the random
number of steps required by the algorithm and also helps to explain the limiting logarithmic
periodicity as a simple discretization phenomenon.
Given a graph with colored edges, a Hamiltonian cycle is
called alternating if its successive edges differ in color. The problem
of finding such a cycle, even for 2-edge-colored graphs, is trivially
NP-complete, while it is known to be polynomial for 2-edge-colored
complete graphs. In this paper we study the parallel complexity of
finding such a cycle, if any, in 2-edge-colored complete graphs. We give
a new characterization for such a graph admitting an alternating
Hamiltonian cycle which allows...
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