Browsing by Subject "Combinatorial mathematics"

Now showing 1 - 4 of 4

Open Access
An improved graph-entropy bound for perfect hashing
(IEEE, 1994-06-07) Arıkan, Erdal
Gives an improved graph-entropy bound on the size of families of perfect hash functions. Examples are given illustrating that the new bound improves previous bounds in several instances.
Open Access
On the single-assignment p-hub center problem
(Elsevier, 2000) Kara, B. Y.; Tansel, B. Ç.
We study the computational aspects of the single-assignment p-hub center problem on the basis of a basic model and a new model. The new model's performance is substantially better in CPU time than different linearizations of the basic model. We also prove the NP-Hardness of the problem.
Open Access
Ordinal covering using block designs
(IEEE, 2010) Atmaca, Abdullah; Oruc, A.Y.
A frequently encountered problem in peer review systems is to facilitate pairwise comparisons of a given set of documents by as few experts as possible. In [7], it was shown that, if each expert is assigned to review k documents then ⌈n(n-1)/k(k-1)⌉ experts are necessary and ⌈n(2n-k)/k 2⌉ experts are sufficient to cover all n(n-1)/2 pairs of n documents. In this paper, we show that, if √n ≤ k ≤ n/2 then the upper bound can be improved using a new assignnment method based on a particular family of balanced incomplete block designs. Specifically, the new method uses ⌈n(n+k)/k2⌉ experts where n/k is a prime power, n divides k2, and √n ≤ k ≤ n/2. When k = √n , this new method uses the minimum number of experts possible and for all other values of k, where √n < k ≤ n/2, the new upper bound is tighter than the general upper bound given in [7]. ©2010 IEEE.
Open Access
The single-assignment hub covering problem: models and linearizations
(Palgrave Macmillan Ltd., 2003) Kara, B. Y.; Tansel, B. C.
We study the hub covering problem which, so far, has remained one of the unstudied hub location problems in the literature. We give a combinatorial and a new integer programming formulation of the hub covering problem that is different from earlier integer programming formulations. Both new and old formulations are nonlinear binary integer programs. We give three linearizations for the old model and one linearization for the new one and test their computational performances based on 80 instances of the CAB data set. Computational results indicate that the linear version of the new model performs significantly better than the most successful linearization of the old model both in terms of average and maximum CPU times as well as in core storage requirements.